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

Abstract

Estimating the medical costs from disease diagnosis to a terminal event is of immense interest to researchers. However, most of existing literature on such research focused on the estimation of cumulative mean function (CMF) for history process. In this paper, the combined scheme of both inverse probability of censoring weighting (IPCW) technique and longitudinal quantile regression model is used to develop a novel procedure to the estimation of cumulative quantile function (CQF) based on history process with time-dependent covariates and right censored time-to-event variable. The consistency of proposed estimator is derived. The extensive simulation study is conducted to investigate the performance of the estimator given in this paper. A medical cost data from a multicenter automatic defibrillator implantation trial (MADIT) is analyzed to illustrate the application of developed method.

Adaptive aggregation for longitudinal quantile regression based on censored history process

“…We implement EAW estimator among Q (1) 𝜏 (y i (t)|x i (t)) and Q (2) 𝜏 (y i (t)|x i (t), u i ) in ( 16) with 50 independent splits (the smoothing parameters h=1 and a(h) = 0.01). Table 5 lists the estimated 5-year and total treatment period cumulative quantile costs under 𝜏 = 0.25, 0.5 and 0.75, and explains similar features with those in Liu et al 8 Note that the fitted residuals (marked by "Res" in Table 5) illustrate that additive quantile mixed effect model (AQMM) is more suitable as it contributes the between-subject variability by means of random effects, the change of cumulative costs is relatively flat among various quantile levels. On the other hand, EAW estimator based on either Liu et al or AQMM could maintain the optimistic result among different probability levels, while candidate models performs differently.…”

“…Without loss of generality, we assume that censoring time is independent of terminal time and the history process for each subject. In the light of Liu et al., 8 the τth quantile state function ( τ-QSF) of (4) at time t is defined as H τ false( t false) = Q τ false( y false( t false) | bold-italicx false( t false) , bold-italicz false( t false) , bold-italicu false). We combine the inverse probability of censoring weighting (IPCW) method with EAW estimator equation (6) to estimate τ-QSF that where K false^ false( t false) = K ^ 1 false( t false) K ^ 2 false( t false), K ^ l false( t false) false( l = 1 , 2 false) are corresponding Kaplan–Meier estimators of K 1 false( t false) and K 2 false( t false), respectively.…”

“…It is obviously shown that the estimation of ( 7) can be expressed by using (8). To be computational convenience for Ĥ𝜏 (t), we use a nonparametric approximation for…”

“…Aforementioned assumptions are widely considered in Zeng and Cai, 29 Deng, 27 and Liu et al, 8 which are essential to longitudinal time-to-event data with censoring mechanism. Condition (B.3) is typically recommended to respond the misspecification of q F,𝜏 (x(t)), and guarantees the convergency of candidate procedures as well.…”

“…To illustrate the practical superiority of the EAW estimation, we apply the methodology to analyze the MADIT data. The dataset has been studies by Deng 27 and Liu et al 8 Note that most of the statistical modeling and estimating are based on the particular specification, and have not explicated the outperformance of the fitted model or estimating methodologies.…”