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Regression Models
Published in Prabhanjan Narayanachar Tattar, H. J. Vaman, Survival Analysis, 2022
Prabhanjan Narayanachar Tattar, H. J. Vaman
When interpretable results are required, the Buckley-James estimator offers a rare approach in survival analysis in which we can directly call out the influence of the covariates on the failure times. With strong theoretical backing going for it, the Buckley-James estimator will often come handy. However, regression analysis is predominantly carried out in the area using the Cox relative risk model. It is sometimes popularly known as the Cox proportional hazards model. The proportional hazards model is a particular case of the relative risk model and we will take up the discussion and development in the next section.
Average Power in Non-Normal Settings
Published in Andrew P. Grieve, Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials, 2022
Suppose we have samples of survival times xi : i = 1, …. ., n and yj : j = 1, …. ., n from two exponential distributions with means μx and μy, respectively. Then standard properties of exponential distributions mean that the ratio of means is distributed as whereis the F-distribution with ν and ν0 degrees of freedom. Under a proportional hazards model, is the hazard ratio.
Real-World Data and Real-World Evidence
Published in Wei Zhang, Fangrong Yan, Feng Chen, Shein-Chung Chow, Advanced Statistics in Regulatory Critical Clinical Initiatives, 2022
Multivariate regression models are the most commonly used statistical analysis methods to adjust confounding factors in estimating the effects of treatment or exposure (table 5.1)60. The regression model is selected considering the forms of outcomes, exposure of interest, and study covariates. However, several important factors should be considered when applying these models: (i) the underlying assumptions of the model should be checked for the study data, for example, the proportional hazards assumption should be assessed for the Cox proportional hazards model. (ii) Whether important covariables are adjusted? (iii) The number of study subjects (and cases) is sufficient for model, typically the number of study subjects is at least 20 to 30 times the number of covariates, and the number of patients with an outcome event is recommended to be at least ten times the number of covariates. (iv) Whether aggregated covariates, such as propensity scores, are included when dealing with high-dimensional confounders? (v) Whether the non-linear form, such as polynomial, are taken into account for important covariates? (vi) Whether the interactions between different covariates are considered?
A risk set adjustment for proportional hazards modeling of combined cohort data
Published in Journal of Applied Statistics, 2022
Statistical procedures for modeling the relationship between failure time random variables and associated covariate data arising exclusively from either an incident or prevalent cohort have been thoroughly examined in the survival analysis literature. The proportional hazards model is a commonly used model which relates the conditional hazard function (conditional on the covariate values) to a product of the baseline hazard function (covariate independent) and a regression based covariate risk function [7]. By applying the mathematical tools from counting processes and martingale theory, the asymptotic properties for the estimators of the unknown parameters and baseline hazard function can be derived [2]. In a prevalent cohort study, as the observed failure/censoring are sampled biasedly, alternative estimation approaches must be used [11]. When the underlying onset process of the failure times is assumed to arise from a stationary Poisson process (which will be referred to as the ‘stationarity assumption’ throughout the text), we term the observed failure time data as being ‘length-biased’ [3]. To test the validity of the stationary Poisson process assumption, Addona et al. proposed various methods based on the observed failure/censoring time data [1].
Maximum likelihood estimation for the proportional odds model with mixed interval-censored failure time data
Published in Journal of Applied Statistics, 2021
Liang Zhu, Xingwei Tong, Dingjiao Cai, Yimei Li, Ryan Sun, Deo K. Srivastava, Melissa M. Hudson
Future research on this problem can go in several directions. First, note that for each subject, it was assumed that there exists two random observation time points. Such data are often referred to as Case-2 interval-censored data [19]. A more general situation corresponding to this is the so-called case-K interval-censored data, where there exists K observation points or a sequence of observation time points. It would be useful to generalize the proposed method to case-K interval-censored data. In addition, the focus of this paper is the proportional odds model. Sometimes neither the proportional odds model or the proportional hazards model fits the data well; thus, one may consider other models, such as the additive hazards model or linear transformation model. Model checking is another possible direction for future research.
Regression analysis of case-cohort studies in the presence of dependent interval censoring
Published in Journal of Applied Statistics, 2021
Mingyue Du, Qingning Zhou, Shishun Zhao, Jianguo Sun
It is well-known that although the proportional hazards model is one of the most commonly used models for regression analysis of failure time data, sometimes one may prefer a different model or a different model may fit the data or describe the problem of interest better (Kalbfleisch and Prentice [16]). For example, the additive hazards model is usually preferred if the excess risk is of interest and one may want to consider the linear transformation model if the model flexibility is more important. Some literature has been developed for these and other models for regression analysis of general interval-censored data or the analysis of case-cohort studies that yield right-censored data. However, there does not seem to exist an established estimation procedure for the problem discussed here under other models. In other words, it would be useful to generalize the proposed method to the situation under the additive hazards or linear transformation model.