We propose a novel kernel estimator of the baseline function in a general highdimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a LASSO procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Br...

The Cox (1972) regression model is extended to include discrete and mixed continuous/discrete failure time data by retaining the multiplicative hazard rate form of the absolutely continuous model. Application of martingale arguments to the regression parameter estimating function show the Breslow(1974) estimator to be consistent and asymptotically Gaussian under this model. A computationally co...

In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional odds parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data is available for all time on all cohort members, even when the covariates are time dependen...

In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data is available for all time on all cohort members, even when the covariates are time dependent. Wh...

Cox (1972) proposed the partial likelihood technique to estimate the risk coefficients of proportional hazards regression model without specify the baseline hazards function. Once the risk coefficients β are estimated, we may interest in estimating the corresponding baseline survival function. Therefore, Breslow (1972) and Kalbfleisch & Prentice (1973) provided two different procedures as the b...

In meta-analysis of odds ratios (ORs), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative REM for ORs uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intra-class correlation (ICC) parameter. This model naturally arises when the probabilities of an event in on...

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King, a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, λ(t|x) = exp{ψ(x)}λ(0)(t). The estimator, ψ̂(x), reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consi...

Most survival analysis textbooks explain how the hazard ratio parameters in Cox's life table regression model are estimated. Fewer explain how the components of the nonparametric baseline survivor function are derived. Those that do often relegate the explanation to an "advanced" section and merely present the components as algebraic or iterative solutions to estimating equations. None comment ...