Clinical Research Module: Biostatistics

Transcription

1 Clinical Research Module: Biostatistics Lecture 1 Alberto Nettel-Aguirre, PhD, PStat These lecture notes based on others developed by Drs. Peter Faris, Sarah Rose Luz Palacios-Derflingher and myself

2 Who am I? Alberto Nettel-Aguirre, PhD, PStat Assocciate professor with the Departments of Paediatrics and Community Health Sciences, Adjunct Professor Faculty of Kinesiology Statistician with the Research Methods Team Biostats, Social network Analysis, Statistical Learning, Functional Data Analysis; injury prevention, Nephro, Neo collaborations.

3 Material Covered in the Biostatistics Lectures Lecture 1A- Background material: Why statistics? Variables and scales of measurement Distributions and measures of central tendency and dispersion Data presentation

4 Why Statistics? Statistics provides a means of evaluating evidence from medical research. Allows one to address questions such as: How likely are the effects observed in a study not due to chance? Can we trust the validity of conclusions? How accurate are the estimates provided by the research? Were the researchers conclusions trustworthy, given the number of patients they used to test their hypotheses?

5 A field of study concerned with the 1. Collection, organization, summarization, and analysis of data; 2. Drawing of inferences about a body of data (population) when only a part of the data is observed (sample) Statistics

6 Population vs. Sample Population the collection of all individuals or items under consideration in a study. Sample a part of the population from which information is obtained. Population Sample

7 Why are Statistics Important in health research? Statistical Analysis (correctly done) is a vital part of good research Statistics are needed to draw conclusions from any data you have collected Your statistical analysis plan should be worked into the design of your study from the beginning Often after you have collected your data it is too late to change your analysis plan

8 Sampling Designs Probabilistic designs Simple Random Sampling Systematic Sampling Cluster Sampling Stratified Sampling Non-probabilistic designs Convenience Ad hoc quota Volunteer Purposive Snowball sampling

9 Statistical Analysis Methods Describe the descriptive statistics used to describe the population Assuming you have a representative sample of the population Identify each statistical test or method used for each comparison, in the order in which they were addressed Cite a reference for complex or uncommon statistical tests used to analyze the data If necessary more detail can be provided online in a supplement

10 Statistical Analysis Methods Describe how you checked the assumptions of your statistical methods. Provide a sample size calculation (which should have been done at the proposal stage)

11 Statistical Analysis Methods Prior to Report Careful Graphical and Exploratory Analysis Aids in data cleaning and the decision about the appropriateness of different statistical methods In the Report Descriptive Statistics (informs the reader about the participants that you are examining) Comparison of individual variables between two groups Multivariable Analysis (another time)

12 Material Covered in the Biostatistics Lectures Lecture 1A- Background material: Why biostatistics? Variables and scales of measurement Distributions and measures of central tendency and dispersion Data presentation

13 Types of Measures To use statistical methods we make use of quantifying our observations Sometimes this is simple: e.g. blood pressure, height, weight, body mass index. Quantification can present challenges: e.g. how should we quantify tissue damage? Socioeconomic status? We must also decide on an appropriate way to measure to be able to assess an effect Proportion of successes? Number of relapses per patients? Difference in means? Comparison of changes?

14 Types of Measures We then have to choose appropriate methods to display data and perform statistical tests. The statistical methods we use will depend on the scale of measurement whether the variable is measured on a categorical (nominal or ordinal), numerical (interval or ratio) scale and the design of the study. In the case of numerical, we have two types of variables: continuous and discrete.

