Sampling. Vorasith Sornsrivichai, M.D., FETP Cert. Epidemiology Unit, Faculty of Medicine, PSU

Transcription

1 Sampling Vorasith Sornsrivichai, M.D., FETP Cert. Epidemiology Unit, Faculty of Medicine, PSU

2 Objectives 1. Explain the need for survey sampling 2. Define the following terms: Reference population, study population, study sample Internal validity, external validity Probability sampling, equal probability selection method, disproportionate sampling Stratification, design effect 3. Describe principles of & steps in sampling for a household survey Simple, systematic, stratified random sampling, cluster sampling 2

3 Outline of Presentation Population & sample Validity, precision, representativeness Non-probability VS probability sample Proportionate VS disproportionate sampling Sampling error, sampling variation, sampling bias Methods in probability sampling 3

4 POPULATION SAMPLE 4

5 Population (N) The whole collection of units (the universe ), from which a sample may be drawn The units may be records or events, not necessarily a population of persons 5

6 Sample (n) A selected subset of a population Random or nonrandom Representative or nonrepresentative The sample is intended to give results that are representative of the whole population 6

7 Wisdom Score y Population (N=100) Does wisdom come with age? x 7 Age (yr)

8 Wisdom Score y Sample (n=10) Does wisdom come with age? x 8 Age (yr)

9 Wisdom Score y Population (N=100) Does wisdom come with age? x 9 Age (yr)

10 Pain makes man think. Thought makes man wise. Wisdom makes life endurable." ~ John Patrick ~

11 Why Do We Sample Populations? Get accurate information from large populations Efficiency of study 11

12 Hierarchy of Population Target population: The general population you want to know about Sample: The part of target population you collect the data We use the estimate from the sample to estimate the parameter in the target population 12

13 Hierarchy of Population Reference/external population Study/target population External Validity (Generalizability) Issue of population difference Internal validity Issue of bias Sampling Actual population Statistical inference Issue of chance Study sample/population (Sample) 13

14 Validity & Precision Valid, and precise Valid, not precise Not valid, but precise Not valid, not precise 14

15 Validity Validity & Precision Measurement reflects true value of population Improved by good design, sampling scheme, quality assurance Precision The measurement results conform to themselves Improved by increasing the sample size 15

16 Truth is (almost) Everything A small sample that gives a true estimate of the target population is better than a big sample that gives a precise but false estimate 16

17 Representativeness Persons Demographic: age, sex, race Socioeconomic: SES Cultural Place Geographical: country, region Sociological: urban VS rural Time Time of the day Day of the week Seasonality 17

18 Type of Samples Non-probability samples : probability of being selected is unknown Convenience or accidental or haphazard samples e.g. Man-in-the-street surveys, grab sample Biased Purposive or subjective samples e.g. expert sample, quota sample Based on knowledge Time/resources constraints Probability (random) samples: every unit in the population has a known probability of being selected 18

19 Probability Sample All individuals have a known chance of selection May have an equal chance of being selected Or, if a stratified sampling method is used, the chance of being selected can be varied 19

20 Created by Probability Sample Assigning an identity (label, number) to all individuals in the population Arranging them in alphabetical order and numbering in sequence, or simply assigning a number to each, or by grouping according to area of residence and numbering the groups 20

21 Probability Sample Select individuals (or groups) for study by a random procedure such as use of a table of random numbers (or comparable procedure) to ensure that the chance of selection is known 21

22 Any questions? :-) "To conquer fear is the beginning of wisdom." ~ Bertrand Russell ~

23 Sampling The process of selecting a number of subjects from all the subjects in a particular group Conclusions based on sample results may be attributed only to the population sampled Any extrapolation to a larger or different population is a judgment or a guess and is not part of statistical inference 23

24 Definition of Sampling Terms Sampling frame Any list of all the sampling units in the population Primary Sampling Unit (PSU) Sample drawn from sampling frame in the first stage of sample selection Sampling scheme Method of selecting sampling units from sampling frame 24

25 EPSM Equal Probability of Selection Method": A sample that each final unit of selection in the population has an equal probability of selection Simple random sampling, systematic random sampling are EPSM samples 25

26 Disproportionate Sampling May be used for Cost efficiency Important small subgroup population Stratified sampling are not EPSM, if the sampling fraction or probability of selection (n/n) is not the same for all strata 26

