Power Analysis

Power analysis is in general not trivial. But, for the most part, while preparing a proposal, it is enough to know how to handle just a couple of paradigmatic situations a t-test to compare the level of a continuous variable in two groups, or a chi-squared test to compare the proportions of a categorical outcome (survival, incidence of a disease, etc.) in two groups. It is quite likely that there will be other factors to be taken into consideration; the final statistical analysis may be quite complex, requiring a statistician (!) to do an analysis of variance with multiple factors (continuous as well as categorical), or a multiple linear or logistic regression to account for other factors, or some other exotic analysis. However, the simplified approach here gives a very good approximation to the sample size needed and the power available.

For a particular study, power analysis can be approached in one of three ways:

1. If published data are available for the difference between two groups (or a treatment effect), the aim is to determine the number of subjects to be studied so that, if the groups differ by the published value, there will be stastistical significance most of the time (e.g., 80% of the time if power is 80%).

2. If it is possible to say what is the smallest difference (or treatment effect) of clinical interest (SDCI), the aim then is to determine the number of subjects to be studied so that there will be statistical significance if the true difference is at least SDCI. If the study is negative, one can conclude (with 80% confidence if the calculation is done at 80% power) that the difference (or treatment effect) if any is not of clinical interest. This approach can also be used for an equivalence study, where the sample size can be calculated for a difference below which two treatments can be considered equivalent.

3. If the number of subjects is fixed and known, as for instance in a retrospective study or in a time-bound prospective study, power analysis is used to determine the smallest difference (or treatment effect) for which the available number of subjects will lead (at the chosen power) to statistical significance.
Unpaired t-test (parallel arm or two groups)

Paired t-test (cross-over, each subject their own control)

Chi-square test (proportions in two groups)

With more than two groups, do the power analysis for the two groups with the smallest anticipated difference in outcome. With just one group (as when the outcome is being compared to a population norm), choose from the options under One Group.

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