Modeling spatial accessibility for in-vitro fertility (IVF) care services in Iowa

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Fall 2014 Modeling spatial accessibility for in-vitro fertility (IVF) care services in Iowa Pedram Gharani University of Iowa Copyright 2014 Pedram Gharani This thesis is available at Iowa Research Online: Recommended Citation Gharani, Pedram. "Modeling spatial accessibility for in-vitro fertility (IVF) care services in Iowa." MA (Master of Arts) thesis, University of Iowa, Follow this and additional works at: Part of the Geography Commons

2 MODELING SPATIAL ACCESSIBILITY FOR IN-VITRO FERTILITY (IVF) CARE SERVICES IN IOWA by Pedram Gharani A thesis submitted in partial fulfillment of the requirements for the Master of Arts degree in Geography in the Graduate College of The University of Iowa December 2014 Thesis Supervisor: Associate Professor Kathleen Stewart

3 Copyright by PEDRAM GHARANI 2014 All Rights Reserved

4 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL MASTER S THESIS This is to certify that the Master s thesis of Pedram Gharani has been approved by the Examining Committee for the thesis requirement for the Master of Arts degree in Geography at the December 2014 graduation. Thesis Committee: Kathleen Stewart, Thesis Supervisor Margaret Carrel James Tamerius

5 To my wonderful mother for her love and invaluable support ii

6 ACKNOWLEDGMENTS The first and the most, I would like to thank my mother. She raised me to who I am today by great devotion, dedication, and sacrificing her dreams. Without her love, I would not have come so far. I would like to express my sincere and deep gratitude to my advisor, Dr. Kathleen Stewart, for her excellent guidance, caring, patience, and providing me with an excellent atmosphere for doing research. I extremely appreciate her constructive comments. I gratefully acknowledge the funding support and generosity of Dr. Ginny L. Ryan from Carver College of Medicine that made this research possible, without whom the present study could not have been completed. I would also like to extend my appreciation to Dr. Margaret Carrel and James Tamerius who served on my thesis committee. This thesis is much improved due to the guidance of my committee members I would also like to thank my elder sister, and elder brother. They have always supported me and encouraged me with their best wishes. Special thanks go to my friends. iii

7 ABSTRACT The challenge of computing a quantitative index for spatial accessibility that describes the degree of access that exists for IVF healthcare in Iowa requires research and evaluation. Our objective was to apply computational methods including a modified gravity model, techniques from spatial interaction modeling, and clustering to discover underserved areas and derive a spatial accessibility surface at the census tract level for IVF centers in Iowa. Key sociodemographic variables (age, median household income, race/ethnicity) describing female patients seeking infertility healthcare services were identified based on a survey of physician and nurses and weighted based on systematically cross-comparing the variables for importance. Self-organizing map techniques (SOM) were used to identify and map clusters capturing the degree of match between sociodemographic data and the expert-identified sociodemographic variables. The computed spatial accessibility surface was then combined with the sociodemographic clusters to identify underserved regions. Accessibility and degree of sociodemographic match were abstracted to three classes each (high, moderate, and low access, and high, moderate, and low sociodemographic match). To determine degree of fit and validation of the model, patient residential data (by zip codes mapped to census tracts) were overlaid on the resulting accessibility map. These results serve as an indicator that enables stakeholders to compare different areas from a spatial and sociodemographic point of view for the comparing potential and real access and how close they are. Combining accessibility results with sociodemographic mapping provides valuable insights into the accessibility of IVF services to a state s population and the degree to which demand for IVF care is being met. Geospatial techniques are a promising tool for IVF providers considering how best to expand access to care. iv

8 TABLE OF CONTENTS LIST OF TABLES... VII LIST OF FIGURES... VIII CHAPTER 1. INTRODUCTION Research objectives Research questions Outline of thesis GIS, HEALTH GEOGRAPHY, AND ACCESSIBILITY Introduction Categories of spatial accessibility Floating Catchment Area (FCA) Kernel Density Estimation (KDE) Gravity model approaches COMPUTING SPATIAL ACCESSIBILITY FOR IVF CARE IN IOWA A computational framework for determining accessibility for IVF care The impedance effect of distance and travel time on accessibility Gravity model Two-Step Floating Catchment Area (2SFCA) CALIBRATING THE SPATIAL ACCESSIBILITY MODEL Spatial Interaction Modeling (SIM) and modified gravity model Calibrating the model and calculating the index score Data for calibration Computing spatial accessibility scores and visualizing the pattern SOCIODEMOGRAPHIC ANALYSIS Key sociodemographic variables for IVF health care Sociodemographic survey and computing the weights of variables Calculating weights for sociodemographic variables Analytic Hierarchy Process (AHP) Multivariate clustering analysis and dimension reduction Self-Organizing Map (SOM) COMBINING SOCIODEMOGRAPHIC AND SPATIAL ACCESSIBILITY MAP Evaluation of results...64 v

9 APPENDIX 7. CONCLUSION AND FUTURE WORKS Summary Future work...69 A. QUESTIONNAIRE OF TYPICAL SOCIODEMOGRAPHIC PROFILE (AGE, MHH, RACE/ETHNICITY, FAMILY SIZE, RELIGION) OF PATIENTS...70 B. PAIRWISE COMPARISONS OF THE DEMOGRAPHIC VARIABLES...73 C. RESULTS OF QUESTIONNAIRE OF TYPICAL SOCIODEMOGRAPHIC PROFILE OF PATIENTS...81 REFERENCES...87 vi

10 LIST OF TABLES Table 2.1 Classification of accessibility measurement...11 Table 4.1 Regression results considering SIM associated with the five impedance functions...33 Table 5.1 The results for question # Table 5.2 The results for question # Table 5.3 The results for question # Table 5.4 The results for question # Table 5.5 The results for question # Table 5.6 The results for question # Table 5.7 Questions of survey Table 5.8 Summary of the results of survey Table 5.9 scale for comparisons...52 Table 5.10 Values of RI...53 Table 5.11 Comparison matrix for sociodemographic parameters...55 Table 5.12 Computed weights for each category in the parameters...56 Table 6.1 The statistics of the census tracts in the integrated map...65 Table 6.2 Patient residence by spatial accessibility and sociodemographic characteristic match...65 vii

11 LIST OF FIGURES Figure 2.1 Kernel Estimation of a point pattern...12 Figure 3.1 IVF service centers' locations...15 Figure 3.2 The service areas for IVF centers in the state of Iowa...16 Figure 4.1 An intuitive example of the flow in a network and the parameters...28 Figure 4.2 Impedance function for gravity accessibility measurement: Exponential Function...29 Figure 4.3 Impedance function for gravity accessibility measurement: Power Function...29 Figure 4.4 Impedance function for gravity accessibility measurement: Gaussian Function...30 Figure 4.5 Access value pattern for the state of Iowa...34 Figure 5.1 Sociodemographic variables that characterize patients seeking infertility care...37 Figure 5.2 Population of Females 20 to 49 Years in Iowa (2010) per census tract...38 Figure 5.3 Median Household Income data by census tract for Iowa (2010)...38 Figure 5.4 Race and Ethnicity distribution...40 Figure 5.5 Female population for Iowa (2010) weighted by age...57 Figure 5.6 Weighted median household income...58 Figure 5.7 Population weighted by race/ethnicity...58 Figure 5.8 SOMVIS (Multivariate Mapping and Visualization with SOM) output...60 Figure 5.9 Degree of match for census tracts with respect to sociodemographic characteristics...61 Figure 6.1 The integrated map of two indices...64 viii

12 1 CHAPTER 1 INTRODUCTION In the United States, approximately 10% to 13% of reproductive-aged individuals are affected by infertility (Commenda 2001; Boyle et al. 2004) that the demand has been met just for an estimation around only %24 a recent (Chambers et al. 2009). These figures highlight the prevalence of this healthcare problem among women of reproductive age. Recent progress in medical technologies have improved the chances of gestation significantly for many couples (Gunby et al. 2009; Hammoud et al. 2009). One of the advanced treatments for this problem is in vitro fertilization (IVF). IVF refers to the process of fertilization by manually combining an egg and sperm in a laboratory setting. When the IVF procedure is successful, the next step is embryo transfer where an embryo is physically placed in the uterus (americanpregnancy.org/infertility/ivf.html). According to a report by the Society for Assisted Reproductive Technologies (SART) in 2012 ( 46.7% of cycles resulted in pregnancies after completed, fresh embryo IVF transfers in women less than 35 years of age. The rates are 37.8% for ages 35-37, and 29.7% for ages ( ). However, the number of IVF cycles performed per capita in the United States remains relatively low among nations in the developed world (Hammoud et al. 2009). Due to the complexity and highly technological nature of this medical treatment, IVF treatments are expensive and time-consuming for patients, and the availability of this care is limited to relatively few centers with the necessary equipment and expertise. As mentioned, recent studies have shown that IVF treatment in the United States meets only less than 25% of estimated demand, and Iowa is in the lowest quartile of states in percentage of reproductive-aged population covered by their own state s IVF centers.