27 Sampling Error That part of the total estimation error of a parameter caused by the random nature of the sample Expressed by standard error of mean, proportion, differences, etc Is a function of Sample size Amount of variability in measuring factor of interest 27

28 Sampling Variation Since the inclusion of individuals in a sample is determined by chance, the result of analysis in two or more samples will differ, purely by chance 28

29 Sampling Bias Systematic error due to study of a nonrandom sample of a population 29

30 Selection Bias E+ E+ E+ E+ D+ D- D+ D- E- D+ n E- D- N E- D+ E- D- E+ E+ E+ E+ D+ D- D+ D- E- E- E- E- D+ D- D+ D- 30

31 "Mistakes are the usual bridge between inexperience and wisdom." ~ Phyllis Theroux ~

32 Selecting a Sampling Method Population to be studied Heterogeneity with respect to variable of interest Size/geographical distribution Resources available Importance of precision of estimate or sampling error 32

33 Methods in Probability Sampling Simple random sampling Systematic sampling Stratified sampling Cluster sampling Multistage sampling 33

34 Simple Random Sampling (SRS) Principle Each person has an equal chance of being selected from the entire population Procedure Assign each person a number, starting with 1, 2, 3, and so on Numbers are selected at random until the desired sample size is attained 34

35 Random Table Row < uniform random digits >

36 Simple Random Sampling 1 Albert D. 2 Richard D. 3 Belle H. 4 Raymond L. 5 Stéphane B. 6 Albert T. 7 Jean William V. 8 André D. 9 Denis C. 10 Anthony Q. 11 James B. 12 Denis G. 13 Amanda L. 14 Jennifer L. 15 Philippe K. 16 Eve F. 17 Priscilla O. 18 Frank V.L. 19 Brian F. 20 Hellène H. 21 Isabelle R. 22 Jean T. 23 Samanta D. 24 Berthe L. 25 Monique Q. 26 Régine D. 27 Lucille L. 28 Jérémy W. 29 Gilles D. 30 Renaud S. 31 Pierre K. 32 Mike R. 33 Marie M. 34 Gaétan Z. 35 Fidèle D. 36 Maria P. 37 Anne-Marie G. 38 Michel K. 39 Gaston C. 40 Alain M. 41 Olivier P. 42 Geneviève M. 43 Berthe D. 44 Jean Pierre P. 45 Jacques B. 46 François P. 47 Dominique M. 48 Antoine C. 36

37 Simple Random Sampling Advantages Simple Sampling error easily measured Disadvantages Need complete & up-to-date list of units For a wide geographic area, travel costs is often the most expensive component Does not always achieve best representativeness 37

38 Principle Systematic Sampling Units drawn with a constant interval between successive units Equal chance of being selected for each unit Procedure Calculate sampling interval (k = N/n) Draw a random number ( k) for random starting point Draw every k th units from first unit 38

39 f=11/93 Systematic Sampling 39

40 Systematic Sampling 40

41 Systematic Sampling Advantages Provide better spread, ensures representativeness across list Can improve precision Easy to implement Disadvantages Dangerous if list has cycles or periodic Travel cost 41

42 f=7/93 Systematic Sampling 42

43 Stratified Sampling Principle Dividing the population into subgroups according to some important characteristic e.g. age Selecting a random sample out of each subgroup If proportion of the sample drawn from each strata is the same as the proportion of the population in each stratum (Probability Proportional to Size-PPS) then all strata will be fairly represented with the sample Procedure Classify population into homogeneous subgroups (strata) Draw sample in each strata Combine results of all strata 43

44 Stratified Sampling with PPS N= Stratification 2 Sampling n=5 44

45 Stratified Sampling Advantages More precise if interesting variable associated with strata All subgroups represented, allowing separate conclusions about each of them Disadvantages Sampling error difficult to measure Loss of precision if very small numbers sampled in individual strata 45

46 Cluster Sampling Principle Each unit selected is a group of units (a village, an ED. etc.) rather than an individual Procedure Random sample of groups ( clusters ) of units In selected clusters, all units or proportion (sample) of units included Sampling within cluster may be simple random or systematic 46

