Sampling technique and sample size calculation

Transcript

1. Sampling & sample size Prof. Dr. Jamalludin Ab Rahman B.Med.Sc., MD, MPH, FPHM, AMM Department of Community Medicine Kulliyyah of Medicine International Islamic University Malaysia
2. Why we sample? =Can’t afford to select the entire population =Do not need to select the entire population 11 November 2019 2 Research Methodology Workshop
3. Population vs. Sample 11 November 2019 Research Methodology Workshop 3 Must be random
4. Sample represents a population =To represent a population at certain location e.g. adults in Malaysia, male in Pahang =To represent population with specific condition e.g. diabetic, pregnant women 11 November 2019 4 Research Methodology Workshop
5. Sampling with purpose Descriptive study =Measure burden of illness e.g. prevalence study or survey; NHMS, NOHSA etc =Sampling by location Analytical study =Causality in mind e.g. new drug for diabetics – assuming diabetic in Malaysia is similar with any diabetic elsewhere =Sampling for specific condition 11 November 2019 5 Research Methodology Workshop
6. Sampling statements 1. Target population 2. Study population 3. Sampling frame 4. Sampling unit 5. Observation unit 11 November 2019 6 Research Methodology Workshop
7. Example – NHMS III 2006 =Target population =Study population =Sampling frame =Sampling unit =Observation unit 11 November 2019 7 All Malaysian Household up to strata 6 List of Enumeration Block & Living Quarters Enumeration Block & Living Quarters All household in the selected Living Quarters Research Methodology Workshop
8. Random Non- random 11 November 2019 8 Research Methodology Workshop
9. Random 1. Simple random sampling (SRS) 2. Systematic 3. Stratified 4. Cluster Non-random 1. Convenience 2. Purposive 3. Snowball 4. Volunteer 5. etc 11 November 2019 # 9 Research Methodology Workshop
10. “ ” If you are not able to determine the sampling frame, it is non- random sampling unless proven otherwise 11 November 2019 10 Research Methodology Workshop
11. Random sampling Random Sampling Simple Systematic Stratified Cluster Multistage 11 November 2019 11 The ideal method. Randomly sample 10 students from a class of 50 students. Follow certain & systematic pattern, order. Only first sample is random. Study population divided intro strata. All strata selected. Portion of sample in each strata sampled. Study population divided intro clusters. Assume all clusters are the same. Not all clusters selected. Only some will be sampled. Several sampling techniques applied at different stage. Research Methodology Workshop
12. Non random sampling Non random Sampling Convenience Purposive Quota Volunteer Snowball 11 November 2019 16 Haphazard. Grab sampling. No rules. Just get the sample most convenience to researcher. Samples that fulfil certain criteria. E.g. diabetic patients on single insulin therapy. When the sampling stop after achieving certain size or number. Sample by reference or recommendation. Research Methodology Workshop Participants self-select to become part of a study because when asked, or respond to an advert.
13. Example – NHMS III 2006 Two stage stratified random sampling = Target population = Study population = Strata = Clusters = Sampling frame = Sampling unit = Observation unit = Sample distribution 11 November 2019 17 All Malaysian Household up to strata 6 List of Enumeration Block & Living Quarters Enumeration Block & Living Quarters All household in the selected Living Quarters State & location (urban or rural) Enumeration Block & Living Quarters Proportionate to size Research Methodology Workshop
14. Example – A clinical trial = Target population All diabetic patients = Study population Diabetic for at least 1 year on insulin therapy who attended MOPD from Jan-Dec 2014 = Sampling frame N/A = Sampling unit Any diabetic who fulfilled the selection criteria = Observation unit Same as SU 11 November 2019 18 Research Methodology Workshop
15. Sample size 19
16. Why we calculate sample size? 1. Represent target population - We can’t afford to sample everyone & everything 2. Enough sample to detect difference statistically 3. Logistic preparation – how much money, time & manpower required 11 November 2019 20 Research Methodology Workshop
17. “ ” Calculate sample size or power before conducting the study 11 November 2019 Research Methodology Workshop 21
18. Justify sample size for 11 November 2019 Research Methodology Workshop 22 1. representing target population, or 2. measure treatment effect
19. “ ” Sample size is always an estimate, never an exact value 11 November 2019 Research Methodology Workshop 23
20. Sample size is an estimate =Never an exact value, always an estimate =Calculated for certain expected estimates (outcomes) at certain degree of precision =Expected values - estimated from previous studies or from intelligent ‘guess’ 11 November 2019 24 Research Methodology Workshop