13 2 1.1 Research objectives In this research, we investigate the topic of spatial accessibility to IVF care in Iowa. The objective of this research is to define a computational model for measuring spatial accessibility for IVF care, i.e., define a quantitative index for spatial accessibility. In Iowa, IVF care is offered by three centers, The Center for Advanced Reproductive Care at the University of Iowa Hospital and Clinics (UIHC) in Iowa City and Mid-Iowa Fertility, P.C. in Des Moines, Iowa, plus an affiliated University of Iowa clinic, the UI Women s-quad Cities Clinic. A number of possible factors relate to the likelihood of a patient seeking infertility treatments including the age of a woman, household income, family size, and possibly race and ethnicity, availability of health insurance, religion, and level of education (Henry et al. 2011; Ginny Ryan, personal communication, December 2013). Spatial accessibility refers to the relative ease by which services can be reached from a given location, so there is a debate about the attribute of different places and locations (Kwan 1998). In other word, spatial access highlights the importance of spatial separation between supply (i.e., IVF care providers) and demand (i.e., population centers) and how they are connected in space. That is a classic example of spatial analysis and well suited for GIS techniques (Wang 2012). This work will demonstrate how spatial accessibility is affected by several factors including the location of the patient population, the location of the centers that offer IVF services, and the transportation network used to travel to the centers. The spatial variables that play key roles in this study of spatial accessibility are the travel time and distance between potential patients residential locations throughout the state of Iowa and the locations of three IVF healthcare centers. The objective of this research is to apply computational methods to define a quantitative index for spatial accessibility. A modified gravity model is used to estimate spatial accessibility at the granularity of census tracts in Iowa, and ESRI s ArcGIS 10.1 and StreetMap Premium road network data for Iowa was used for distance and travel time computation. In order to understand the spatial variability of the potential infertility

14 3 population with respect to sociodemographic variables we gathered, data from the 2010 US Census Bureau ( on female age, household income, race/ethnicity and family size for Iowa, has been used. In addition, a survey of IVF physicians and nurses was undertaken to learn about the typical sociodemographic characteristics of patients with respect to these variables from the physician perspective. Spatial clustering using Self-Organized Map (SOM) techniques is used to classify the sociodemographic data into different clusters, producing a map-based visualization of sociodemographic likelihood of potential infertility patients per census tract. The sociodemographic parameters and analysis will be combined with the spatial accessibility results to determine areas in Iowa that have, for example, low access but high match with respect to sociodemographic profile, or high access but possibly low match sociodemographically. In this way, the variability of access across the state to IVF centers will be understood in light of sociodemographic characteristics of the state s population. 1.2 Research questions There are five major research questions for this thesis: What are the necessary steps for determining an index for measuring spatial accessibility? What are the sociodemographic variables that have an impact on the availability of infertility and IVR healthcare in Iowa? What approach is needed to quantify the qualitative survey and take the sociodemographic variables into account? How should the computed indices for spatial accessibility and sociodemographic variables be considered together? Where in the state of Iowa are there estimated areas that are low in access but potentially a good match for sociodemographic characteristics?

15 4 1.3 Outline of thesis The rest of this thesis is organized as follows. Chapter 2 reviews background and related work on spatial accessibility methods. This chapter describes the very initial thoughts about the idea of accessibility if the context of spatial analysis, then the procedure of development of this concepts will be reviewed and different studies from simple ratios to some sophisticated one are reviewed and discussed. Chapter 3 focuses on the approach used for modeling and defining a computational framework for spatial accessibility for IVF healthcare centers. The gravity model is reviewed more in detail and all the elements are discussed. Two tightly related methods are discussed in this chapter. In Chapter 4, the general modified gravity model from the previous chapter is discussed for some customization in order to determine the type of the function and its parameters according to the study area. We call this customization as calibration and it is done using spatial interaction modeling. Methods for determining key parameters of the gravity model, including for example, the deterrence function and its decay parameter are discussed in detail. A map capturing the spatial accessibility surface for Iowa is presented at the end of the chapter. This map details locations of high and low accessibility for patients traveling to one of the three IVF centers in the state. The analysis of sociodemographic variables is discussed in Chapter 5. This chapter presents the demographic data to be modeled, and discusses the survey that was administered to physicians and nurses in order to determine a weighting scheme for the sociodemographic variables. Self-Organizing Map (SOM) techniques are applied to group and cluster the sociodemographic data and produce a corresponding surface representing most likely and least likely matches with respect to sociodemographic characteristics common to individuals seeking IVF care.

16 5 The major results of this thesis are presented in Chapter 6 where spatial accessibility and sociodemographic attributes are combined and mapped. Conclusions and topics for future research are presented in the last chapter, Chapter 7.

17 6 CHAPTER 2 GIS, HEALTH GEOGRAPHY, AND ACCESSIBILITY 2.1 Introduction Health geography focuses on the analysis of the spatial organization of health services, finding and predicting how services change over time, examining the reasons for change, and investigating the nature of accessibility to health services, as well as the impacts on health relating to accessibility (Fortney et al. 1999; McLafferty 2003). GIS and related spatial analytic techniques comprise a set of computational tools for evaluating the changing spatial organization of health care, especially in regards to health outcomes and access. GIS has a critical role in examining health care needs through facilitating the spatial linking of diverse health, social, and environmental data sets. Geographers and GIScience researchers can take advantage of the capabilities of GIS for mapping and visualizing spatial data and make use of GIS s strong analytic capabilities to generate meaningful spatial solutions for accessibility and health care services, for example, computing service areas for health care. Spatial accessibility is measured using several different methods including counting the number of centers per a predefined area or zone, determining the distance from population centers to facilities, determining the travel time to reach healthcare service centers, and computing the cost of getting an opportunity, and impedance as part of a model of access (Schuurman et al. 2010). Considering more variables is made possible using GIS where all aspects that influence the outcomes of measurements of access are considered, including the use of methods such as geographical aggregation, how to define residential areas, and what distance measurements to use (Apparicio and Séguin 2006). This chapter reviews the state-of-the-art regarding spatial accessibility and spatial knowledge discovery and clustering. First, the history and definition of accessibility are

18 7 examined. Second, improved concepts for measuring spatial accessibility are introduced with a particular emphasis placed on functions that have been developed to support gravity models. In the second section, knowledge discovery and clustering is presented and Self-Organizing Map (SOM) techniques are introduced to illustrate an important way that clustering is being used to reduce multivariate data. 2.2 Categories of spatial accessibility As mentioned above, spatial access has been defined in various ways in different studies. The meaning of access ranges from the capacity to pay (Wilkinson et al. 2001), clinic operation times (Macinko et al. 2004), culturally sensitive services (WHO 2008), and feeling that one has the right to or interest in accessing services (Bernard et al. 2004) mainly in the context of primary health care. Khan and Bhardwaj (1994) also proposed a comprehensive categorization of the concept of access where access is subdivided into four types: potential spatial, potential aspatial, realized spatial and realized aspatial (Khan and Bhardwaj 1994). In this discussion of access, potential access refers to the availability of a service, while realized access refers to actual usage. Kwan (1998) categorizes accessibility into two different types that depend on the problem and the context of the application: place accessibility that is primarily determined by geographic distance and spatial configuration. For this perspective, accessibility is viewed as a property of places that captures how easy a specific location is to reach. Secondly, individual accessibility refers to individual characteristics that are attributes of residents of an area that indicate how easily an individual can reach a service location. McLafferty (2003) extended the study of accessibility and categorized spatial accessibility for health care into two categories: area-based and distance-based methods. Area-based accessibility methods are designed to be used for data of granularities such as states, counties, census tracts, and census blocks, describing the ratio of population needs