15 Types of Data Categorical data(categories) Nominal variables (names): Labels used to identify an attribute of each element two or more categories, no ordering Ordinal variables (order): Have the properties of nominal data and can be used to rank or order the observations for the variable two or more categories, ordered in magnitude Difference between successive not necessarily the same. Numerical data Discrete: can only take on certain numerical values Continuous: Interval : can take any numerical value within a range Ratio data:have all the properties of interval data, and the ratio of two observations is meaningful

16 Nominal Data Examples of Nominal Variables binary or dichotomous variables such as male/female, right or left side injuries Categories of disease, where there is no rationale for ordering the diseases. e.g. Pneumonia, asthma, emphysema

17 Ordinal Data Examples of ordinal variables: Level of severity: fatal, severe, moderate, minor. Degree of difficulty: difficult, doable, easy. Student grades A = excellent understanding, B = Adequate understanding, C = Passable.

18 Discrete Numerical Data Counts of events: Number of children Number of injuries Number of episodes of hypoglycaemia

19 Interval Data Interval variables have properties of order and magnitude. The magnitude between adjacent values are the same (with respect to the attribute being measured) regardless of where these are in the scale. e.g. the difference in kinetic energy between temperatures of 22 and 23 Celsius is the same as that between temperatures of 30 and 31 (1 degree celsius). Dates can be considered as an interval variable. Interval variables are continuous variables that can take on (theoreticaly) any value within a range.

20 Ratio Variables Ratio variables have the properties of order and magnitude, but also have the property that zero indicates the absence of the attribute. Examples include: Weight, height, serum values, age, time to an event, temperature in Kelvin. Interval and ratio variables can be turned into nominal and ordinal variables (careful, loss of info sometimes)

21 Special cases of variables: Dichotomous (Binary) Variables Dichotomous variables have two possible values. These values may/may not reflect the magnitude of some underlying characteristic. e.g. gender (Male/Female), mortality (Alive/Dead), age (Young/Old), diagnosis (Yes/No).

22 Examples: Types of Data Time from treatment to death Serum folate Blood pressure Number of relapses per patient Death Sex Quality of life IQ 7 point question re: satisfaction with treatment

23 Tables / Summaries Categorical data: Summarizing Data Frequencies, Percentages/proportions Numerical data: Measures of central tendency, measures of dispersion (mean or median, SD or IQR (in general))

24 Graphs Categorical data: Summarizing Data Bar charts: the height of each bar shows the frequency (or percentage) per category. The bars don't need to be contiguous (stay away from stacked). Numerical data: Histograms: Classes or bins with group values within a continuous range. The number (percentage or density) in the group is the height of the bar. The bars need to be contiguous. Boxplots: 3 number summary plus outlier candidates for numerical data

25 Material Covered in the Biostatistics Lectures Lecture 1A- Background material: Why biostatistics? Variables and scales of measurement Distributions and measures of central tendency and dispersion Data presentation

26 Probability Distributions Think first of material distribution (boxes of gloves per ward, swabs, etc) Each ward gets a certain amount of material In probability distributions, each possible event gets/has a certain amount of probability (chance) of happening.

27 Features of Distributions Central tendency or location parameters The value that observations are centred around. Dispersion how spread out the observations are in the distribution (sometimes around the centre of). Skewness are observations symmetrically distributed? Do they tend to extend farther to the left or to the right?

28 Measures of Central Tendency (location) Mean average value sum of values divided by the number in the sample Median Value at which 50% of the observations have been accumulated. To calculate: rank data, and find the value for which 50% of observations fall above and 50% below, or use rank formula Mode most frequently observed value

29 Calculations (for completeness) Data: 32, 42, 46, 46, 54 Mean: ( )/5 = 44 Median(via rank formula): Index i = (p th percentile*#observations)/ th percentile*5 observations/100=2.5 If i is not an integer, next value is pth percentile If i is an integer, average i th and i th +1 Median=46 Mode: most frequent value = 46

30 Using Measures of Central Tendency Mean a good representation for a sample when data aren t skewed and no extreme data present. Highly influenced by extreme values. If symmetric distribution, mean median.» Median Better representation when data are skewed or when there are outliers. Robust to extreme values. Mode Check for bimodal distribution. Not useful for small samples.

