Penalized likelihood hazard estimation: Efficient approximation and Bayesian confidence intervals

Penalized likelihood method can be used for hazard estimation with lifetime data that are right-censored, left-truncated, and possibly with covariates. In this article, we are concerned with more scalable computation of the method and with the derivation and assessment of certain interval estimates. The asymptotic convergence rates are preserved when the estimation is restricted to certain q-dimensional spaces with q increasing at a much slower rate than the sample size n, and simulation studies are performed to determine default values of q for practical use; the computation cost is of the order O(nq2). Through a quadratic approximation of the log likelihood, approximate Bayesian confidence intervals can be derived for log hazard, and empirical studies are conducted to assess their properties. The techniques are implemented in open-source R code and real-data example is presented to illustrate the applications of the techniques through the use of the software.