19 8 to services available. Many studies have developed measures involving physician to population ratio that are used to explain geographical disparities in access to physicians across the US. For example, an analysis of measuring the ratio of dentists to population at county and zip code level was undertaken (Susi and Mascarenhas 2002). This work shows the significant differences in access to dental services in Ohio, with access in the rural and Appalachian areas of Ohio being lower than other areas. Using simple ratios of physicians to denominator population as a means of measuring potential spatial access to health services, could be useful for some health services that are not susceptible to the modifiable areal unit problem (MAUP). MAUP is a fundamental methodological problem in all geographic and spatial studies, as they examine the effects of area-based attributes on individual behaviors. The outcomes of these researches could be affected by geographic scale of the areal units (Openshaw 1984; Fotheringham and Wong 1991; Kwan 2012). For example, public health care centers are well separated service centers that are available in each census tract, but not all health care centers have that property. For residents living in any of the 825 census tracts in Iowa, there are just three IVF health care centers. Using the above methods, the numerator of the ratio becomes null for 823, since there are IVF centers in only two census tracts. This problem is common with most area measures as they do not consider cross-area travel (McLafferty, 2003). Another set of methods is distance-based measures that focus on the distance or travel time or cost between the population center and health service providers. The weaknesses of the above approaches are avoided by using distance-based methods. The choice of the method for computing the distance has a significant impact on the outcomes. In these studies, straight-line or Euclidean distance (crow flies distance) is used. Love and Lindquist (1995) used GIS to calculate straight-line distance from elderly populations to hospital services. The researchers were able to identify elderly populations with low access to health services. Euclidean distance, however, fails to incorporate the

20 9 ease, cost and time of travel, and access to transportation (Martin et al. 2002) as well as other key factors such as network travel that will be discussed later in this thesis. Recent advances in geographic information science (GIScience) makes it possible to have more sophisticated spatial analysis and consider the inclusion of spatial information such as street network data, transportation data such as the number of commutes along the street network and the attributes of the line segments such as speed limit and so on, and socio-demographic data to create improved measures of geographic access. For example, for a study of access to primary health care in regions of Bolivia, and how this care could be accessible for populations in mountainous areas, topography was incorporated into access models. For this work, crow flies distance was not be helpful and instead they tried using DEMs and considering the rugged topography of that area. A one hour walk to obtain healthcare was considered meaningful in this study, and therefore, an equivalent 5 km area around the centers in the mountainous area was mapped and then adjusted based on the DEM (Perry and Gesler 2000). Other studies have evaluated accessibility using data on commuting along transportation networks, and network distance has become increasingly used in accessibility studies (Walsh et al. 1997; Fortney et al. 1999). This includes computing travel time from origin (e.g., residents locations) to destination (e.g., service locations) based on a consideration of road type and quality (Ramsbottom-Lucier et al. 1996; Haynes et al. 1999). GIS software offers tools for computing network distance. Gutiérrez and García-Palomares (2008) assessed overestimation of the straight-line distance method by comparing it with the network distance. Their evaluation consists of considering some different variables and factors that are influencing the outcomes such as density of stops, the coverage of distance thresholds and some characteristics of the area such as the design of the network, barriers, and the distribution of population. It was concluded that the network distance method leads to higher quality results than Euclidean distance methods (Gutiérrez and García-Palomares 2008).

21 Floating Catchment Area (FCA) Talen (2003) introduced five general approaches for measuring accessibility (Table 2.1). A simple and straightforward method for measuring accessibility is container measures. In this method the number of facilities should be counted within a given geographical area. The second approach which is similar one to the container method is coverage measures in which the number of facilities are counted within a given distance from a point e.g. the centroid of an area (Morrissey et al. 2013). In the minimum-distance method access is computed in terms of the distance to the closest facility. In travel cost approach the access is calculated by measuring distance, cost, or travel time from origin to all destinations. In gravity method, an index is computed which considers the size of facilities by weighting. The weighting could be evaluated according to any other characteristics. In gravity methods, distance or travel time impedes the travel which is modeled by some functions. In the measurement of accessibility due to coverage measurement approach, the container is called catchment area which is not defined formally. This method is the foundation of a modified container measure which is called floating catchment area (FCA) (Talen 2003; Luo and Wang 2003; Luo 2004; Wang and Luo 2005). In studies by (Talen 2003; Luo and Wang 2003; Luo 2004; Wang and Luo 2005) GIS is used to compute buffer areas around centers that are the centroid of the boundaries. The size of buffer zone could be very significant in terms of the distance that patients or in general commuters could travel. Although the improvement of defining floating catchment area technique is undeniable, there are two major challenges. The first one is the travel distance that should be defined for the floating catchment area. It is supposed to be a reasonable distance for the service, so according to the way that patients might travel there could be different catchment area distances, but it is still a subjective concept and could be easily influenced by sociodemographic factors such as age, income and even the characteristics of the place (Morrissey et al. 2013). Another challenge is about the service

22 11 provided by different facilities; in the context of retail it is mentioned that larger facility centers are more to attractive (Birkin and Clarke 1991). Patients might be willing to travel further in order to get better quality service. This parameter is typically not be considered in FCA approaches. Table 2.1. Classification of accessibility measurement Approach Container Coverage Minimum distance Travel cost Definition The number of facilities contained within a given unit The number of facilities within a given distance from a point of origin The distance between a point of origin and the nearest facility The average distance between a point of origin and all facilities An index in which the sum of all facilities (weighted by size or supply Gravity side characteristics) is divided by the frictional effect of distance Source: Talen, E Neighborhoods as service providers: a methodology for evaluating pedestrian access. Environment and Planning B: Planning and Design 30 (2): Kernel Density Estimation (KDE) Another approach for container and coverage methods for estimating access is kernel distance estimation (KDE). KDE shows the density of point occurrences as spatially continuous variables. On a map, peaks represent high density of services and valleys represent low densities (McLafferty and Grady 2005). In general, KDE is used to estimate a smooth probability histogram for univariate data or a smooth density surface from a set of bivariate data points (Silverman1986). For each point in the dataset there is a bandwidth, which indicates the radius of density surface, and a function. The value of bandwidth should be selected based on the data and the desired level of detail. This parameter has a large impact on the outcomes, whilst the kernel function has a small impact on the surface (Schuurman et al. 2010). In health GIS KDE is used for modeling a disease risk surface using a set of location data that shows the occurrence of disease

23 12 (Gatrell et al. 1996). Guagliardo (2004) applied this model to generate a surface that models spatial access for primary health care, where two kernel density surfaces were generated, first for location of doctors and the other one modeling population centroids. Although kernel density estimation can be used for modeling the distribution of healthcare services, as seen in Figure 22.1, the distance is typically assumed to be straight-line and that is not always very reliable. In this study, we are using the Iowa road network for computing distances. KDE will not be able to take this kind of network into account. Bandwidth can be another weakness where simplified concentric rings that arise from considering straight line distances, that do not show the actual travel patterns that are used (Guagliardo et al. 2004; McLafferty and Grady 2005). Finally, population density is not efficiently modeled using kernel density estimation. For example, KDE approaches may assume that most of the population lives near the centroid, which is not necessarily true. Another false assumption assumes that further from the centroids, there is lower population density. The centroid of the areal unit could in fact be located in a low population area leading to wrong conclusions (Schuurman et al. 2010). Figure 2.1 Kernel Estimation of a point pattern Source: Gatrell, A. C., T. C. Bailey, P. J. Diggle, B. S. Rowlingson, and C. Bailey analysis and its Spatial point pattern application in geographical epidemiology. 21 (1):

24 Gravity model approaches By means of all the methods that we explained by now, we can see the lack of an indicator for measuring the spatial interaction and they only measure the opportunities that are available for residents. Gravity model approaches were developed in order to devise a decent indicator for not only the opportunities, but also the interaction between facility center and population centers. So, these models have some basic parameters which are needed for computing the index. The major parameters of the gravity model approaches for measuring accessibility are the location of the population, location of facilities, an indicator for the attractiveness and the frictional effect of distance decay (Schuurman et al. 2010;Wang 2012; Morrissey et al. 2013). Guagliardo (2004) considers gravity models as a combined indicator for accessibility and availability. Gravity model is based on Newton s law of gravitation, the attraction of two objects is in proportion to their masses and the inverse of the distance in between them. In the context of health geography higher attraction indicates of higher interaction. Gravity model used by Hansen (1959) for the first time for measuring accessibility and it could provide us the most valid measures of spatial accessibility (Hansen 1959; Guagliardo 2004). So, the equation developed to model potential spatial access to general practitioners (Joseph and Bantock 1982). This model was applied in many other studies in health geography (Luo and Wang 2003; Schuurman et al. 2010; Shi et al. 2012; Wang 2012) FCA was enhanced by Luo and Wang (2003). They merged the discussed floating catchment area (FCA) method and gravity based model. In other words, the catchment area which is actually a service area should be defined by travel time threshold then considering a gravity method in order to determine the attractiveness and propulsiveness of the facility and population centers. This method was named two steps floating catchment area (2SFCA), and it could be proved that is a special case of the gravity model (Shi et al. 2012).