47 EPI 30 Clusters Survey Community Pop. size Cum. pop. size Divide total population of the communities (4000) by the number of clusters to be selected (30) = sampling interval (133) 2. Choose a random number between 1 and 133 (118.) Since 118 lies between 110 and 210, community 2 will be chosen 3. Now add the sampling interval: = 251, so community 3 is chosen and so on 4. In each cluster choose 7 children (total sample size/no. of clusters 47 = 210/30 = 7)

48 Cluster Sampling Section 1 Section 2 Section 3 Section 5 Section 4 48

49 Cluster Sampling Advantages List of sampling units within population not required Less travel/resources required Disadvantages Imprecise if clusters homogeneous and therefore sample variation greater than population variation (large design effect) Sampling error difficult to measure 49

50 Steps in Cluster Sampling Clarify the rationale Set up specific objective. This technique is suitable for survey for estimating proportion not so good for testing hypothesis Define study population particularly geographic definition such as rural/urban area in the specific province(s) Define eligibility of the informant Calculate sample size and estimate number of households to be visited 50

51 Steps in Cluster Sampling Obtain the enumeration district (ED), a list of districts and villages in the study province(s). Each village should have the most recent number of population or household. Assuming the proportion of population among different districts in the study province is relative stable over time, this enumeration table (with name of village in the first and its population size in the second column) will be use as sampling frame. In the first stage of sampling, the PSU is village Calculate cumulative population for each village. Place the number in the third column Calculate sampling interval if the no. of cluster is 30 then sampling interval = total pop. / 30 = i 51

52 Steps in Cluster Sampling Select a random start which must fall between 1 to the sampling interval. Say r The first village is the village with cumulative population is just over r The second village is the village with cumulative population is just over r + i The third village is the village with cumulative population is just over r + 2 i The other consecutive village can be sampled similarly At the end, there will be 30 selected villages 52

53 Steps in Cluster Sampling Prepare the questionnaire Prepare initial field visit with the responsible officers. Check information related to transportation, security and availability of other facilities: shelters, food Make an appointment with key persons in each selected village. Have an initial visit. Employ 1-2 locals to facilitate the survey. Make sure that there would be no serious problem during the day of survey Pre-test the questionnaire and train the interviewers in a non-selected village 53

54 Steps in Cluster Sampling Visit the village on the day of appointment. Choose a random starting point and visit consecutive nearest household. Ask for eligible subject. Conduct interview When a sample size in that cluster reach the desire number, check the completeness of the questionnaire and leave the village Continue until all 30 clusters are finished 54

55 Design Effect Global variance p(1-p) Var srs = n Cluster variance Σ (pi-p)² Var clust = k(k-1) Var clust Design effect = Var srs p= global proportion pi= proportion in each stratum n= number of subjects k= number of strata 55

56 Design Effect = Actual sample size (SS) / Effective SS e.g. cluster sampling SS / SRS SS = 1+(m 1)ρ If m = cluster size k = no. of cluster ρ = Intracluster correlation coefficient 56

57 The Intracluster Correlation Coefficient (ICC, ρ-rho) A measure of the relatedness of clustered data; by comparing the variance within clusters with the variance between clusters. Mathematically, it is the between-cluster variability divided by the sum of the withincluster and between-cluster variabilities. ICC (ρ) = S b 2 (S b2 + S w2 ) 57

58 Effective Sample Size If we have 4 physicians recruiting 32 patients each (total 128 patients.) Given ρ = 0.017, what is the effective sample size (ESS) after adjusting for clustering? Design Effect = Actual SS / Effective SS ESS = m k / 1+(m 1)ρ If m = cluster size = 32, k = no. of cluster = 4, ρ = ESS = 32x4 / (32-1) = 84 58

59 Multistage Sampling Principle Several chained samples Several statistical units Advantages No complete listing of population required Most feasible approach for large populations Disadvantages Several sampling lists Sampling error difficult to measure 59

60 Example: Multistage Sampling Determine hepatitis A susceptibility among school children in a country Sample of regions drawn from country Sample of provinces drawn from each selected region Sample of schools drawn in each selected province Sample children within selected schools 60

61 "A prudent question is one half of wisdom." ~ Francis Bacon ~ Any questions? :-)

62 "The rain is famous for falling on the just and unjust alike, but if I had the management of such affairs I would rain softly and sweetly on the just, but if I caught a sample of the unjust outdoors I would drown him ~ Mark Twain ~