Variable selection in proportional odds model with informatively interval-censored data

The proportional odds (PO) model is one of the most commonly used models for regression analysis of failure time data in survival analysis. It assumes that the odds of the failure is proportional to the baseline odds at any point in time given the covariate. The model focus on the situation that the ratio of the hazards converges to unity as time goes to infinity, while the proportional hazards (PH) model has a constant ratio of hazards over time. In the paper, we consider a general type of failure time data, case K interval-censored data, that include case I or case II interval-censored data as special cases. We propose a PO model-based unified penalized variable selection procedure that involves minimizing a negative sieve log-likelihood function plus a broken adaptive ridge penalty, with the initial values obtained from the ridge regression estimator. The proposed approach allows dependent censoring, which occurs quite often and could lead to biased or misleading estimates without considering it. We show that the proposed selection method has oracle properties and the estimator is semiparametrically efficient. The numerical studies suggest that the proposed approach works well for practical situations. In addition, the method is applied to an ADNI study that motivates this investigation.