25 14 Access to IVF service centers is a crucial issue for the doctors in hospitals and stakeholders in the health related sectors. Some barriers and obstacles could make problems for patients and who are in need for obtaining care. Access describes people s ability to use health services when and where they are needed (Aday L and Anderson R. 1981). The problem of spatial access is also an important issue from the health equity perspective. Attention has recently been drawn to the mismatch between the spatial distribution of inhabitants and that of PHC providers (Pong and Pitblado 2005). This phenomenon could be understood easier using spatial analysis and it plays an undeniable role.

26 15 CHAPTER 3 COMPUTING SPATIAL ACCESSIBILITY FOR IVF CARE IN IOWA In this chapter, an approach for computing a measure for spatial accessibility of Iowan residents to IVF health care service centers is developed using a gravity-model. In Iowa, there are three IVF service centers including The University of Iowa Hospitals and Clinics (UIHC) Center for Advanced Reproductive Care (CARC) in Iowa City, an associated UIHC clinic, University of Iowa Women's Health Quad Cities in Davenport, and the MidIowa Fertility, P. C.at Des Moines (Figure 3.1). Figure 3.1 IVF service centers' locations

27 16 Using GIS for computing service areas for the IVF centers in the state of Iowa makes it possible to define different catchment areas. As it could be understood from Figure 3.2, the centers were assigned the same weight and the population of each census tract was ignored, so for measuring the spatial accessibility we have to move forward and implement some more sophisticated methods Figure 3.2 The service areas for IVF centers in the state of Iowa In this chapter, the approach used to compute spatial accessibility for IVF care in Iowa is presented. The key elements of the gravity model based approaches such as modified gravity model and two-step floating catchment area (2SFCA) are introduced. 3.1 A computational framework for determining accessibility for IVF care Classical gravity model approaches determine an index for accessibility to services according to the locations of residents, the locations of health care services, the

28 17 attractiveness of the service, and the frictional effect of distance decay. Gravity models have been frequently used in geography, urban and regional planning, and transportation studies (Fotheringham 1981; Khan 1992; Love and Lindquist 1995; Kwan 1998; Rushton 1999; Baradaran and Ramjerdi 2001; Luo and Wang 2003; Talen 2003; Guagliardo et al. 2004; Wang and Luo 2005; Reggiani et al. 2010a; Schuurman et al 2010; Henry et al. 2011; Shi et al. 2012; Morrissey et al. 2013). The model is called a gravity model because of the analogy to Newton s law of universal gravitation. (3.1) Newton s formula describes how two bodies with masses attract each other with force F. As seen in the above formula, the amount of force, F, is in proportion to the masses of the objects and the inverse of the squared distance between these objects. In a spatial analysis context, the force is interpreted as a criterion for interaction between health care service centers and the demand side (e.g., residents). Interactions can exist between two zones, areas, regions, and so on. The gravity model also handles the problem of a distance decay effect through a specific decay parameter. The initial deployment of gravity models in spatial analysis was a simple one by Hansen used for modeling employment accessibility (1959): ( ) (3.2) Where is an index of accessibility in area i to employment in zone j, is the cost of travelling from i to j and opportunity is taken into account by is a distance decay parameter. The scale of. In this work, the cost of travel was estimated instead of distance. Distance, cost, and time can be used interchangeably with a gravity model, making it very useful for spatial applications.

29 18 In this way, the gravity model index captures the potential of opportunities and can be expressed as ( ) (3.3) where defines the accessibility of polygon or point i, is size of the activity in zone j, such as the number of physicians (Schuurman, Bérubé, and Crooks 2010; Shi et al. 2012; Morrissey et al. 2013). Another element of the model is ( ), which is the impedance function from i to j. The impedance function, ( ), can have different forms, for example, power-decay function or the exponential decay function. For different applications and contexts, different impedance functions hold and for each application the function needs to be computed (Kwan 1998; Reggiani, Bucci, and Russo 2010a). To compute spatial accessibility using the classic gravity model, the supply parameter refers to the size of the activity in zone j, but there is no specific parameter for demonstrating demand, and this needs to be modeled explicitly. For modeling potential spatial access to health services, a new equation has been proposed that tries to consider both supply and demand aspects for healthcare accessibility (Luo and F. Wang 2003; Wang 2012). An updated and modified expression for the gravity model (Schuurman et al 2010) is: ( ) (3.4) where describes demand that is computed as: ( ) (3.5)

30 19 In this expression, refers to population unit used in this study. In this research, these units are census tracts (829 census tracts in Iowa) and population estimates coincide with the centroid of each census tract. It should be noted that for this research, population refers to the population of females in Iowa between the ages of So far, we have an equation in which supply and demand are represented in the computation of accessibility. Most gravity-based models use a supply-side approach that counts and measures, for example, the number of physicians associated with certain healthcare facilities giving a mapped result that shows accessible areas around the facilities (Shi et al. 2012). There are also demand-side methods including, for example, kernel density estimation techniques that measure accessibility centered more on the location of population rather than the facilities. Different outcomes result depending on which type of accessibility is the focus of study. The general structure of supply-side approaches can be depicted as: ( ) ( ) (3.6) where S indicates supply and D shows demand and ( ) and ( ) are general function forms (Shi et al. 2012). In opposite side, the demand-side approach could be defined as the following formulation (Shi et al. 2012): ( ) ( ) (3.7) 3.2 The impedance effect of distance and travel time on accessibility The impedance effect of distance, travel time, or cost of travel is an integral part of measuring accessibility in general. In this study, for IVF care in Iowa travel time is considered and it is the most substantial parameter in measuring the spatial accessibility.

31 20 The spatial accessibility index computed using the gravity model has two major components, to weight the opportunities for considering the potential of each center and to quantify the relative attractiveness of each site, and the amount of deterrence created by the separation among service centers and population centers and measured by an impedance function. Impedance functions have an important role in determining accessibility, and different forms for the functions are used depending on the application. A power decay function ( ) is one of the well-known impedance functions et al. 2010). Another common form, is an exponential decay function ( ) (Kwan 1998; Reggiani et al. 2010a). There are other forms of impedance functions such as, the exponential-normal decay function ( ), the exponential-square root decay function ( )=, and the log-normal decay function ( ) ( ) (Reggiani et al. 2010a). A general form of the impedance function, is presented as (Reggiani et al. 2010b).: ( ) (3.8) In these equations represents a connection between origin i and destination j. This is a general form and can be replaced by distance, travel time, or cost. In this study we consider travel time for accessibility and revise the formula to ( ). In this expression, the coefficients and are treated as time-sensitivity parameters or decay parameters. These decay parameters represent the difficulty associated with travel for any given time or distance. For many healthcare accessibility studies, it is assumed that accessibility improves as the number of provider points increases, the capacity at any provider location increases, the distance to provider decreases, or the travel friction decreases. The coefficients and measure the relationship between actual population-service interaction and time (or distance or cost) (Fotheringham 1981) so in the other words these

32 21 coefficients ( and ) represent the time-sensitivity (Reggiani, Bucci, and Russo 2010b). In Schuurman et al. (2010) measuring access to primary health care (PHC) across Canada especially in rural and remote regions was the focus of the study. The study tried to use gravity model instead of classical ratio for measuring accessibility. So, spatial analytical techniques were discussed to measure potential spatial access. Research on a modified version of the gravity model was developed for computing potential spatial access to PHC physicians in the Canadian province of Nova Scotia. The proposed model used a distance decay function which considers travel time that better represents relative spatial access to PHC. The study shows that the outcomes of the modified gravity model represented greater nuance with respect to potential access scores. The study also considered the lack of a decay coefficient as a drawback of using gravity model. 3.3 Gravity model Guagliardo (2004) in a study of physician accessibility used a kernel density model to measure spatial accessibility. In spite of using it, he mentioned that the gravity model is the most reliable model for measuring spatial accessibility and he presents the gravity equation developed by Joseph and Bantock to model spatial accessibility to general practitioners in rural areas of Southern Ontario, Canada (Joseph and Bantock 1982). At the beginning, gravity models, developed by Hansen for land use planning (Hansen 1959). His study yields a combined indicator of distance and availability, and can provide the most valid measures of spatial accessibility. In fact, Gravity models assess the potential spatial interaction between any population point and all service points within a reasonable travel time. The basic and general form of the accessibility based on gravity model is (Wang 2012): [ ( )] (3.9)

