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- 1. Sample Size Calculation Dr P Raghavendra 2nd Year Post-Graduate Dept of Community Medicine, Siddhartha Medical College, Vijayawada
- 2. What is Sampling?• A sample is a part of the population under study.• In most situations, it might not be possible to study an entire population.• We typically draw a subset of people drawn from a larger population and then use inferential statistics to make an inference from the sample and apply it to the whole population.
- 3. What is sampling?• We try to study the characters of the population by measuring them from a smaller number of subjects.• Sample is expected to be the MIRROR of the population.• Cook sees only a handful of rice to check if it is cooked or not.
- 4. Attributes of a good sampleTo extrapolate the inference of the sample to the population, the sample should be:• A representative of the population.• Should be large enough.
- 5. If sample is too large…Good precisionLess errorsLess biasBut, Wastage of time, money and resources Resources could be as well be deviated to other projects. Not cost-effective
- 6. If sample is too small… Inaccurate results. More source of bias. Power of the study comes down. Study fails to give meaningful information. Waste of resources on a inaccurate study. Ethical issues about recruiting patients into a meaningless study.
- 7. The usual QuestionHow big asample is a good
- 8. How big should a sample be?• Formulae are present.• The forthcoming formulae are tailor-made for a power of 80% and a Confidence Interval of 95%. (Acceptable levels)• Power of the study is the ability to detect the true significance.• 95% CI means 5% of erroneous significance.
- 9. Types of studies• Based on what we are measuring, there are 4 types of studies: 1. Calculating the proportion Qualitative 2. Calculating the difference of proportions 3. Calculating the mean Quantitative 4.Calculating the difference in means
- 10. Qualitative v/s Quantitative• Qualitative are those which can be answered as YES or NO, Male or Female, etc.• We can only measure their numbers, eg: Number of males, Number of MDR-TB cases among TB patients, etc.• A set of qualitative data can be expressed as proportions. Eg: Prevalence, success rate.
- 11. Qualitative v/s Quantitative• Quantitative are those which can be measured in numbers, like Blood pressure, Age, etc.• A set of quantitative date can be expressed in mean and its standard deviation.• Mean is the average of all variables in the data.• Standard deviation is a measure of the distribution of variables around the mean.
- 12. 1. Calculating Proportion• This is used in cases where we are trying to find proportions.• Eg: for studies like:- – Estimation of prevalence of tuberculosis in Vijayawada city in 2012. – Prevalence of malignant hyperthermia as a complication of enflurane administration.
- 13. 1. Calculating Proportion N= 4PQ/d 2Where,• P = Prevalence (from previous studies)• Q = 100 – P• d = allowable error (5-20% of P)
- 14. Exercise - 1• Calculate the sample size required to find out the proportion of children receiving BCG vaccination if the BCG coverage of that area in previous studies was 80%.• Sol: P = 80; Q = 100-P = 20; d= 20% 0f P = 16. N= 4PQ/d2 = 4x80x20 16x16 = 25
- 15. 2. Calculating Difference in proportion• This is used when we measure the significance of difference between two proportions.• Eg: For studies like:- – Diagnostic supremacy of CT Chest v/s X-ray chest in pulmonary tuberculosis. – Success rate of Streptomycin v/s Kanamycin in cure of MDR-TB
- 16. 2. Calculating Difference in proportion N= 15.7 x x Q (P1-P2 )2Where,• P1 and P2 are the proportions of the 2 groups• is the average of P1 and P2• Q is 100 -
- 17. Exercise - 2• A new treatment regimen for Tuberculosis was planned. The success rates of DOTS was 75%. The success rate of the new treatment in a pilot study was 85%. Calculate the sample size for a study to compare the success rates of the two regimen. Hint: N= 15.7 x x Q (P1-P2 )2
- 18. Solution to exercise - 2Here, P1 = 75; P2 = 85%; = 80 Q = 100 - = 20; P1-P2 = 10Hence N = (15.7 x 80 x 20) / (10 x 10) = 251
- 19. 3. Calculating the mean• This formula is used in quantitative studies where we are estimating the mean of the study group.• Eg: For studies like:- – Estimation of mean age at diagnosis of tuberculosis in Vijayawada city – Bacteriological index at the initiation of DOTS in TB patients attending DOTS centre of GGH, Vijayawada – Mean time of onset of action of Sevoflurane
- 20. 3. Calculating the mean N= 4 2/d2Where,• (Sigma) is the Standard deviation as in similar studies done previously• d = allowable error (5-20% of )
- 21. Exercise - 3• We are planning to do a study regarding Age of onset of smoking practice among youth in rural Vijayawada. A previous such study done in Andhra Pradesh gave a mean age at onset as 25 years with a standard deviation of 10 years. Calculate the sample size required to do the planned study. Hint: N= 4 2/d2
- 22. Solution to exercise - 3Here, = 10.So, d = 20% of = 2.Hence, N = (4 x 10x10) / (2 x 2) = 100
- 23. 4. Calculating Difference in Means• This is used in studies where we are calculating the difference achieved quantitatively during the study.• Eg: For studies like:- – Average weight gain in patients of tuberculosis before and after DOTS. – Mean fall in Blood pressure due to propofol infusion.
- 24. 4. Calculating Difference in Means N = 15.7 ( x 2 1 2)/d Where,• 1 and 2 are the standard deviations of the 2 study groups,• d is the smallest meaningful difference that can be measured.In before-after type of studies, 1 = 2 =
- 25. Exercise - 4• Determine the sample size required to detect an increase of 10 cells/cu.mm in CD4 counts of HIV patients those receiving HAART, assuming the standard deviation of CD4 counts to be 70 cells/cu.mm. Hint: N = 15.7 ( 1x 2)/d2
- 26. Solution to exercise - 4Here, 1 = 2 = 70, d = 10N = (15.7 x 70 x 70) / (10 x 10) = 769
- 27. Frequently asked questions• Where can we get the values of or P?
- 28. Frequently asked questions• When already we know the P, why should we do the study again?
- 29. Frequently asked questions• How big should be the sample of a pilot study?
- 30. Frequently asked questions• What should we do if we are not getting enough cases or if the sample size is bigger than the total number of cases?
- 31. Any Questions or Doubts??

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