I agree with Dr. Harrel. But I think an argument for adjustment could be made, in addition to the known gain in precision in the estimate of effect. Randomizing treatments is not a full proof method. Even if you randomize a million patients, there is no guarantee the potential outcomes will be the same in treated and “untreated”. It would be very unlikely if the potential outcomes are not very similar, but unlikely/rare things do happen. They are bound to happen due to the very nature of randomization. If we put aside issues of variable selection and how variables will be modelled, adjusting will provide evidence about the exchangeability of the treatment groups beyond the evidence provided in the traditional Table 1 comparing prognostic factors in treated and untreated. Even if each prognostic factor in Table 1 is balanced, this does no imply combinations of multiple prognostic factors are also balanced. In other words, prognostic factors and treatment may not be associated in a crude analysis (presented in Table 1), but may be associated in a multivariate analysis (never presented). To avoid conscious or unconscious manipulation of the analysis, we could decide on what variables we would adjust for pre-facto, as part of the study protocol. Actually, what we report in Table 1 is a list of the variables we believe we should adjust for. These variables could be selected using the same substantive-based approaches we use in observational studies. There doesn’t seem to be a methodological reason for adjusted effect estimates from RCT to be more biased than crude estimates (again, assuming modeling assumptions are correct). In most cases, particularly in mid-size and small trials, the validity of the estimate of the effect of the treatment will be enhanced, and credibility of the RCT findings would increase, if crude and adjusted estimates are consistent.
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