33 22 Where in the formula indicates the spatial accessibility of point i. is population at location k, is the supply at IVF center location which is determined by information from Society for Assisted Reproductive Technologies (SART), d is the distance, travel time, or cost between them, β is the travel friction coefficient, and n and m are the total numbers of IVF centers and centroid of census tracts, respectively. It is essentially the ratio of supply (S) to demand ( ). The impact of distance or travel time is obviuos on both of them. In this formula the population is the weight of each population unit. In this research, enumeration units are census tracts and the population is assigned to the centroid of each tract. In this study, population referrs to females between years. Distance or travel time between points i (centroid of census tracts) and j (location of IVF center), and friction coefficient. is a gravity decay coefficient, sometimes referred to as the travel represents the difficulty associated with travel for any given time or distance. Accessibility improves as the number of provider points increases, the capacity at any provider location increases, the distance to provider decreases, or the travel friction decreases. In this model, a female population tract s access is equal to the sum of the supply and demand ratios, weighted based on distance/travel time from the population centroid at all physician locations. Demand at each location must be determined at the denominator. The demand is equal to the sum of all nearby populations weighted by distance/ travel time. The most challenging part of the modeling is distance decay coefficient. It measures the relationship between actual population-service interaction and distance, assuming other possible factors influencing interaction are constant (Fotheringham 1981). In order for calculating this parameter we used actual data of visits from zip codes to the

34 23 centers and the model was calibrated using Spatial Interaction Modeling (SIM) and regression (Reggiani et al. 2010a), which is described in later sections. The magnitude of the decay parameter depends on how far people are traveling to access a service (Schuurman et al. 2010). A high exponent, which increases the rate at which the distance weight increases with increasing distance, means that people tend not to travel far for a service, while a low exponent means that people are willing to travel farther for a service (Black 1973). A lower decay parameter results in a smoother access surface while a higher decay parameter makes rougher variation. Some authors have experimented with various exponents (Luo and Wang 2003), while others have chosen exponents based on published precedents (Joseph and Bantock 1982). In this research we calibrated the model according to the travel behavior of our patients. The impedance function, in the gravity formula, can be replaced by other forms of functions which we call them ( ) from now. 3.4 Two-Step Floating Catchment Area (2SFCA) Two Step Floating Catchment Area (2SFCA) was devised and applied by Luo and Wang (2003). They proved that 2SFCA is a special case of the gravity model (Luo and Wang 2003). There some other works that took advantage of this method (Wang and Luo 2005; Langford and Higgs 2006; McGrail and Humphreys 2009; Cheng et al. 2012). The procedure of computing Two-Step Floating Catchment Area (2SFCA) index was developed in two steps or stages. Step one is for calculation potential service intensity of service facility. Step two is for computing the accessibility index. ( ) (3.10) Where is an indicator for the potential service intensity of service facility at location k, which is originating from the ratio of doctor/patient; is k s service capacity;

35 24 indicates the number of potential patients; is a weight determined by, the travel impedance between k and j; T is a threshold that defines k s catchment; and j ( < T) indicates that only the patients within k s catchment will be counted (Shi et al. 2012). ( ) (3.11) Where is the spatial access at location i; is a weight determined by, the travel impedance between i and k; and k ( < T) indicates that only the services from those facilities accessible to i will be summed up (Wang and Luo 2005; Shi et al. 2012).

36 25 CHAPTER 4 CALIBRATING THE SPATIAL ACCESSIBILITY MODEL In this chapter, the focus is on the dynamics of spatial accessibility using the street network for the state of Iowa (ESRI street network data) assuming different behavioral patterns and preferences. Behavioral patterns are typically modeled by means of impedance functions, and each function (as discussed in the previous chapter) is representative of a specific type of impedance. Impedance is not the only parameter that influences travel patterns. The street network itself is also highly relevant. Different types of networks or networks with different attributes could potentially lead to different accessibility patterns. As part of this research, some improvements that have been proposed for gravity models based on recent research in the field relating to Spatial Interaction Modeling (SIM) is used for constructing different types of accessibility functions. Our SIM work takes into account five different impedance functions (the exponential, exponentialnormal, exponential-square root, log-normal, and power form), and consequently five typologies of SIM have been calibrated, and five typologies of accessibility indicators have been constructed. Each indicator yields a different value that highlights different patterns, essentially the accessibility embedding the power decay form versus the accessibility derived from the other types of decay functions (exponential, exponentialnormal, exponential-square root, and log-normal form). In this chapter we review spatial interaction modeling, and some different types of SIM are presented. We discuss the calibration of these impedance functions, and the corresponding group of five accessibility indicators that results from this analysis. The chapter discusses how these elements will be determined and calibrated using spatial interaction techniques.

37 26 The discussion of decay parameters in the gravity model shows that it depends on how far people are willing to travel to access a service, and often values for the decay parameters are tightly correlated to each other. A higher exponent represents cases where greater distances to healthcare services would be more prohibitive (Black 1995). Conversely, a lower exponent means that people are willing to travel farther for a service (Black 1995). The mapped outcomes of the values are also significantly different. A lower decay value results in a smoother access surface while a higher decay parameter generates rougher variation (Joseph and Bantock 1982; Luo and Wang 2003; Schuurman et al. 2010). The challenge for determining spatial accessibility to IVF services in Iowa is to determine the type of impedance function and the value of the decay parameters for the accessibility surface computed for this case. In order to determine these values, we apply SIM techniques. Determining the best impedance function and most accurate value of the decay parameter is determined as part of calibrating the model. 4.1 Spatial Interaction Modeling (SIM) and modified gravity model In this research, we investigate spatial accessibility and the dynamics of traveling for infertility care in Iowa assuming different behavioral patterns and preferences. In transportation planning, SIMs are used for analyzing transport demand, for example, for analyzing trip generation/attraction, as well as trip distribution (Reggiani et al. 2010a). Reggiani et. al. (2010) conducted a study for evaluating the accessibility for home-towork commuters travelling between 439 German districts, for both 2003 and Their research focused on the determination of the impedance function. In general, to determine an impedance function, different types of decay functions are used. In the study, Reggiani et al. (2010) also examined what type of accessibility index best matched the commuting network.

38 27 To capture the notion of behaviors on a network, the flow of residents (potential patients) using Iowa street network data is used to determine a best fitted function. As a first step, we adopt an unconstrained SIM based on the following expression (Morrissey et al. 2013): ( ) (4.1) where, is the flow on the network from origin i (centroid of census tracts) to the destination j (IVF care center locations). The flow is a function of (outflow from census tract) and (inflow to each hospital). The deterrence function ( ) is the same as previously defined for the gravity model; and coefficient K is a scaling factor. Figure 4.1 shows a schematic diagram of a network and shows the inflows and outflows for each node. Node b is an example destination that has only inflows. The value for inflow at node b is the summation of all connected edges to the node, a value of 23 in this example.

39 28 Figure 4.1 An intuitive example of the flow in a network and the parameters Work by Olsson (1980), on using the above model with the power function (as described in Chapter 3) for different spatial areas in Sweden (rural vs. agglomerated areas), revealed higher negative values of the decay parameter γ for rural areas, and less negative γ values for agglomerated zones (Reggiani et al. 2010b, 2010a). The exponential functional form is consistent with the assumption of a constant distance decay parameter for all trip makers who are then considered to be homogenous with respect to this dimension. On the other hand, the power function form is consistent with a gamma distribution for the distance decay parameter, i.e., the population of trip makers is heterogeneous with respect to this parameter (Fotheringham and O Kelly 1989). Figure 4.2, Figure 4.3, and Figure 4.5 illustrate different forms for these impedance functions based on different decay parameter values.

