Tobit regression for modeling mean survival time using data subject to multiple sources of censoring

Abstract

Mean survival time is often of inherent interest in medical and epidemiologic studies. In the presence of censoring and when covariate effects are of interest, Cox regression is the strong default, but mostly due to convenience and familiarity. When survival times are uncensored, covariate effects can be estimated as differences in mean survival through linear regression. Tobit regression can validly be performed through maximum likelihood when the censoring times are fixed (ie, known for each subject, even in cases where the outcome is observed). However, Tobit regression is generally inapplicable when the response is subject to random right censoring. We propose Tobit regression methods based on weighted maximum likelihood which are applicable to survival times subject to both fixed and random censoring times. Under the proposed approach, known right censoring is handled naturally through the Tobit model, with inverse probability of censoring weighting used to overcome random censoring. Essentially, the re-weighting data are intended to represent those that would have been observed in the absence of random censoring. We develop methods for estimating the Tobit regression parameter, then the population mean survival time. A closed form large-sample variance estimator is proposed for the regression parameter estimator, with a semiparametric bootstrap standard error estimator derived for the population mean. The proposed methods are easily implementable using standard software. Finite-sample properties are assessed through simulation. The methods are applied to a large cohort of patients wait-listed for kidney transplantation.

Co-Occurrence of Metal Contaminants in United States Public Water Systems in 2013–2015

“…Tobit regression models account for censored data [18][19][20][21] and mixed-effect Tobit models further account for clustering of observations in a dataset [21]. Mixed-effect Tobit regression models of the log-transformed contaminants, left-censored at the logtransformed MRL, with normally distributed random intercepts for public water system and state, but no fixed effects, were used to predict the mean log-concentrations of each contaminant for each public water system.…”

Comparison of parametric and semi-parametric models with randomly right-censored data by weighted estimators: Two applications in colon cancer and hepatocellular carcinoma datasets

“…Within this context, the IPCW-Tobit introduced by Gong and Schaubel 20 can be considered. Gong and Schaubel 20 used D i for the death time.…”

“…Within this context, the IPCW-Tobit introduced by Gong and Schaubel 20 can be considered. Gong and Schaubel 20 used D i for the death time. 0.25em D i denotes for two types of right censoring ( C i fand C i represent the known-fixed right censoring time and the random right censoring time, respectively).…”

“…In recent years, some studies have adapted estimators and models for censored data analysis to new disciplines. As an innovative example, Gong and Schaubel 20 have proposed a Tobit regression based on the weighted maximum likelihood for survival times subject to random and fixed censoring times. Gong and Schaubel 20 used the inverse probability of censoring weighting (IPCW) procedure to overcome random censoring.…”

“…As an innovative example, Gong and Schaubel 20 have proposed a Tobit regression based on the weighted maximum likelihood for survival times subject to random and fixed censoring times. Gong and Schaubel 20 used the inverse probability of censoring weighting (IPCW) procedure to overcome random censoring. It is crucial that the classical Tobit model, which is frequently used in econometrics in cases of fixed censorship, becomes available in cases of random censorship with the help of IPCW.…”