Introduction
Sample size calculation is an integral part in the inferential statistics, in which we are estimating a population parameter (our interest) from a sample statistic (data available to us). We carry out experiment on a finite numbered sample and calculate a summary measure out of it (sample statistic, lets say, sample mean) with an intent to estimate the unknown population parameter (population mean).
The basic premise of statistical estimation is that as the sample size increases, the sample statistic will be reflecting the population parameter more accurately (its variation will be less around the population parameter). So, sample size may be titrated to achieve the required accuracy in estimation.
The software, PS, whose link is given below will help us in standardising calculation of sample size for our research works.
The software
The intended software is PS - Power and Sample Size Program, a freely downloadable
and distributable software for Windows user made by the Biostatistics Department of
Vanderbilt University. The software is downloadable from http://biostat.mc.vanderbilt.edu/wiki/Main/PowerSampleSize
as pssetup3.exe file.
The study designs for which the software can be used
Case control studies: Corrected and uncorrected chi squared contingency table tests and Fisher’s exact test. The alternative hypotheses may be specified in terms of odds ratio or exposure prevalence rates.
Matched case control studies: McNemar test. The alternative hypothesis may be specified in terms of odds ratio.
Multiple 2x2 tables: Mantel Haenszel test. Assume that each 2x2 table consists of cases and controls selected from a different stratum that is defined by one or more confounding variables. The odds ratio of disease in the the exposed and subjects compared to unexposed subjects is assumed to be equal within all the strata. The alternative hypothesis is specified in terms of this odds ratio.
Cohort studies with Dichotomous Outcomes: Independent contingency table tests, McNemar’s test. The alternative hypotheses may be specified in terms of relative risks or outcome probabilities.
Linear regression (1 treatment): Testing the slope of a simple linear regression line. The investigator wishes to detect a regression slope a given magnitude. The values of the independent variable may either be specified by the investigator or determined observationally when the study is performed. In the later case, the investigator must estimate the standard deviation of the independent variable(s).
Linear regression (2 treatments): Comparing the slopes and intercepts of two linear regression lines. The investigator wishes to determine whether the difference in slopes and intercepts is of a given magnitude. The values of the independent variables may either be specified by the investigator or determined observationally when the study is performed. In the later case, the investigator must estimate the standard deviations of the independent variables.
Survival studies: Evaluating independent cohorts using log rank test. The ratio of number of controls per experimental subject may be specified by the investigator. The alternative hypothesis may be specified in terms of hazard ratio of control subjects relative to experimental subject or median survival times for the control and experimental subjects.
Continuous response measures in two groups: Paired and independent t tests. The ratio of number of control subjects per experimental subject may be specified by the user.
How to cite the software
Dupont WD, Plummer WD: ‘Power and Sample Size Calculations: A Review and Computer Program’, Controlled Clinical Trials 1990; 11: 116-28
or
Dupont WD, Plummer WD: ‘Power and Sample Size Calculations for studies involving Linear Regression:‘, Controlled Clinical Trials 1998; 19: 589-601