The impact of randomization on the analysis of clinical trials

The design of a comparative clinical trial involves a method of allocating treatments to patients. Usually, this assignment is performed to achieve several objectives: to minimize selection and accidental bias, to achieve balanced treatment assignment in order to maximize the power of the comparison, and most importantly, to obtain the basis for a valid statistical inference. In this paper, we are concerned exclusively with the last point. In our investigation, we will assume that measurements can be decomposed in a patient-specific effect, a treatment effect, and a measurement error. If the patient can be considered to be randomly drawn from a population, the randomization method does not affect the analysis. In fact, under this so-called population model, randomization would be unnecessary to obtain a valid inference. However, when individuals cannot be considered randomly selected, the patient effects may become fixed but unknown constants. In this case, randomization is necessary to obtain valid statistical analyses, and it cannot be precluded that the randomization method has an impact on the results. This paper elaborates that the impact can be substantial even for a two-sample comparison when a standard t-test is used for data analysis. We provide some theoretical results as well as simulations.