Testing the proportionality assumption for specified covariate in the cox model

In this paper, I propose a test for proportional hazards assumption for specified covariates. The testis based on a general alternative in sense that hazards rates under different values of covariates therate is not only constant as in the Cox model, but it may cross, go away, and may be monotonicwith time. The limit distribution of the test statistic is derived. Finite samples properties of thetest power are analyzed by simulation. Application of the proposed test on Real data examples areconsidered.

Comparison of survival distributions in clinical trials: A practical guidance

Background In randomized clinical trials with censored time-to-event outcomes, the logrank test is known to have substantial statistical power under the proportional hazards assumption and is widely adopted as a tool to compare two survival distributions. However, the proportional hazards assumption is impossible to validate in practice until the data are unblinded. However, the statistical analysis plan of a randomized clinical trial and in particular its primary analysis method must be pre-specified before any unblinded information may be reviewed. Purpose The purpose of this article is to guide applied biostatisticians in the prespecification of a desired primary analysis method when a treatment effect with nonproportional hazards is anticipated. While articles proposing alternate statistical tests are aplenty, to the best of our knowledge, there is no article available that attempts to simplify the choice and prespecification of a primary statistical test under specific expected patterns on nonproportional hazards. We provide such guidance by reviewing various tests proposed as more powerful alternatives to the standard logrank test under nonproportional hazards and simultaneously comparing their performance under a wide variety of nonproportional hazards scenarios to elucidate their advantages and disadvantages. Method In order to select the most preferable test for detecting specific differences between survival distributions of interest while controlling false positive rates, we review and assess the performance of weighted and adaptively weighted logrank tests, weighted and adaptively weighted Kaplan–Meier tests and versatile tests under various patterns of nonproportional hazards treatment effects through simulation. Conclusion We validate some of the claimed properties of the proposed extensions and identify tests that may be more preferable under specific expected pattern of nonproportional hazards when such knowledge is available. We show that versatile tests, while achieving robustness to departures from proportional hazards, may lose interpretation of directionality (superiority or inferiority) and can only be seen to test departures from equality. Detailed summary and discussion of the performance of each test in terms of type I error rate and power are provided to formulate specific guidance about their applicability and use.

Dietary Patterns May Be Nonproportional Hazards for the Incidence of Type 2 Diabetes: Evidence from Korean Adult Females

This study aimed to examine the association between the incidence of type 2 diabetes and various risk factors including dietary patterns based on the rigorous proportional hazards assumption tests. Data for 3335 female subjects aged 40–69 years from the Korea Genome and Epidemiology Study were used. The assumption of proportional hazards was tested using the scaled Schoenfeld test. The stratified Cox regression was used to adjust the nonproportionality of diabetic risk factors, and the regression was adjusted for potential confounding variables, such as age, marital status, physical activity, drinking, smoking, BMI, etc. Metabolic syndrome and meat and fish pattern variables were positively associated with diabetes. However, dietary patterns and metabolic syndrome variables violated the proportional hazards assumption; therefore, the stratified Cox regression with the interaction terms was applied to adjust the nonproportionality and to allow the possible different parameters over each stratum. The highest quartile of meat and fish pattern was associated with diabetes only in subjects aged over 60 years. Moreover, subjects who were obese and had metabolic syndrome had higher risk in bread and snacks (HR: 1.85; 95% CI: 1.00–3.40) and meat and fish pattern (HR: 1.82; 95% CI: 1.01–3.26), respectively. In conclusion, a quantitative proportional hazards assumption test should always be conducted before the use of Cox regression because nonproportionality of risk factors could induce limited effect on diabetes incidence.

Survival forests under test: Impact of the proportional hazards assumption on prognostic and predictive forests for amyotrophic lateral sclerosis survival

We investigate the effect of the proportional hazards assumption on prognostic and predictive models of the survival time of patients suffering from amyotrophic lateral sclerosis. We theoretically compare the underlying model formulations of several variants of survival forests and implementations thereof, including random forests for survival, conditional inference forests, Ranger, and survival forests with L1 splitting, with two novel variants, namely distributional and transformation survival forests. Theoretical considerations explain the low power of log-rank-based splitting in detecting patterns in non-proportional hazards situations in survival trees and corresponding forests. This limitation can potentially be overcome by the alternative split procedures suggested herein. We empirically investigated this effect using simulation experiments and a re-analysis of the Pooled Resource Open-Access ALS Clinical Trials database of amyotrophic lateral sclerosis survival, giving special emphasis to both prognostic and predictive models.

VP82 Impact of Evidence Synthesis Methods on Outcome of Economic Evaluation

IntroductionEvidence synthesis (ES) is often required for economic evaluation (EE) of pharmaceuticals. Commonly used methods are based on the assumption of proportional hazards in trial data, using the hazard ratio (HR). Alternative methods for ES are increasingly used in EE, in situations where the pattern of hazards in the trial data indicates that the proportional hazards assumption may be violated. The impact of these methodological choices on model outcomes is explored.MethodsA network of trials of BRAF-targeted treatments for advanced melanoma, derived using a systematic review of the literature, is chosen for the study. Guyot's method is used to create individual-patient Kaplan-Meier (K-M) data from published survival curves. Log-cumulative hazard plots and Schoenfeld residuals are derived to examine patterns in hazards within the trial data. All analyses are conducted in R version 3.5.0©. Three alternative methods for ES are tested: 1) Network meta-analysis (NMA) based on published HRs and the assumption of proportional hazards. 2) NMA using fractional polynomials (FP) based on digitised K-M data, allowing the relaxation of the proportional hazards assumption. 3) NMA using an accelerated failure time (AFT) model based on digitised K-M data, allowing the relaxation of the proportional hazards assumption. The derived estimates of relative efficacy from each method are applied in a partitioned survival cost-effectiveness model programmed in Microsoft Excel™.ResultsThe model outcomes predicted by each method (HR, FP and AFT) are presented and compared. Both deterministic and probabilistic results are presented, alongside a discussion around how the uncertainty in these structural assumptions may be captured in EE.ConclusionsStructural assumptions in ES may lead to differences in model outcomes. The impact of these differences may be important in situations where decision uncertainty is high. Methods should be chosen and justified based on patterns of hazard present in the trial data.