I am a clinician like Erin. I think that there are two issues here:
- Statisticians minimising the size of a random sample from a data set required to detect a specified P value with specified null hypothesis and a specified power indicating a high probability of a ‘real effect’.
- Clinicians interpreting the above information to arrive at clinical decisions (ideally in conjunction with a patient).
Statistical considerations
If the predictor variable (e.g., age) and outcome variable (e.g. BMI) are both numerical, it seems to me that the optimum P value would be arrived at by calculating a correlation coefficient and a P value based on a t-test. I did this and got a P value of 0.000000008. I then divided the (predictor) ages into two groups, up to 40 years and over 40 years (thus losing the details of actual age). A t-test of the differences in the outcome of numerical BMI in both groups gave a P-value of 0.0000004. I then divided the outcome variable into BMIs of up to 25 and over 25 and got a P value of 0.00001. So, as expected intuitively, the P value is lowest when both the predictor and outcome variables are numerical and highest when both are dichotomised and obscuring the data. The corollary to this is that the sample size will be smallest when both predictor and outcome variables are numerical and highest when they are both dichotomised.
Clinical decisions
In order to make any decision there is usually a trigger. One of these triggers is the action that leads to the greatest expected utility (i.e. the best calculated bet). The clinician must therefore consider the options addressed by a RCT and results arising from it. By making various assumptions, by applying various reasoning processes, guesswork or calculations (ideally in conjunction with the patient), a decision is made. If the RCT outcome are probability densities in the form of distributions of some surrogate outcome on treatment and control (e.g. a highly statistically significant change in the BMI due to a new weight reducing drug), then its application can be difficult. I gave an outline of such a complex rationale required in a previous post (https://discourse.datamethods.org/t/some-thoughts-on-uniform-prior-probabilities-when-estimating-p-values-and-confidence-intervals/7508/45?u=huwllewelyn ).
I have painful memories of a long discussion about fixed responders and fixed non-responders in regard to counterfactuals when they were classified into 4 groups of always recover responders, never recover responders, always benefit responders and always harm responders, without recognising that for stochastic reasons, individuals tend to move from one group to another in different studies (https://discourse.datamethods.org/t/individual-response/5191/226?u=huwllewelyn ). For this reason, I would agree that the term ‘responder’ should be avoided!