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Abstract
The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.
Highlights
In many experimental and observational studies such as randomized clinical trials, agricultural experiments, and engineering and industrial production commonly we obtain time-to-end outcomes so-called survival time or failure time
To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models
The semiparametric transformation models which have been attracted by several authors have been an important concept in the study of right censored survival time
Summary
In many experimental and observational studies such as randomized clinical trials, agricultural experiments, and engineering and industrial production commonly we obtain time-to-end outcomes so-called survival time or failure time. Censoring is the problem of not finding the exact time of an event during the experimental or observational studies, which makes the analysis much more complex. The semiparametric transformation models which have been attracted by several authors have been an important concept in the study of right censored survival time. The another important concept in analysing survival data is proportionality assumption. Because the effect of covariate may vary over time breaking the proportionality assumption for Cox proportional hazards model of [2]. In this situation, we need to consider the time-varying coefficient to our model.
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