Continuing on the topic of clinical trials I am going to give a quick blog explaining what power is and why we care about it in the context of clinical trials.
When we do a hypothesis test in clinical trials, most of the time we have 2 hypotheses. The first (null hypothesis \( H_0 \) ) is that the new treatment has equal effect on patient’s improvement to the current treatment or the placebo (depending on if we are doing an active or placebo clinical trial). The second (alternative hypothesis \( H_A \) ) is that the new treatment has a different effect on the amount patients’ improve compared to the current treatment or the placebo.
The power of a test is the probability that we reject \( H_0 \) when it is false, Bowers (2002). Which means we conclude that the new treatment is better or worse than the current treatment or placebo when this is true.
In a clinical trial we want to have a high power, as we only want to be able to bring a new treatment to market if we are sure that it is going to give patients an improvement compared to treatment already available. Both the \( H_0 \) and \( H_A \) have a distribution, such as standard Gaussian, Student’s t and chi-squared, which depend on the independence beliefs as discussed in Hanin (2017) .
As you can see in the diagram as we are to increase the sample size this results in an increase in power. This is why power is one of the key factors when calculating sample size. Therefore overall we have seen that power is very important and is used in the calculation of sample size needed for a clinical trial. Further reading on power in clinical trials can be found in Healy (1988), Miller & Homan (1988) and Azriel & Feigin (2014).
For further blogs in the field of medical statistics please read Multi-Arm Multi-Stage Trials and Clinical Trial Design for Rare Diseases – Should we use Random design trials?
References:
- Bowers, D. (2002), Medical statistics from scratch
- Hanin, L. (2017), Why statistical inference from clinical trials is likely to generate false and irreproducible results. (Report)
- Healy, M. J. R. (1988), Determining Power In Clinical Trials
- Miller, D. K. and Homan, S. M. (1988), Determining power in clinical trials
- Azriel, D. and Feigin, P. D. (2014), Adaptive Designs to Maximize Power in Clinical Trials with Multiple Treatments
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