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# 3. Calculate samplesize for prevalence studies

Part 3 of 9; Calculate samplesize for prevalence studies, dichotomous outcome

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### 3. Calculate samplesize for prevalence studies

1. 1. © Dr Azmi Mohd Tamil, 2012 Calculate Your Own Sample Size – Part 3 Cross-Sectional Study – Measuring Prevalence 1
2. 2. © Dr Azmi Mohd Tamil, 2012 Cross-Sectional What is the outcome being measured?  Is it the prevalence of disease/risk factor?  In the specific objective, it is stated that the study is conducted to determine the prevalence of the disease/risk factor. 2
3. 3. © Dr Azmi Mohd Tamil, 2012 Prevalence in Cross-Sectional Do a literature review to estimate the prevalence being studied. Determine the absolute precision required i.e. 5 percentage points (usually between 3 to 5). Calculate using (Kish L. 1965) n = (Z1-α)2(P(1-P)/D2) or refer to a table in S.K. Lwanga, S. Lemeshaw 1991, Sample Size Determination in Health Studies, pg 25 Or use StatCalc from EpiInfo6. 3
4. 4. © Dr Azmi Mohd Tamil, 2012 Example – To determine Prevalence of Obesity Confidence interval = 1 - α = 95%; Z1-α = Z0.95 = 1.96 (from normal distribution table). Prevalence = P = 20% Absolute precision required = 5 percentage points, (therefore if the calculated prevalence of the study is 20%, then the true value of the prevalence lies between 15-25%). 4
5. 5. © Dr Azmi Mohd Tamil, 2012 Calculate Manually n = (Z1-α)2(P(1-P)/D2) where Z1-α = Z0.95 = 1.96 (from normal distribution table. This value of 1.96 is standard for CI of 95%). P = 20% = 0.2 in this example D = 5% = 0.05 in this example n = 1.962 x (0.2(1-0.2)/0.052) = 245.84 5
6. 6. © Dr Azmi Mohd Tamil, 2012 Refer to Table Refer to the table in S.K. Lwanga, S. Lemeshaw 1991, Sample Size Determination in Health Studies pg 25. With a Prevalence (P) of 20%, precision of 0.05, the table indicates that the sample size required is 246. 6
7. 7. © Dr Azmi Mohd Tamil, 2012Prevalence = 20%precision = 0.05 7
8. 8. © Dr Azmi Mohd Tamil, 2012 Alternative to table http://www.palmx.org/samplesize/Calc_Samplesize.xls 8
9. 9. Or use StatCalc (Step 1)© Dr Azmi Mohd Tamil, 2012 P = 20% = 0.2 in this example D = 5% = 0.05 therefore the true value of the prevalence lies between 15- 25%. So worse acceptable result is either 15% or 25% Press F4 to calculate. 9
10. 10. StatCalc (Step 2)© Dr Azmi Mohd Tamil, 2012 Using 95% confidence level, the sample size required is 246, the same value as manual calculation & the table. 10
11. 11. Formula for Sample Size of© Dr Azmi Mohd Tamil, 2012 A Prevalence Study It is the same since all calculations uses the same formula. 11
12. 12. © Dr Azmi Mohd Tamil, 2012 If Prevalence Below 10% or Above 90% If the prevalence being studied is below 10%, therefore the level of precision should be half of the prevalence; i.e. prevalence of Diabetes Mellitus is 6% therefore d must be set at 3%. The same applies to prevalence of above 90%. The level of precision should be half of the (1-prevalence); i.e. prevalence of BCG vaccination is 96% therefore d must be set at 2%. 12
13. 13. © Dr Azmi Mohd Tamil, 2012 SS Calculation for a Known Population What if the required sample size is larger than the population being studied? i.e. study on stress among staff at Rembau Health Clinic. Expected rate of stress is 50% therefore at 5% precision, the required sample size is 384. But the number of staff is only 30! 13
