Introduction to smlePH package

Introduction

smlePH is the R package to fit the proportional hazards model with a sieve-based maximum full likelihood approach.

Assume that there are n patients in a cohort. Denote T_i as the survival time and x_i as the p-dimensional covariates. We observe (Y_i = min (T_i, C_i), δ_i = I(T_i < C_i)) under the right-censoring, thus the effective sample consists of {Y_i = T_i ∧ C_i, δ_i = I(T_i < C_i), x_i}_i = 1ⁿ. Let β be the p-dimensional regression coefficient. We posit the PH model as follows where Λ(t|x_i) and Λ₀(t) are the conditional cumulative hazard function given x_i and the baseline cumulative hazard function, respectively.

Instead of using the partial likelihood approach (Cox, 1972), we utilize a full log-likelihood with respect to (β, Λ) to estimate ,

References