Estimating the cumulative mean function for history process with time‐dependent covariates and censoring mechanism

Abstract

In this paper, an approach to estimating the cumulative mean function for history process with time dependent covariates and right censored time-to-event variable is developed using the combined technique of joint modeling and inverse probability weighting method. The consistency of proposed estimator is derived. Theoretical analysis and simulation studies indicate that the estimator given in this paper is quite recommendable to practical applications because of its simplicity and accuracy. A real data set from a multicenter automatic defibrillator implantation trial is used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

Estimating the quantile medical cost under time-dependent covariates and right censored time-to-event variable based on a state process

“…Note that, according to the law of large number, we can obtain the following form as n→∞, which is similar as that in Deng. 7 Therefore, K∼(t(k)) can be regarded as an estimator of survival function K ( t ). Replacing K∧(t(k))=K∧1(t(k))K∧2(t(k)) in equation (6) by K∼(t(k)) from equation (7), an alternative estimator of Hτ(t) has the form …”

“…The terminal time T is generated from a lifetime variable with the hazard function where the definition of w and α can be found in Deng. 7 Considering an AR(1) structure of ετ(t), let the variance–covariate matrix of ετ(t) be as the following expression where ρ=0.2 generates error with low correlation, ρ=0.5 with medium correlation and ρ=0.8 with high correlation, respectively.…”

“…Thus, in the light of model 15, steps (1) to (4) for generating the process are also similar as that in scenario 2 of Deng. 7 Here, in step (3), we obtain that …”

“…For example, the estimation of medical costs and quality-adjusted survival function have been studied in literature. 2–6 Recently, Deng 7 studies the cumulative mean function (CMF) for history process with time-dependent covariates and censoring mechanism using the joint modelling method.…”

“…The traditional Cox proportional hazards model and the accelerated failure time (AFT) model have adopted the quantile methods. The research efforts have been devoted to developing quantile regression methods to handle time-to-event data with known censoring time, such as Powell, 17 Fitzenberger, 18 Buchinsky and Hahn, 19 or random censoring, 7,20,21 among others. At the same time, for the linear model, the censored QR was first studied by Powell 22 for the case of fixed censoring that assumes known censoring time for all observations.…”