Sampling and Sample Size in Epidemiology

1. Sampling and Sample Size in Epidemiology Dr. Papia Sultana Associate Professor Department of Statistics University of Rajshahi Dr. Papia Sultana

2. Sampling The sample The population Dr. Papia Sultana

3. Representative sample Every person in the population has the equal possibility to be chosen to be in the sample Dr. Papia Sultana

4. Not representative sample Dr. Papia Sultana

5. Selection bias • Selection bias occurs then patients included in the study are not representative of the population to which the results will be applied • Example • Patients who agree to participate in a study may differ from those who do not agree to participate Dr. Papia Sultana

6. The sample must be a small picture of the entire population The sample The population Dr. Papia Sultana

7. Selection biased should be avoided Population Sample Dr. Papia Sultana

8. Internal and external validity Reference population External validity Study population New treatment Current treatment Internal validity Dr. Papia Sultana

9. Internal & external validity • Internal validity - refers specifically to whether an experimental treatment/condition makes a difference or not, and whether there is sufficient evidence to support the claim • External validity – refers to whether you can generalize the findings to the population of interest Dr. Papia Sultana

10. External validity • Place of the study?? • Subjects of the study?? Dr. Papia Sultana

11. Sampling in Epidemiology • Any proper sampling method is used -Simple Random Sampling (SRS) - Cluster Sampling - Systematic Sampling - Stratified Sampling - PPS Sampling - Multistage Sampling • Sometimes combination of more than one sampling scheme. Dr. Papia Sultana

12. Randomization in Experimental study • Controlled trial – trials with control groups • Randomized controlled trials • Quasi randomized trials • Non randomized trials • Phase III trial Treatment 1 Treatment 2 Dr. Papia Sultana

13. Randomization in Experimental study • Randomized controlled trials – interventions allocated randomly • Coin tossing is not proper way • Throwing a dice can be used: if the outcome is 1,2 &3 the subject will be allocated to treatment 1 group, otherwise in treatment 2 group. • In RCT, people are randomly allocated to treatment groups and therefore all characteristics such as confounders and other variables should be evenly distributed in the different treatment groups Dr. Papia Sultana

14. Zinc supplementation in children with cholera in Bangladesh: randomized controlled trial • Table 1  Baseline characteristics of study children. • Values are mean (SD) unless stated otherwise Dr. Papia Sultana

15. Randomization in Experimental study • Quasi-randomized controlled trials – allocation using schemes such as every alternate person, or according to date of birth (odd or even) etc Dr. Papia Sultana

16. Sample size • Duringthe planning stage of a study, the following questions are of particular interest to the investigators: (i) how many subjects are needed in order to have a desired power for detecting a meaningful difference (e.g., an 80% chance of correctly detecting a meaningful difference), and (ii) what’s the trade-off between costeffectivenessand power if only a small number of subjects are available for the study due to limited budget and/or some medical considerations. • Sample size calculation plays an important role for assuring validity, accuracy, reliability, and integrity of the intended study. • Ethical issues may come in front, too. Dr. Papia Sultana

17. Calculation of sample size • What is the study objectives (outcome variable)? • What type of variable it is? • What study design is involved? • Is there any information related to that published in anywhere (historical information)? • Do you need to conduct a pilot study? Dr. Papia Sultana

18. Calculation of sample size • Basically, sample size calculation can be classified into sample size estimation/ determination (SRS), sample size justification (Lab trial & clinical trial), sample size adjustment (cluster sampling), and sample size re-estimation (in the mid stage of the study). • Level of significance and power play very important role in calculation of sample size. Dr. Papia Sultana

19. Calculation of sample size • Researcher fixes probabilities of type I and II errors • Prob (type I error) = Prob (reject H0 when H0 is true) =  • Smaller error  greater precision  need more information  need larger sample size • Prob (type II error) = Prob (don’t reject H0 when H0 is false) =  • Power =1-  • More power  smaller error  need larger sample size Dr. Papia Sultana

20. Calculation of sample size • Single Proportion n = required sample sizeZ= Standard Normal value at confidence level at 100(1- )% (ideal value is1.96 at 95%)p = referred prevalence for the study d = margin of error (ideal value is 0.05) Dr. Papia Sultana

