scholarly journals A proportional hazards model for time-to-event data with epidemiological bias

2016 ◽  
Vol 152 ◽  
pp. 224-236
Author(s):  
Qiaozhen Zhang ◽  
Hongsheng Dai ◽  
Bo Fu
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Event Data ◽  
Time To Event ◽  
Time To Event Data ◽  
Hazards Model

scholarly journals An Updated Algorithm for Moderate Censoring in Time-to-Event Data Using Rank-based Regression

2019 ◽  
pp. 1-18
Author(s):  
Milind A. Phadnis
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Failure Time ◽  
Real Life ◽  
Dispersion Function ◽  
Event Data ◽  
Time To Event ◽  
Karnofsky Score ◽  
Time To Event Data

Aim: To propose an updated algorithm with an extra step added to the Newton-type algorithm used in robust rank based non-parametric regression for minimizing the dispersion function associated with Wilcoxon scores in order to account for the effect of covariates. Methodology: The proposed accelerated failure time approach is aimed at incorporating right random censoring in survival data sets for low to moderate levels of censoring. The existing Newton algorithm is modified to account for the effect of one or more covariates. This is done by first applying Mantel scores to residuals obtained from a regression model, and second by minimizing the dispersion function of these scored residuals. Diagnostic check of the model fit is performed by observing the distribution of the residuals and suitable Bent scores are considered in the case of skewed residuals. To demonstrate the efficacy of this method, a simulation study is conducted to compare the power of this method under three different scenarios: non-proportional hazard, proportional and constant hazard, and proportional but non-constant hazard. Results: In most situations, this method yielded reasonable estimates of power for detecting an association of the covariate with the response as compared to popular parametric and semi-parametric approaches. The estimates of the regression coefficient obtained from this method were evaluated and were found to have low bias, low mean square error, and adequate coverage. In a real-life example pertaining to pancreatic cancer study, the proposed method performed admirably well and provided a more realistic interpretation about the effect of covariates (age and Karnofsky score) compared to a standard parametric (lognormal) model. Conclusion: In situations where there is no clear best parametric fit for time-to-event data with moderate level of censoring, the proposed method provides a robust alternative to obtain regression coefficients (both adjusted and unadjusted) with a performance comparable to that of a proportional hazards model.

scholarly journals A tutorial on frailty models

2020 ◽  
Vol 29 (11) ◽  
pp. 3424-3454 ◽  
Author(s):  
Theodor A Balan ◽  
Hein Putter
Keyword(s):  
Random Effects ◽  
Recurrent Events ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Unobserved Heterogeneity ◽  
Frailty Models ◽  
Survival Outcomes ◽  
Time To Event ◽  
Homogeneous Population ◽  
Hazards Model

The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.

Group sequential monitoring based on the maximum of weighted log-rank statistics with the Fleming–Harrington class of weights in oncology clinical trials

2020 ◽  
Vol 29 (12) ◽  
pp. 3525-3532
Author(s):  
Thomas J Prior
Keyword(s):  
Clinical Trials ◽  
Treatment Effect ◽  
Proportional Hazards ◽  
Rank Test ◽  
Event Data ◽  
Time To Event ◽  
Survival Curves ◽  
Delayed Treatment ◽  
Time To Event Data ◽  
Log Rank Test

Clinical trials in oncology often involve the statistical analysis of time-to-event data such as progression-free survival or overall survival to determine the benefit of a treatment or therapy. The log-rank test is commonly used to compare time-to-event data from two groups. The log-rank test is especially powerful when the two groups have proportional hazards. However, survival curves encountered in oncology studies that differ from one another do not always differ by having proportional hazards; in such instances, the log-rank test loses power, and the survival curves are said to have “non-proportional hazards”. This non-proportional hazards situation occurs for immunotherapies in oncology; immunotherapies often have a delayed treatment effect when compared to chemotherapy or radiation therapy. To correctly identify and deliver efficacious treatments to patients, it is important in oncology studies to have available a statistical test that can detect the difference in survival curves even in a non-proportional hazards situation such as one caused by delayed treatment effect. An attempt to address this need was the “max-combo” test, which was originally described only for a single analysis timepoint; this article generalizes that test to preserve type I error when there are one or more interim analyses, enabling efficacious treatments to be identified and made available to patients more rapidly.

A censored quantile regression approach for the analysis of time to event data

2016 ◽  
Vol 27 (3) ◽  
pp. 955-965 ◽  
Author(s):  
Xiaonan Xue ◽  
Xianhong Xie ◽  
Howard D Strickler
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Time To Event ◽  
Censored Quantile Regression ◽  
Quantile Regression Model ◽  
Hazards Model

The commonly used statistical model for studying time to event data, the Cox proportional hazards model, is limited by the assumption of a constant hazard ratio over time (i.e., proportionality), and the fact that it models the hazard rate rather than the survival time directly. The censored quantile regression model, defined on the quantiles of time to event, provides an alternative that is more flexible and interpretable. However, the censored quantile regression model has not been widely adopted in clinical research, due to the complexity involved in interpreting its results properly and consequently the difficulty to appreciate its advantages over the Cox proportional hazards model, as well as the absence of adequate validation procedure. In this paper, we addressed these limitations by (1) using both simulated examples and data from National Wilms’ Tumor clinical trials to illustrate proper interpretation of the censored quantile regression model and the differences and the advantages of the model compared to the Cox proportional hazards model; and (2) developing a validation procedure for the predictive censored quantile regression model. The performance of this procedure was examined using simulation studies. Overall, we recommend the use of censored quantile regression model, which permits a more sensitive analysis of time to event data together with the Cox proportional hazards model.

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