![]() ![]() This is especially true of clinical trialists believing in a new therapy who wished and hoped for a favorable outcome (rejecting the null hypothesis). When the conclusion of an observational study or clinical trial is negative, namely, the data observed (or more extreme data) fail to reject the null hypothesis, people often argue for calculating the observed statistical power. The most egregious example is post hoc power calculations. The authour discusses how we sometimes misuse statistical analyses after a study is completed and analyzed to explain the results. The extra increase in power from increasing the case:control ratio falls dramatically once the ratio goes beyond 1:4, so there is little extra gain in power from recruiting more than 4 controls to one case.We are pleased to add this typescript, Inappropriate use of statistical power by Raphael Fraser to the BONE MARROW TRANSPLANTATION Statistics Series. While this is also dependent the parameters that go into a power calculation, in particular the effect size and sample size of the case group, there is a useful rule of thumb that is worth remembering. Directly following on from the previous paragraph, we can also work out the extra increase in power from increasing the ratio of controls to cases in a case control study. The behaviour of this is complex as it depends on the size of the smaller group and the SD.Īs mentioned above, in a case-control study it is often easier to recruit more controls since we often use the case-control design to study rare outcomes. ![]() So there is a limit to how much power we can get by recruiting more controls. ![]() However if we had 25 mums in the intervention group then even if we were able to recruit over 25000 controls, we would still not achieve the same power as the 1:1 study of 100 patients. You can see that if we had 33 mums in the intervention group, then we need 106 mums in the control group to get 88% power. The last row column shows the number of controls needed to achieve the same power as that for the 1:1 ratio in the study of 100 mums (0.88). N of controls needed to get the same power as a 1:1 ratioĪnother learning point about power comes from table 1. So we get maximum power for a given Total sample size when the groups are of equal size. The power reduces as the group sizes become more and more unequal. The study has an 87% chance of detecting a true difference in birth weight of 250g. Table 1 below shows that if the groups are of equal size (a 1:1 ratio), then the power is 0.87. We assume the population SD in each group is 400g and the total sample size is 100. One group of mothers received an intensive education and consultation programme to help them eat and exercise healthily during pregnancy. To illustrate the effect of unequal groups on power, let’s suppose we want to detect a difference of 250g in birth weight between two groups of babies born to overweight mums. There are many reasons why we might have unequal size groups. For example, in an observational study, this might just reflect the proportion of people exposed and not exposed to the factor of interest in a case-control study, the outcome may be rare and so we choose to sample more controls to increase study power as they are easier and less costly to recruit in a randomised controlled trial, the treatment may be expensive and so is only given to a smaller proportion of patients. In such settings we need a bigger TOTAL sample size to get the SAME statistical power for a given effect size (δ) and level of significance (α). In many scenarios the ratio of participants in the control to treatment group, or in the exposed to not exposed group, is unequal. This information was omitted from the video and so is included here as text. ![]() Some notes on the behaviour of sample size calculations and power for unequal group sizes ![]()
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