21. Calculation of sample size Example: In the Al Haouz project in Morocco, it has been estimated that roughly 30% (0.3) of the children in the project area suffer from chronic malnutrition. This figure has been taken from national statistics on malnutrition in rural areas. Use of the standard values listed above provides the following calculation. n=1.96² x .3(1-.3) .05² = 322.72 ~ 323 Dr. Papia Sultana

22. Calculation of sample size Design effect: • The anthropometric survey is designed as a cluster sample (a representative selection of villages), not a simple random sample. To correct for the difference in design, the sample size is multiplied by the design effect (D). • The design effect is generally assumed to be 2 for nutrition surveys using cluster-sampling methodology. • n x D = 323 x 2 = 646 Dr. Papia Sultana

23. Calculation of sample size Contingency: • The sample is further increased by 5% to account for contingencies such as non-response or recording error (provide proper logic). • n + 5% = 646 x 1.05 = 678.3 ˜ 678 Dr. Papia Sultana

24. Calculation of sample size • In clinical Trial or for the rare diseases we need to analyze power. • I have 2 years to finish my research, of which one year is for data collection. I think I can get data on 50 people in that year. Is 50 a sufficient sample size to test my hypothesis with the significance level I want? Dr. Papia Sultana

25. Calculation of sample size =Z value at power (at power 80% this value is 0.84) Dr. Papia Sultana

26. Calculation of sample size • Example: Assuming 30% prevalence of the study area with margin of error 0.05 and 95% confidence a sample size 659 is required to achieve 80% power. Dr. Papia Sultana

27. Calculation of sample size • Example: Assuming 30% prevalence of the study area with margin of error 0.05 a sample size 60 can achieve a power 80%. Dr. Papia Sultana

28. Calculation of sample size Difference between two proportions: • Comparison between two treatments • To observe the effect of an intervention Dr. Papia Sultana

29. Calculation of sample size • = prevalence of group 1 • = prevalence of group 2 • = difference between the two groups Equal sample size will be taken in both groups [ total 2n] Dr. Papia Sultana

30. Calculation of sample size Dr. Papia Sultana

31. Calculation of sample size • the variable is continuous • Information about mean and sd are available Dr. Papia Sultana

32. Calculation of sample size • Single mean test n = required sample sizeZ= Standard Normal value at confidence level at 100(1- )% (ideal value is1.96 at 95%) = referred sd for the variable d = margin of error (ideal value is 0.05) Dr. Papia Sultana

33. Calculation of sample size • Equality of two mean test Dr. Papia Sultana

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35. Calculation of sample size • Only population size is known Dr. Papia Sultana

36. Calculation of sample size • Odd Ratio • Chi-square • Linear model • Logistic model • Factorial model Not in handy Dr. Papia Sultana

37. Calculation of sample size • Computer Software: • PASS • EpiCalc 2000 • Online supports are also available Dr. Papia Sultana

38. Using PASS: Z-test example • Question: does exercise help to decrease body weight? • Study design: participants will be randomized into two groups (exercise and control) • Outcome: change in weight • Want to detect: a change of at least 15 pounds • Known: from past studies, the standard deviation varies between 10 and 15 pounds. Dr. Papia Sultana

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43. Example: One-way ANOVA • Number of Groups: 4 • Hypothesized means: 35, 20, 25, 18 (possibly from a pilot study) • Sample size pattern: same number in each group • SD of subjects: 18 (from a previous study) •  = 0.01 and 0.05 • Find power for sample sizes from 5 to 30 per group (increments of 5) Dr. Papia Sultana

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47. Example: Linear Multiple Regression • Research Question: is depression score an important factor in explaining pain ratings, after adjusting for age and sex? • Statistical question: does adding depression score increase the explained variation of pain ratings, in a linear regression model that already has age and sex in it and has R2 =.2? • Suppose I may have sample sizes of 20, 30, 50, 70, and 100. What is the minimum R2 change I can detect with power .8? Dr. Papia Sultana

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50. Other Types of Hypothesis Tests • Different methods of data analysis require different input for sample size calculations Dr. Papia Sultana