40 29 Figure 4.2 Impedance function for gravity accessibility measurement: Exponential Function Source: Kwan, M.P Space-Time and Integral Measures of Individual Accessibility: A Comparative Analysis Using a Point-based Framework. Geographical Analysis 30 (3): Figure 4.3 Impedance function for gravity accessibility measurement: Power Function Source: Kwan, M. P Space-Time and Integral Measures of Individual Accessibility: A Comparative Analysis Using a Point-based Framework. Geographical Analysis 30 (3):

41 30 Figure 4.4 Impedance function for gravity accessibility measurement: Gaussian Function Source: Kwan, M. P Space-Time and Integral Measures of Individual Accessibility: A Comparative Analysis Using a Point-based Framework. Geographical Analysis 30 (3): To model spatial flows needed to calculate decay parameter in the gravity model, it is necessary to extract the time-sensitivity parameters (α and β) and the impedance function. We use Spatial Interaction Modeling (SIM) with the aim of describing and predicting the processes or spatial flows that emerge from a given spatial configurations. As shown in the SIM equation, the travel flows from origin i to destination j, have three components: outflows, inflows, and the impedance function. This expression can be transformed to a logarithmic form in order to make it linear and have a simpler form: ( ) ( ( )) (4.2) In this study we have three healthcare service centers. The granularity for calculation of accessibility is census tract, so for each census tract, we use the centroid and the properties and attributes of the census tract are assigned to that centroid. In this work, a census tract s access is equal to the summation of the supply/demand ratio that is

42 31 weighted by a function of travel time from centroid of census tracts to the service centers. In the next section the model is calibrated and for the calibrated one, the access index is computed for the introduced data. 4.2 Calibrating the model and calculating the index score The gravity model is calibrated for determining the decay parameter and figuring out the best form of the impedance function. In other words, finding the best fitted impedance function to the data of flow in a network and computing the decay parameter is called calibration. The calibrated model is utilized to compute an accessibility score for each census tract that is the value of the index for spatial accessibility. In the next section each phase is described Data for calibration In this section we introduce data that is needed for calibrating the model and computing the spatial access score. The data consists of: Residential travel data (Phase 1) To determine movement flows in the network, a dataset provided by the UIHC CART IVF center for 2005 to 2010 provides data on the flow of patients to the main IVF center as well as its associated clinic. The number of patients in each areal unit (zip code) is stored in the database. In this way, the model is calibrated based on actual patient residential data. The model is calibrated at the level of zip codes and then mapped to the coarser granularity of census tracts, which is the principal granularity used in this research for the accessibility modeling. IVF Centers (Phase 1,2)

43 32 The gravity model includes a supply parameter and for this work we use the capacity (i.e., number of cycles) for each of the service centers as extracted from the SART directory on IVF centers ( Locations and addresses for the three IVF care centers in Iowa are obtained from SART. Census data (Phase 2) The gravity model has a population parameter that refers to the number of patients. In this study, the patient population are females aged from 20 to 49. The population data is based on 2010 Iowa census data ( Road network (Phase 1,2) Road network data is used for computing travel time between population centers (census tracts) and the IVF centers. Network analysis was run using Network Analyst that is an extension for ArcGIS 10.1 ( The road network data is a clean data set with all topological relations and includes detailed non-spatial information about road features such as distance, speed limit and direction of travel. The non-spatial joined data is used to compute travel time. Travel time and Origin-Destination (OD) matrix (Phase 2) The travel times from all census tracts centroids to the IVF care centers are calculated using ESRI s Origin Destination (OD) Cost Matrix tool, a tool in the Network Analyst extension. The resulting OD matrix was imported to the database and each record was fetched by the application for calculating the spatial accessibility value. Table 4.1 shows the values for five different forms of impedance functions and corresponding decay parameters. Based on the results, the relatively the best impedance

44 33 function is Power decay function, but the log-normal decay function performed similarly. The power decay function is used as the impedance function along with the corresponding decay parameter. Table 4.1 Regression results considering SIM associated with the five impedance functions Function R2 Decay Parameters exponential function exponential-square root function E-07 exponential-square root function log-normal function power function Computing spatial accessibility scores and visualizing the pattern The OD matrix computes the travel time based on travel from the centroids of all census tracts to the IVF service centers, and each row is an input parameter for the impedance function (t ij ). After calculating the OD matrix using ArcGIS s Network Analyst extension, all the rows were exported to a SQL Server Database. To compute the accessibility scores for each tract, the travel time values were queried and fetched and used in the computations. The algorithm for this process was developed in Visual Studio 2012 C#. For each census tract, one accessibility score was computed. Using these scores, it becomes possible to interpolate a surface for showing the pattern of accessibility for the state (Figure 4.5).

45 34 Figure 4.5 Access value pattern for the state of Iowa As seen in Figure 4.5 shows the distribution of potential spatial accessibility to IVF care service centers. The value of the access is relatively higher around the three centers and the access score decreases as you go farther from the centers. So, the access for Iowa City, Des Moines, and Davenport is much higher than any other places in the state. This was a predictable result. There are also some areas in the corners of the state such as northeastern, southwestern, and especially northwestern areas where the level of access is lower than other areas. These underserved regions are potential targets for adding IVF-related services if there is a high demand and a likely match of sociodemographic characteristics. These specifications of the places are discussed in the next chapter.

46 35 CHAPTER 5 SOCIODEMOGRAPHIC ANALYSIS Detecting, discovering, and interpreting multivariate spatial patterns are ways to understand complex geographic problems. Identifying such patterns becomes even more challenging as powerful data collection and distribution techniques produce geographic datasets of unprecedented size in a variety of application and research areas (Guo et al. 2005; Jin and Guo 2009; Feng et al. 2014). One of the challenges encountered when working with multivariate spatial analysis in geographic applications is high dimensionality. The challenge of interrelating variables meaningfully and interpreting these variables given the many different attributes can be a difficult problem. Another challenge is discovering the hidden relationships among variables, as potential patterns can contain different relationships, for example, linear or non-linear and spatial or nonspatial. In order to work with multivariate data, and interpret and evaluate the discovered patterns, it is helpful to get some insights from experts who have experience with a domain and can often be helpful distinguishing and evaluating patterns that exist in their domain (Guo et al. 2005, 2006; Jin and Guo 2009). The detection of unknown multivariate spatial patterns or relationships between sociodemographic characteristics of individuals and the accessibility of these individuals to healthcare services such as IVF care, is such a complex challenge, and one where the knowledge of experts in IVF care can be tapped, and computational methods, such as the application of knowledge discovery methods, can be useful for discovering and processing the relations. In this chapter, we discuss sociodemographic data, for example, age, median household income, race and ethnicity, that describes the nature of residents (i.e., potential patients seeking IVF care) and map this data for Iowa. The goal is to detect and specify different areas in the state with similar sociodemographic properties that could be grouped or clustered together. These groups should have some attributes in common,

47 36 especially for characteristics such as household income, race/ethnicity, family size, and an age range that matches that of women typically seeking infertility care. The results of clustering sociodemographic characteristics of residents will be combined with the spatial accessibility surface derived in Chapter 4 to obtain a more meaningful understanding of accessibility in light of the potential patients seeking IVF care. The following chapter (Chapter 6) will present this final fusion of data. In order to use the sociodemographic data that has been collected, the data is classified, weighted, and categorized into a small number of groups in order to weight and compare the parameters with each other. An integrated geographic knowledge discovery or clustering method self-organizing maps (SOM) along with an associated multivariate visualization tool parallel coordinate plots (PCP) is applied to detect and reveal spatial patterns that are present in the sociodemographic data, visualizing the discovered patterns as a mapped surface. For this research, SomVis (Multivariate Mapping and Visualization) software is used. SomVis is an integrated software tool for multivariate analysis, dimensional reduction, and data reduction using self-organizing maps (SOM) ( 5.1 Key sociodemographic variables for IVF health care Although travel time and distance are key for computing an index of spatial accessibility, this index is also influenced by the sociodemographic characteristics of Iowa s population. In consultation with physicians in the Department of Obstetrics and Gynecology at the University of Iowa Hospitals and Clinics who are involved with infertility care, the key sociodemographic variables that characterize typical patients seeking infertility and IVF care are the age of women, median household income, family size (i.e., whether there are children or not), race/ethnicity, availability of health insurance, education, and religion.

48 37 Religion Female Age Median Household Income Education Sociodemographic variables Race/ Ethnicity Family Size Health Insurance Figure 5.1 Sociodemographic variables that characterize patients seeking infertility care. For this research, we considered the first three of these variables, female age, median household income, and race and ethnicity. Future work will see the research being extended to include the other variables. The source of data for female age, median household income, and race/ethnicity for Iowa is the US Census Bureau 2010 ( The data has two components, the non-spatial demographic data and the spatial data at the granularity of census tracts. The census tract shapefiles are TIGER files that are downloadable over the Web ( The non-spatial attribute data is available from American FactFinder website ( Regarding age of women seeking infertility care in Iowa, women are commonly between the ages of Figure 5.2 presents the choropleth map of females aged by Iowa census tract for 2010.

