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Abstract:
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We propose using the weighted likelihood method to fit the Cox-type regression model with a general form of relative risk for current status data when covariates are missing at random and the probability of missingness is either known or can be reasonably estimated from observed data. The considered model includes Cox proportional hazards model as a special example. Asymptotic properties of the proposed estimator are established, showing that the relative hazard parameter is estimable at the usual root-n rate and asymptotically normal, although the estimator of the infinite dimensional baseline cumulative hazard function converges at the cubic-root-n rate. Furthermore, when the estimated missing probability is used in the weight function, the proposed method can be more efficient. A case-cohort study from an HIV vaccine trial is used to demonstrate the proposed method.
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