This paper develops interval censoring likelihood methods in the context of parametric proportional hazard (PH) and non-PH regression models in the longitudinal study setting to reanalyze the medical research council's randomized controlled trial of teletherapy in age-related macular degeneration. We compare the performance of the interval censoring likelihood with proxy likelihoods that were used to analyze the original data. It is shown, analytically, that the use of such proxy likelihoods in selected PH models leads to biased estimators. Such estimators are artificially precise; further, the magnitude of their percentage bias is quantified in a data-directed simulation study. For non-PH models, we demonstrate that these results obtained from PH models do not hold uniformly and explain the implications of this finding for the reanalysis of proxy likelihood trial data. Our final analysis, of the age-related macular degeneration trial data, based on fitting PH and non-PH models, reassuringly confirms the published findings from the original trial.
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