49 38 Figure 5.2 Population of Females 20 to 49 Years in Iowa (2010) per census tract. Figure 5.3. Median Household Income data by census tract for Iowa (2010).

50 39 It is thought based on physician experience that median household income is also relevant for patients seeking infertility care. The choropleth map for median household income by census tract for Iowa in 2010 shows greatest values of median household income are located at Des Moines, Cedar Rapids, Iowa City, Sioux City, Dubuque, Davenport, and Council Bluffs. The third sociodemographic parameter investigated in this work is race and ethnicity. In the context of Iowa, six different groups are mapped including non-hispanic white, non-hispanic black, Hispanic, American Indian/ Alaska Native (AI/AN), Asian Pacific Islander (API), and Other. In figure 5.4 in six choropleth maps show the spatial distribution of race and ethnicity data for Iowa (2010) by census tract.

51 40 Non-Hispanic White Population Non-Hispanic Black Population Hispanic Population American Indian/ Alaska Native Population Asian Pacific Islander (API) Population Other Race/ Ethnicity Population Figure 5.4 Race and Ethnicity distribution

52 41 For each census tract, therefore, three sociodemographic attributes need to be grouped together so that a value representing these variables may be assigned to each tract. To support this, the sociodemographic data was structured in a matrix where each row represents a census tract. The number of rows indicates the size of data and in this schema, data size is represented as m. The first column in the matrix represents location (census tract) and the other columns represent each of the three sociodemographic variables. In this way the matrix has four columns, as we are dealing with three parameters. ( ) (5.1) ( ) Once the data has been organized in this way, it is possible to derive an index that shows the likelihood or match of tract based on the sociodemographic data. In other words, the dimensionality of the data is reduced and the matrix above is converted to a more comprehensible form that has just one attribute for each location. This process makes it possible to interpret the data more comprehensively and consider all of the variables together. However, from expert knowledge we know that the variables have different roles, and their importance or relevance for individuals seeking infertility care varies resulting in the case that the variables do not all have the same impact and weight. A procedure was conducted for weighting the sociodemographic variables including weighting the various subcategories of each variable. For example, median household income is categorized into three subclasses of income that each may have different weightings. For this research therefore, two types of weighting are needed. For continuous variables such as the age of women and median household income that vary

53 42 over certain subclasses, different subclasses will have different weights. For a discrete variable such as race/ethnicity, different weights will be assigned for each racial/ethnic group. In order to assign weights appropriately, a survey was designed and distributed using Qualtrics ( to physicians and nurses at UIHC experienced in infertility care in order to understand the typical sociodemographic profile with respect to age, median household income, and race/ethnicity of patients that they see on a daily basis. Pairwise comparisons of the demographic variables was undertaken to determine the significance of each variable and subcategory with respect to the others. The survey questions and the results are presented in Appendixes A, B, and C. 5.2 Sociodemographic survey and computing the weights of variables Two questionnaires were developed regarding the sociodemographic characteristics of infertility patients and made available online to infertility physicians and nurses of UIHC Department of Obstetrics and Gynecology physicians. The survey consisted of additional variables beyond those that we have considered in this study, and will be helpful for future research. The first questionnaire has 6 questions and 10 responses were obtained. The results for the first survey are presented in tabular form and statistics including min, max, mean, variance, and standard deviation have been calculated (Appendix C). The complete questions and the results are presented in appendices A and C:

54 43 1. Women's age at time of IVF treatment (higher value represents most likely cases) Table 5.1 The results for question #1 # Question Total Responses Mean 1 a. Under 30 years old b. Between 30 and c. Older than 40 years old Median household income of patients seeking IVF treatment (higher value represents most likely cases): Table 5.2 The results for question #2 # Question Total Responses Mean 1 a. Less than $50, b. Between $50,000 to $100, c. More than $100,

55 44 3. Ethnicity of women patients seeking IVF treatment (Select 5 for most likely case and 1 for least likely case) Table 5.3 The results for question #3 # Question Total Responses Mean 1 a. non-hispanic White b. non-hispanic Black d. Asian Pacific Islander (API) e. American Indian/Alaska Native (AI/AN) f. Other Ethnicity c. Hispanic Family size at time patients present for IVF treatment: (Higher value represents most likely cases) Table 5.4 The results for question #4 # Question Total Responses Mean 1 a. No children b. One child c. Two or more children

56 45 5. Health Insurance: Table 5.5 The results for question #5 # Question a. government insurance (Medicaid, Medicare ) b. private insurance that covers IVF care Total Responses Mean d. No insurance c. private insurance that does not cover IVF care likely cases) 6. Religion of patients seeking IVF treatment: (Higher value represents most Table 5.6 The results for question #6 # Question Total Responses Mean 1 a. Catholic Christian b. Other Christian c. Other religion

57 46 A second survey was also undertaken where specialists were asked to weigh pairwise comparisons of each of the sociodemographic variables and indicate the significance of each variable with respect to the others. For this survey, seven responses were collected from the experts. Appendix B contains the questions for the second survey. The results are summarized in Table 5.7 based on the perspective of physicians and nurses about relevance of the sociodemographic variables. The results and statistics about the second survey are also represented. In total seven doctors responded to the question

58 47 Table 5.7 Questions of survey 2 # Question 1 Compare criteria 1 against criteria 2:Woman's age at time of IVF treatment vs. median household income of patients seeking IVF treatment 2 Median household income of patients seeking IVF treatment vs. woman's age at time of IVF treatment 3 Ethnicity/race of patients seeking IVF treatment vs. woman's age at time of IVF treatment 4 Woman's age at time of IVF treatment vs. ethnicity/race of patients seeking IVF treatment 5 Family size at time patient seeks IVF treatment vs. woman's age at time of IVF treatment 6 Woman's age at time of IVF treatment vs. family size at time patients seek IVF treatment 7 Median household income of patients seeking IVF treatment vs. ethnicity/ race of patients seeking IVF treatment 8 Ethnicity/ race of patients seeking IVF treatment vs. median household income of patients seeking IVF treatment 9 Family size at time patients seek IVF treatment vs. median household income of patients seeking IVF treatment 10 Median household income of patients seeking IVF treatment vs. family size at time patients seek IVF treatment 11 Ethnicity/ race of patients seeking IVF treatment vs. family size at time patients seek IVF treatment 12 Family size at time patients seek IVF treatment vs. ethnicity/ race of patients seeking IVF treatment 13 Having health insurance that offers coverage for IVF treatments vs. woman's age at time of IVF treatment 14 Woman's age at time of IVF treatment vs. having health insurance that offers coverage for IVF treatments 15 Having health insurance that offers coverage for IVF treatments vs. median household income of patients seeking IVF treatment 16 Median household income of patients seeking IVF treatment vs. having health insurance that offers coverage for IVF treatments 17 Having health insurance that offers coverage for IVF treatments vs. ethnicity/race of patients seeking IVF treatment 18 Ethnicity/race of patients seeking IVF treatment vs. having health insurance that offers coverage for IVF treatments

59 48 Table 5.7 continued 19 Having health insurance that offers coverage for IVF treatments vs. family size at time patient seeks IVF treatment 20 Family size at time patient seeks IVF treatment vs. having health insurance that offers coverage for IVF treatments 21 Having health insurance that offers coverage for IVF treatments vs. religion of patients seeking IVF treatments 22 Religion of patients seeking IVF treatments vs. having health insurance that offers coverage for IVF treatments 23 Religion of patients seeking IVF treatments vs. woman's age at time of IVF treatment: 24 Woman's age at time of IVF treatment vs. religion of patients seeking IVF treatments: 25 Religion of patients seeking IVF treatments vs. median household income of patients seeking IVF treatment 26 Median household income of patients seeking IVF treatment vs. religion of patients seeking IVF treatments 27 Religion of patients seeking IVF treatments vs. ethnicity/race of patients seeking IVF treatment 28 Ethnicity/race of patients seeking IVF treatment vs. religion of patients seeking IVF treatments 29 Religion of patients seeking IVF treatments vs. family size at time patient seeks IVF treatment 30 Family size at time patient seeks IVF treatment vs. religion of patients seeking IVF treatments

60 Question a. Not as important b. Equally important c. Slightly more important d. Much more important Question a. Not as important b. Equally important c. Slightly more important d. Much more important 49 Table 5.8 Summary of the results of survey 2 # % # % # % # % # % # % # % # %

61 Question a. Not as important b. Equally important c. Slightly more important d. Much more important Question a. Not as important b. Equally important c. Slightly more important d. Much more important 50 Table 5.8 continued # % # % # % # % # % # % # % # %

62 Calculating weights for sociodemographic variables The information collected through the survey provides physicians perspectives on patients seeking infertility care in Iowa. Using the survey results, the next step is to determine the value of weights for each variable. In order to calculate and quantify the value of weights, the analytic hierarchy process (AHP) introduced by Saaty (1977) is used. This is a popular method to calculate the weighting parameters by means of a preference matrix where all relevant variables are compared against each other with reproducible preference factors (Dai et al. 2001; Marinoni 2004) Analytic Hierarchy Process (AHP) The sociodemographic variables are compared against each other in a pair-wise comparison matrix that is used to express relative preferences among the factors. Numerical values expressing judgment of the relative importance (or preference) of one variable (factor) against another are assigned to each variable. According to psychological studies, individuals cannot simultaneously compare more than 7 ± 2 elements (Miller 1956), and Saaty (1977, 2008) as well as Saaty and Vargas (1991) suggested a scale for comparison consisting of values ranging from 1 to 9 that describe the intensity of importance (preference/dominance). A value of 1 expresses equal importance and a value of 9 is given for those factors having an extreme importance over another factor (Table 5.9).