21. Principle =Calculated for certain expected estimates (outcomes) at certain degree of precision =Adjusted for design effect (based on type of sampling), alpha error, power, stratification and anticipated response rate 11 November 2019 Research Methodology Workshop 25
22. So, what do you need to calculate sample size? = Objective determined = Sampling method known = Estimate the outcome = Precision required = Statistical test used is known = Set the power (b) and confidence level (a) = Anticipated non-response rate 11 November 2019 26 Research Methodology Workshop
23. Calculate Power or Margin of Error instead =If the sample size is pre-determined – e.g. You have fixed budget, so sample size depends on the budget. Sample size is not a variable. 11 November 2019 Research Methodology Workshop 27
24. Common formulae Depends on your objective, it could be 1. Calculate single proportion 2. Compare two proportions 3. Calculate single mean 4. Compare two means 11 November 2019 Research Methodology Workshop 28
25. Sample size to represent population 29
26. Representing population =Represent population e.g. state, district, village, institution etc =Usually for prevalence study e.g. to measure prevalence of hypertension in Malaysia; or mean DMF among adult in Pahang 11 November 2019 30 Research Methodology Workshop
27. Single proportion = = #$/& &'()*') ,& = Where z = value from standard normal distribution corresponding to desired confidence level, a (.// =1.96 for 95%CI) = p is expected true proportion = d is desired precision = For small populations n can be adjusted so that 0 = 12 132 11 November 2019 31 Research Methodology Workshop
28. 11 November 2019 32 95% CI is a = 0.05 a/2 = 0.025 .// =1.96 Power 80% or 0.8 1-b = 1-0.8 = 0.2 b = 0.2 4 =0.84 Research Methodology Workshop
29. Example =Study to measure prevalence of hypertension in a village of 1000 people =Expected prevalence = 40%, Precision = 5%, CI=95%, expected non-response 20% = = ).67& ∗9.:()*9.:) 9.9;& = 369 ≅ 370 =Anticipating non response, = 450 11 November 2019 33 Research Methodology Workshop
30. Single mean =Study to measure one sample mean = = (#$/&∗D , )/, where s = expected standard deviation (SD) =We use smallest d to get largest n possible 11 November 2019 34 Research Methodology Workshop
31. Example =Study to measure average DMF among adults in a village of 2000 people =Estimated DMF = 11 (SD 10) with the precision of 2 at 95%CI = = ().67∗)9 / )/= 96.04 ≅ 100 11 November 2019 35 Research Methodology Workshop
32. Sample size to measure effect size 36
33. Hypothesis testing =How one variable is different from the other =E.g. different % of hypertension between male & female 11 November 2019 37 Research Methodology Workshop
34. Compare two proportions = = (#$ & 3#F)&∗('G )*'G 3'& )*'& ) ('G*'&)& = Total sample size = 2*n = Where p1 and p2 are the expected sample proportions of the two groups; za/2 is the critical value of the Normal distribution at a/2 and zβ is the critical value of the Normal distribution at β (e.g. for a power of 80%, β is 0.2 and the critical value is 0.84) 11 November 2019 38 Research Methodology Workshop
35. Example = A study to compare prevalence of diabetes mellitus between male and female. Expected prevalence are 30% vs. 40% respectively. Power 80% at 95% confidence level. = = (1.96 + 0.84)/∗ 9.J )*9.J 39.: )*9.: 9.J*9.: & = 7.9 ∗ 45=355.5 ≅ 360 = Total sample size = 360 * 2 = 720 11 November 2019 39 Research Methodology Workshop
36. Compare two means = = /∗ #$ & 3#F &∗D& ,& =Where d=smallest means difference and s = standard deviation =Total sample size = 2*n 11 November 2019 40 Research Methodology Workshop
37. Example =A study to compare means of HbA1c between diabetic treated with new drug versus the standard drug (control). Expected difference of 10.5% vs. 11.5% with SD estimated of 5% = = /∗;& )& ∗ 1.96 + 0.84 / = 395 =Total sample size = 790 11 November 2019 41 Research Methodology Workshop
38. Sample size applications 42
39. Using applications 1. PS: Power and Sample Size Calculation http://biostat.mc.vanderbilt.edu/wiki/Main/PowerS ampleSize 2. Epi Info http://wwwn.cdc.gov/epiinfo/7/ 3. OpenEpi http://www.openepi.com/oe2.3/menu/openepime nu.htm 11 November 2019 43 Research Methodology Workshop
40. Epi Info – Population survey 11 November 2019 44 Research Methodology Workshop
41. Epi Info – Cohort & Cross-sectional 11 November 2019 45 Research Methodology Workshop
42. Open Epi – Compare two means 11 November 2019 46 Research Methodology Workshop
43. PS - Dichotomous 11 November 2019 47 Research Methodology Workshop
44. PS – Compare two means 11 November 2019 48 Research Methodology Workshop
45. Summary 49
46. Sampling & sample size =Decide best design to represent your study population – random vs. non random =Calculate sample size for a specific purpose =Sample size is an estimate 11 November 2019 Research Methodology Workshop 50