31 Cont. IF Data now : 32, 42, 46, 46, 254 Mean: ( )/5 = 84 Median: Median= STILL 46 Mode: most frequent value =

32 Effects of Skewness on Measures of Central Tendency

33 The data sets have the same Mean, Median, and Mode yet clearly differ! Measures of Variation or Measures of Spread

34 Measures of dispersion Range Difference between largest and smallest values Interquartile range Difference between the third quartile (75 th percentile) and first quartile (25 th percentile) central 50% of the data Sample variance sum of squared deviations from the mean divided by n-1 For sample, denoted as S 2 Standard deviation square root of the variance For sample, denoted as S

35 Calculating the variance and standard deviation (X=total cholesterol) Subject (i) X

36 Calculating the variance and standard deviation (X=total cholesterol) X (X- X)

37 Calculating the variance and standard deviation (X=total cholesterol) i X X (X- X) 2 (X- X) å X n 1 = å X n i= 1 i = 4.99 S 2 = n å i= 1 ( X i n -1 - X ) 2 = 0.87 S = 0.87 = 0.93

38 Material Covered in the Biostatistics Lectures Lecture 1- Background material: Why biostatistics? Variables and scales of measurement Measures of central tendency and dispersion Data presentation

39 Some plots for numerical data: Good graphical methods are essential for understanding and describing data Histograms: Bars representing frequency or percentages of data observed within values or groups of values. Boxplots: 3 number summary plus outlier identification 25%, 50%, 75% Best for visually comparing two or more groups

40 Frequency Distribution of Immunoglobulin IgM data for 298 healthy children (age 2-6 yrs) Class Frequency Class Frequency 0.1 to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < to < Data from Altman, 1995, Practical Statistics for Medical Research, Table 3.2, p. 23

41 Histogram of IgM (g/l) Frequency IgM (g/l)

42 CTFC In coronary angiography, the corrected TIMI frame count (CTFC) is the number of frames required for dye to reach a standardized distal landmark. The following boxplots show the CTFC before and after angioplasty in approximately 1000 patients. Note the skewness in the distributions.

43 The Box and Whisker Plot: Anatomy Birth Weight (grams) 1,000 2,000 3,000 4,000 5,000 Box Outliers Whiskers Outliers

44 CTFC pre and post-angioplasty difference in CTFC CTFC Post-CTFC - pre-ctfc Pre-pci Post-pci

45 Boxplots The top of the box is the 75 th percentile (i.e. 75% of the observations fall below this value) The bottom of the box is the 25 th percentile. Hence the box has the middle 50% of data. The line in the middle of the box is the median. Points above and below the whiskers are considered to be outliers. These outliers are not representative of the general distribution of values.

46 Displaying Categorical Data Tables / Summaries Frequencies Percentages/proportions Tabulations and cross-tabulations Graphs Bar charts: the height of each bar shows the frequency (or percentage) per category. The bars don't need to be contiguous.

47 Displaying Categorical Data - Example In a study, there are 747 men and 434 women. Of these, 276 men and 195 women had cardiac arrests. Gender Frequency % Male Female Total Cardiac arrest Frequency % Yes No Total

48 Displaying Categorical Data - Example N Row % Cardiac arrest No cardiac arrest Total Col % Male Female Total

49 Example 2

50 DO NOT!! Mean Hba1c Use Barplots with SD for numerical Data. A bar is useful when it represents accumulation as in a histogram (% or frequency from 0 up) not when it is supposed to represent actual numbers.

51 Stay away!!! From stacked bar graphs. The idea of a graph is to make comparison easy and not repeat all numbers, otherwise use a table. In stacked bars you can not easily tell different heights of different bars, whereas in side by side you can. 70% 60% 50% 40% 30% Banana Orange Apples 20% 10% 0% Sandra Susie Jamie Jorge Alberto

52 Stay away!! From adding dimensions that are not real dimensions and distort the graph. From Pie charts; you usually end up having to add numbers to each slice as the slices are not easily comparable. Hence it is just a colored disarrayed table!!!!