The Causal Inference Models For The Survival Studies Under A Randomized And Broken Randomized Clinical Trials

Survival analysis is a major area of interest in clinical trials and biomedical researches.Survival data systematically arise when the duration from a defined to kkkkk time of origin until the occurrence of an event.In this research,the broad aim was to investigate the causal effect of active treatment on survival outcomes under randomized and broken randomized clinical trials.The theory of causal inference provides a useful account of how to measure the pragmatic effect of a certain action on the outcome of interest.Due to their flexibility in specifying the effect of covariates on survival times,linear transformation models have been paid increasing attention to overwhelming some practical problems.Typically,this research motivated on some contextual problems in estimating the causal effect of active treatment on survival outcome.In its nature survival outcome is a victim of many irregularities,namely,censoring,truncation,missing covariates,and time-varying covariates.These problems have great roles in estimating the causal effect and require high attention to managing.In the lack of careful management,they led to obtaining a biased estimate of the causal effect.On top of these,the presence of noncompliance(all-or-nothing and partial compliance)that raised due to postrandomization are other vital problems in estimating the causal effect.In this research,these problems have been seen carefully and are managed coherently step by step.Therefore,to investigate the treatment effect on left-truncated and right censored survival outcome given possibly time-varying covariates,a causal effect based on the semi-parametric transformation model was proposed.The role of semi-parametric transformation models in survival analysis has been taken as a central concern by several authors.Similar to that,in this research,the proposed method is expected to estimate the causal effect of treatment on survival time of interest.To estimate the consistent estimators of unknown parameters and unspecified transformation function,the modified estimating equations were adopted.An Estimating equation technique is an alternative method of the widely used maximum likelihood methods,which enables us to ease some complexity due to the complex characteristics of time-varying covariates.In the situation,when both the time-varying covariates and left-truncation are considered in the model,the maximum likelihood estimation procedures become much more burdensome and complex.To ease the complexity,the modified estimating equations that have been given high attention in many types of research was proposed under the semi-parametric transformation model.To tackle the problems of missing covariate and randomization bias,the research adopted the propensity and linearized propensity score balanced inverse probability weighted estimating equation techniques.The weighted estimating equations and propensity score methods provide a plausible role in estimating a causal effect of entire treatment on the survival outcome.An elegant notion in this was implementing the modified weighted estimating equations for semi-parametric transformation models to estimate the causal effect of treatment on survival outcome.The novel idea of this was to overwhelm the problem of missing covariates in estimating the causal effect for survival outcome.The proposed method is expected to contribute a tremendous role in academics,in terms of restoring randomization bias.The randomization bias was restored by using propensity score and linearized propensity score.The proposed weighted estimating equations were adjusted for propensity and linearized propensity scores.The inverse probability weighted estimators have been derived after the bias adjustment through the linearized propensity score.Under missing at random,the non-missingness probability was estimated nonparametrically by kernel smoothing technique.On top of the mentioned problems,the unexpected noncompliance to treatment assignment is more likely to intricate the inference of causal effect in clinical trials.In the presence of all-or-nothing compliance,the causal inference adopted for the right-censored survival outcome conditional to covariates and latent compliance type comprises three estimands.Depending on the distributions the theories for the three estimands,namely,the complier average causal effect(CACE),the complier effect beyond time t(CESP(t)),and the complier quantile causal effect(CQCE)were technically obtained.To obtain the estimates for unknown parameters,the maximum likelihood function with the mixture structure of the problems was constructed under the principal stratification framework.However,modeling the partial compliance,with the usual principal stratification framework is really tricking.Because the continuous nature of the strata raises subtle specification issues.Consequently,an application of principal stratification to model partial compliance needs a strong assumption for identifiability to estimate the treatment efficacy.In this research,the homogeneous semi-Markov model was adopted as a framework illustration.The transition probabilities are considered under the homogeneous semi-Markov model for the continuous duration of the transition.The framework of Markov model was adopted under the semi-parametric transformation models for survival data.The maximum likelihood constructed for all-or-nothing compliance was extended to the Markov model by incorporatingthe transition probabilities of an exponential distribution.The three unconditional estimands and their corresponding conditional estimands can be estimated in a similar fashion by extending the model to the homogeneous semi-Markov model framework.To sum up,the characteristics of estimators,in the finite sample performance of the proposed model were illustrated by simulation studies.Besides,the Stanford heart transplant and MCPBC real data application were well fitted for the semi-parametric transformation models of left-truncated and right censored survival data with a time-varying covariate.However,the only simulation studies carried out to test the performance of semi-parametric transformation models for causal inference of survival outcome with missing covariates.In contrast,in the presence of all-or-nothing and partial compliance,neither practical applications were adopted.To this end,the effect of treatment on survival time was adjusted for biases raised due to left-truncation in treatment and possibly time-varying covariates.The bias in covariates was restored,by estimating density function for left-truncation.The left-truncation variable was also incorporated in the model as a covariate,to relax the independence assumption of failure time and truncation time.Moreover,the expectation-maximization(EM)algorithm was employed for the estimation of iterative unknown parameters and unspecified transformation function.In addition,the randomization bias was adjusted by estimating the propensity and linearized propensity score.After adjusting for bias raised in the model due to the randomization bias and missing covariates,the causal effect was derived by a ratio of cumulative hazard functions of active and passive experiments.