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Title: Empirical likelihood inference to compare t-year absolute risks with right censored competing risks data Authors:  Paul Blanche - University of Copenhagen (Denmark) [presenting]
Abstract: The t-year absolute risk, also called the cumulative incidence function at time t, is an interesting quantity routinely estimated in the competing risks setting. It is often estimated with the non-parametric Aalen-Johansen estimator. This estimator handles right-censored data and has desirable large sample properties, as it is the non-Parametric maximum likelihood estimator (NPMLE). Inference for comparing of absolute risks, via risk difference or risk ratios, can therefore be done via usual asymptotic normal approximations and the use of the delta-method. However, the small sample performance of this approach can be modest. Especially (i) coverage of confidence intervals can be poor, and (ii) inference using risk ratios and risk difference can lead to inconsistent conclusions, in terms of significant differences. We, therefore, introduce an empirical likelihood ratio based inference as an alternative. One advantage is that it always leads to consistent conclusions when comparing absolute risks via either risk ratios or risk differences, in terms of significance. Simulation results also suggest that small sample inference using this approach can be more accurate. We present how to compute the new confidence intervals and p-values. Novel technical results include formulas and algorithms to compute constrained NPMLE, from which likelihood ratios and inference procedures are derived. Examples using medical data are provided.