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Sample Size Calculation Dr P Raghavendra 2nd Year Post-Graduate Dept of Community Medicine, Siddhartha Medical College, Vijayawada
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.
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.
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.
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
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.
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.
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
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.
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.
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.
1. Calculating Proportion N= 4PQ/d 2Where,• P = Prevalence (from previous studies)• Q = 100 – P• d = allowable error (5-20% of P)
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
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
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 -
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
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
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
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 )
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
Solution to exercise - 3Here, = 10.So, d = 20% of = 2.Hence, N = (4 x 10x10) / (2 x 2) = 100
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.
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 =
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
Solution to exercise - 4Here, 1 = 2 = 70, d = 10N = (15.7 x 70 x 70) / (10 x 10) = 769
Frequently asked questions• Where can we get the values of or P?
Frequently asked questions• When already we know the P, why should we do the study again?
Frequently asked questions• How big should be the sample of a pilot study?
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?