Inference for blocked randomization under a selection bias model

We provide an asymptotic test to analyze randomized clinical trials that may be subject to selection bias. For normally distributed responses, and under permuted block randomization, we derive a likelihood ratio test of the treatment effect under a selection bias model. A likelihood ratio test of the presence of selection bias arises from the same formulation. We prove that the test is asymptotically chi‐square on one degree of freedom. These results correlate well with the likelihood ratio test of Ivanova et al. (2005, Statistics in Medicine 24, 1537–1546) for binary responses, for which they established by simulation that the asymptotic distribution is chi‐square. Simulations also show that the test is robust to departures from normality and under another randomization procedure. We illustrate the test by reanalyzing a clinical trial on retinal detachment.