63 52 Table 5.9 Scale for comparisons Intensity of importance Description 1 Equal importance 3 Moderate importance of one factor over another 5 Strong or essential importance 7 Very strong importance 9 Extreme importance 2, 4, 6, 8 Intermediate values Reciprocals Values for inverse comparison Source: Saaty and Vargas, 1991, Prediction, Projection and Forecasting. Kluwer Academic Publishers For example, for the case where there are three parameters such as P 1, P 2, and P 3, the comparison matrix will be, a square matrix of order three, where all factors are compared to each other. ( ) (5.2) A comparison matrix was created for this work, and after assigning the values in the comparison matrix, the weights can be calculated. The assigned preference values determined by the survey responses are synthesized to determine a numerical ranking of the variables that also serves as the weights for the variables. To accomplish this, the eigenvalues and eigenvectors of the square preference matrix are calculated. The square matrix of order three gives three eigenvalues with three eigenvectors each having three vector components. It is sufficient to calculate only the eigenvector resulting from the largest eigenvalue, since this eigenvector contains enough information based on its

64 53 eigenvector components to provide the relative priorities of the variables being considered (Saaty and Vargas 1991). The values of the pair-wise comparison matrix will normally not be set arbitrarily. However, people s feelings and preferences are subjective and this may result in perturbations in the eigenvector calculations. Such inconsistencies might be, for example, that factor A i is preferred over another factor A j with A j being preferred over a factor A k is not preferred over A i (A i must be preferred over A k in this case). Saaty (1977) provided a consistency ratio CR that is an averaged index that expresses the consistency of the pairwise comparison matrix. This index is defined as the ratio of the consistency index CI to an average consistency index RI, thus (5.3) Table 5.10 Values of RI n (order of matrix) RI Source: Saaty and Vargas, 1991, Prediction, Projection and Forecasting. Kluwer Academic Publishers

65 54 Using Saaty (1977) s results, matrices with an order greater than 8 have an RI order of magnitude value of about The consistency index CI can be directly calculated from the preference matrix as follows: (5.4) where is the greatest eigenvalue of the preference matrix, and n indicates the order of matrix. Saaty and Vargas (1991) recommend a revision of the preference matrix if the consistency ratio CR exceeds a value of 0.1. In this survey, since we considered six variables consisting of age, median household income, race/ethnicity, family size, health insurance, and religion, so the comparison matrix is of order six, and all variables are compared against each other. For the qualitative responses, there were four different choices for experts to select. Not as important, Equally important, Slightly more important, Much more important that were assigned 1 to 4 respectively. Table 5.11 demonstrates the comparison matrix for the sociodemographic variables.

66 55 Table 5.11 Comparison matrix for sociodemographic parameters Age Median Household Income Ethnicity Family Size Health Insurance Religion Age Median Household Income Ethnicity Family Size Health Insurance Religion

67 56 Table 5.12 Computed weights for each category in the parameters Sociodemographic Parameters Categories Weight 20<age<29 2 Age 30<age< <age< Non-Hispanic White 4.89 non-hispanic Black 2.11 Ethnicity Hispanic 2.33 API 1.67 AI/AN 1 Other 1.67 HHI < $50K 1.33 Median Household Income $50K <HHI < $100K 2.67 HHI > $ No children 3 Family Size one 2 more 1.11 gov 1 Health Insurance private 2.44 No ins 1.44 private no IVF 2.33 Catholic Christian 1.89 Religion other Christian 2.67 Other religions 1.56 Considering the weights in Table 5.12 for each variable, the subclasses are weighted and summed up. For the age variable, three separated layers are created for the three subclasses and then the weight values are summed. This results in a single weighted layer. Figure 5.5 shows the female population for Iowa in 2010 by census tracts and weighted by age.

68 57 Figure 5.5 Female population for Iowa (2010) weighted by age This same approach was also applied to the layer modeling median household income for Iowa by census tracts (2010). In this case, the income data was divided into three income subclasses and for each group a weight was calculated. For the third variable, race/ethnicity there were six categories for which weights are calculated. In this case, the values of each race/ethnicity are multiplied by the defined weights and they are summed up.

69 58 Figure 5.6 Weighted median household income Figure 5.7 Population weighted by race/ethnicity

70 Multivariate clustering analysis and dimension reduction Now we have three layers, age, household income, and race/ethnicity that we further classify into three subgroups: areas that are most likely to match, possible match, least likely to match. To derive these three subgroups, a clustering approach using selforganizing maps (SOM) is applied to the data Self-Organizing Map (SOM) Self-Organizing Map (SOM) is an artificial neural network method for unsupervised clustering that takes a set of multi-dimensional data as input to a training procedure during which adjustments are made to multi-dimensional vectors associated with a grid of predetermined number of neurons. The SOM will be ready for clustering multi-dimensional data after running a training procedure on a large dataset, which training data is a sub group of the dataset. The neural network will tend to replicate topological structures inherent in the training data. The three sociodemographic variables serve as the input data for the SOM component. The weights for each variable capture a specified level of impact on the similarity measure. SOM nodes are organized in a two-dimensional, hexagonal layout of SOM nodes. A rule of thumb suggested by Kohonen is that the number of iterations must be at least 500 times the number of SOM nodes (Kohonen 1990; Guo et al. 2005). In order to measure the similarity, Euclidean distance is adopted. The Euclidian distance points out to the well-known formula ( [( ) ]). Each node in the SOM is related to a vector, which represents the position of this node in the input attribute space. The SOM first initializes each node by assigning its codebook vector randomly (or using a specific initialization method) (Kohonen 2001). During the iterative learning process, each codebook vector is adjusted according to the data items falling inside and the codebook vectors of its neighboring nodes are adjusted accordingly. After the learning process is complete, each node has a new position in the

71 60 input attribute space. With their new positions and topologic relationships in the 2D layout, the SOM nodes form a nonlinear, smooth surface in the input attribute space, which can be regarded as the result of a nonlinear regression. The nodes are not equally spaced on the regression surface, rather, the positions of the nodes in the input data space tend to approximate the density function of the input data items (i.e., dense areas tend to have more nodes). Figure 5.8 SOMVIS (Multivariate Mapping and Visualization with SOM) output Figure 5.8 presents the results for the clustering process when the number of clusters is reduced from 25 to just 3. The resulting map shows the degree of match for census tracts with respect to sociodemographic characteristics. In the figure three windows are shown. The top left one is SOM window that represents SOM map and you can see the hexagonal adjacency matrix as a result of clustering. The top right window shows the areal units and spatial data. Here the census tracts are shown. In the bottom of the figure you can see PCP diagram that each vertical axis or pipeline is a representative

72 61 of one variable and each connecting line through the pipelines indicates a cluster. All the colors in the above diagrams are meaningful and they are connected. Here in this screenshot 25 ( ) clusters are presented. These clustered outcomes should be interpreted based on the result of PCP diagram to three classes such as most likely, possible, and least likely that is useful for the study. Figure 5.9 Degree of match for census tracts with respect to sociodemographic characteristics Figure 5.9 shows the census tracts of state of Iowa categorized according to the three classes, theses three classes are Most likely", Possible, and Least likely that present the level of match with respect to sociodemographic variables in different areas. More likely areas are often around cities and it is expectable. In different application and