14. 14. © Dr Azmi Mohd Tamil, 2012 SS Calculation for a Known Population Krejcie & Morgan  Krejcie, R.V. & Morgan, D.W. (1970). Determining sample size for research activities. Educational & Psychological Measurement, 30, 607-610.  S = required sample size N = the given population size P = prevalence d = the degree of accuracy X2 = 3.841 for the .95 confidence level 14
15. 15. © Dr Azmi Mohd Tamil, 2012 Table - Krejcie, R.V. & Morgan, D.W. (1970). Assumption of the table; prevalence = 50%. So need only 28 out of 30 for the study on stress, not 384. If population > 250,000, sample size equal to Kish’s formula. 15
16. 16. © Dr Azmi Mohd Tamil, 2012 Kish, L (1960) = Krejcie, R.V. & Morgan, D.W. (1970) ? Kish, L (1960) Krejcie, R.V. & Morgan, D.W. (1970) n = (Z1-α)2(P(1-P)/D2) S = n/(1+(n/population) (Z1-α)2 = X2 = 3.841 Population = N So we can use STATCALC P= P to calculate sample size for D2 = d2 = 0.0025 (for 5%) a known population! We usually use only 1st half of the formula! 16
17. 17. StatCalc© Dr Azmi Mohd Tamil, 2012 Using 95% confidence level, the sample size required is 28, the same value as in the table. 17
18. 18. © Dr Azmi Mohd Tamil, 2012 What If There Is No Prior Information? Instead of saying "Sample sizes are not provided because there is no prior information on which to base them“, do this instead;  Find previously published information  Conduct small pre-study  If a very preliminary pilot study, sample size calculations not usually necessary  Assume that the prevalence is 50% since that will give you the largest required sample size. 18
19. 19. © Dr Azmi Mohd Tamil, 2012 Conclusion You can calculate your own sample size. Tools are available and most of them are free. Decide what is your study design and choose the appropriate method to calculate the sample size. If despite following ALL these notes fastidiously, your proposal is still rejected by the committee due to sample size, kindly SEE THEM, not us. 19
20. 20. © Dr Azmi Mohd Tamil, 2012 References (incl. for StatCalc) Fleiss JL. Statistical methods for rates and proportions. New York: John Wiley and Sons, 1981. Gehan EA. Clinical Trials in Cancer Research. Environmental Health Perspectives Vol. 32, pp. 3148, 1979. Jones SR, Carley S & Harrison M. An introduction to power and sample size estimation. Emergency Medical Journal 2003;20;453-458. 2003 Kish L. Survey sampling. John Wiley & Sons, N.Y., 1965. Krejcie, R.V. & Morgan, D.W. (1970). Determining sample size for research activities. Educational & Psychological Measurement, 30, 607-610. Snedecor GW, Cochran WG. 1989. Statistical Methods. 8th Ed. Ames: Iowa State Press. 20
21. 21. © Dr Azmi Mohd Tamil, 2012 References (PS2) Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations: A Review and Computer Program. Controlled Clinical Trials 11:116-128, 1990 Dupont WD, Plummer WD, Jr: Power and Sample Size Calculations for Studies Involving Linear Regression. Controlled Clinical Trials 19:589-601, 1998 Schoenfeld DA, Richter JR: Nomograms for calculating the number of patients needed for a clinical trial with survival as an endpoint. Biometrics 38:163-170, 1982 Pearson ES, Hartley HO: Biometrika Tables for Statisticians Vol. I 3rd Ed. Cambridge: Cambridge University Press, 1970 Schlesselman JJ: Case-Control Studies: Design, Conduct, Analysis. New York: Oxford University Press, 1982 Casagrande JT, Pike MC, Smith PG: An improved approximate formula for calculating sample sizes for comparing two binomial distributions. Biometrics 34:483-486, 1978 Dupont WD: Power calculations for matched case-control studies. Biometrics 44:1157-1168, 1988 Fleiss JL. Statistical methods for rates and proportions. New York: John Wiley and Sons, 1981. 21
22. 22. © Dr Azmi Mohd Tamil, 2012 THANK YOU 22