Non-parametric estimation of relative risk in survival and associated tests (original) (raw)
Statistics and Its Interface, 2014
In this paper we consider a group sequentially monitored trial on a survival endpoint, monitored using a weighted log-rank (WLR) statistic with deterministic weight function. We introduce a summary statistic in the form of a weighted average logged relative risk and show that if there is no sign change in the instantaneous logged relative risk, there always exists a bijection between the WLR statistic and the weighted average logged relative risk. We show that this bijection can be consistently estimated at each analysis under a suitable shape assumption, for which we have listed two possibilities. We indicate how to derive a design-adjusted p-value and confidence interval and suggest how to apply the bias-correction method. Finally, we document several decisions made in the design of the NLST interim analysis plan and in reporting its results on the primary endpoint.
Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples
Computational and Mathematical Methods in Medicine
This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that t...
K-sample omnibus non-proportional hazards tests based on right-censored data
Statistical Methods in Medical Research, 2020
This work presents novel and powerful tests for comparing nonproportional hazard functions, based on sample-space partitions. Right censoring introduces two major difficulties which make the existing sample-space partition tests for uncensored data non-applicable: (i) the actual event times of censored observations are unknown; and (ii) the standard permutation procedure is invalid in case the censoring distributions of the groups are unequal. We overcome these two obstacles, introduce invariant tests, and prove their consistency. Extensive simulations reveal that under non-proportional alternatives, the proposed tests are often of higher power compared with existing popular tests for non-proportional hazards. Efficient implementation of our tests is available in the R package KONPsurv, which can be freely downloaded from https://github.com/matan-schles/KONPsurv. 1. Introduction. For the task of comparing survival distributions of two or more groups using censored data, the logrank test is the most popular choice. Its optimality properties under proportional-hazard functions are well known. Although the logrank test is asymptotically valid,
On summary estimators of relative risk
Journal of Chronic Diseases, 1981
Two summary relative risk estimators, which are analogues of the Mantel-Haenszel summary odds ratio, are derived for use in prospective studies with stratified data. One of the proposed summary relative risks is shown to be closely related to the maximum likelihood estimator of a common risk ratio, assuming a Poisson distribution for the number of cases in each stratum. This estimator is compared to a recently proposed index of mortality, the Relative Risk Index [l].
Tests for equivalence of two survival functions: Alternative to the tests under proportional hazards
Statistical methods in medical research, 2014
For either the equivalence trial or the non-inferiority trial with survivor outcomes from two treatment groups, the most popular testing procedure is the extension (e.g., Wellek, A log-rank test for equivalence of two survivor functions, Biometrics, 1993; 49: 877-881) of log-rank based test under proportional hazards model. We show that the actual type I error rate for the popular procedure of Wellek is higher than the intended nominal rate when survival responses from two treatment arms satisfy the proportional odds survival model. When the true model is proportional odds survival model, we show that the hypothesis of equivalence of two survival functions can be formulated as a statistical hypothesis involving only the survival odds ratio parameter. We further show that our new equivalence test, formulation, and related procedures are applicable even in the presence of additional covariates beyond treatment arms, and the associated equivalence test procedures have correct type I er...
Biometrics, 2005
This research sequentially monitors paired survival differences using a new class of nonparametric tests based on functionals of standardized paired weighted log-rank (PWLR) and standardized paired weighted Kaplan-Meier (PWKM) tests. During a trial, these tests may alternately assume the role of the more extreme statistic. By monitoring PEMAX, the maximum between the absolute values of the standardized PWLR and PWKM, one combines advantages of rank-based (RB) and non-RB paired testing paradigms. Simulations show that monitoring treatment differences using PEMAX maintains type I error and is nearly as powerful as using the more advantageous of the two tests in proportional hazards (PH) as well as non-PH situations. Hence, PEMAX preserves power more robustly than individually monitored PWLR and PWKM, while maintaining a reasonably simple approach to design and analysis of results. An example from the Early Treatment Diabetic Retinopathy Study (ETDRS) is given.
arXiv: Methodology, 2020
The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan-Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards commonly a log-rank test is performed in order to investigate whether there is a difference in survival, or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inferiority trials, the commonly performed log-rank based tests are similarly affected by a violation of this assumption. Here we propose a parametric framework to assess equivalence or non-inferiority for survival data. We derive pointwise confidence bands for both, the hazard ratio and the difference of the survival curves. Further we propose a test procedure addressing non-inferiority and equiv...
arXiv (Cornell University), 2022
A very classical problem in statistics is to test the stochastic superiority of one distribution to another. However, many existing approaches are developed for independent samples and, moreover, do not take censored data into account. We develop a new estimand-driven method to compare the effectiveness of two treatments in the context of right-censored survival data with matched pairs. With the help of competing risks techniques, the so-called relative treatment effect is estimated. It quantifies the probability that the individual undergoing the first treatment survives the matched individual undergoing the second treatment. Hypothesis tests and confidence intervals are based on a studentized version of the estimator, where resampling-based inference is established by means of a randomization method. In a simulation study, we found that the developed test exhibits good power, when compared to competitors which are actually testing the simpler null hypothesis of the equality of both marginal survival functions. Finally, we apply the methodology to a well-known benchmark data set from a trial with patients suffering from with diabetic retinopathy.
Estimation and testing of survival functions via generalized fiducial inference with censored data
2017
Fiducial Inference, introduced by Fisher in the 1930s, has a long history, which at times aroused passionate disagreements. However, its application has been largely confined to relatively simple parametric problems. In this paper, we present what might be the first time fiducial inference, as generalized by Hannig et al. (2016), is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one sample and two sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein-von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test comparing chemotherapy against chemotherapy combined with radiotherapy using data from the treatment of locally unresectable gastric cancer.