Testing for a Changepoint in the Cox Survival Regression Model (original) (raw)
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A sequential testing approach to detecting multiple change points in the proportional hazards model
Statistics in Medicine, 2012
The semi-parametric proportional hazards model has been widely adopted in clinical trials with time-to-event outcomes. A key assumption in the model is that the hazard ratio function is a constant over time, which is frequently violated as there is often a lag period before an experimental treatment reaches its full effect. One existing approach uses maximal score tests and Monte Carlo sampling to identify multiple change points in the hazard ratio function, which requires the number of change points that exist in the model to be known. Copyright
Robust Hypothesis Testing and Model Selection for Parametric Proportional Hazard Regression Models
arXiv (Cornell University), 2020
The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the presence of outliers in the data under such fully parametric proportional hazard models, a robust estimation procedure has recently been proposed extending the concept of the minimum density power divergence estimator (MDPDE) under this setup. In this paper, we consider the problem of statistical inference under the parametric proportional hazards model and develop robust Wald-type hypothesis testing and model selection procedures using the MDPDEs. We have also derived the necessary asymptotic results which are used to construct the testing procedure for general composite hypothesis and study its asymptotic powers. The claimed robustness properties are studied theoretically via appropriate influence function analyses. We have studied the finite sample level and power of the proposed MDPDE based Wald-type test through extensive simulations where comparisons are also made with the existing semi-parametric methods. The important issue of the selection of appropriate robustness tuning parameter is also discussed. The practical usefulness of the proposed robust testing and model selection procedures is finally illustrated through three interesting real data examples.
A Simple Test of the Proportional Hazards Assumption
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Towards an omnibus distribution-free goodness-of-fit test for the Cox model
Statistica Sinica
A new goodness-of-fit test for Cox's proportional hazards model is introduced. The test is based on a transformation of the difference between nonparametric and Cox model specific estimators of the doubly-cumulative hazard function used by McKeague and Utikal (1991). The transformation is designed to give an asymptotically distribution-free test. The test is shown to be consistent against all alternatives except those in which the baseline hazard is linearly dependent on the covariate.
A simple test for the absence of covariate dependence in hazard regression models
2004
This paper extends commonly used tests for equality of hazard rates in a two-sample or -sample setup to a situation where the covariate under study is continuous. In other words, we test the hypothesis 0 : (j) = () for all against the omnibus alternative ( 1 : not 0) as well as more speci…c alternatives, when the covariate is continuous. The tests developed are particularly useful for detecting trend in the underlying conditional hazard rates (i.e., when the alternative hypothesis is ¤ 1 : (j 1)¸(j 2) for all whenever 1 2), or changepoint trend alternatives (such as ¤¤ 1 : there exists ¤ such that (j) " whenever ¤ and (j) # whenever ¤). Asymptotic distribution of the test statistics are established and small sample properties of the tests are studied. An application to the e¤ect of aggregate Q on corporate failure in the UK shows evidence of trend in the covariate e¤ect, whereas a Cox regression model failed to detect evidence of any covariate e¤ect. Finally, we discuss an important extension to testing for proportionality of hazards in the presence of individual level frailty with arbitrary distribution.
Estimation in the Cox survival regression model with covariate measurement error and a changepoint
Biometrical Journal, 2020
The Cox regression model is a popular model for analyzing the relationship between a covariate vector and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulation-extrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM10 and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 and MPPLE.
Testing proportional hazards for specified covariates
Modern Stochastics: Theory and Applications
Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data may be right censored. The limit distribution of the test statistic is derived. Power of the test against approaching alternatives is given. Real data examples are considered.
Change detection in the Cox Proportional Hazards models from different reliability data
Quality and Reliability Engineering International, 2010
The Proportional Hazards (PH) model is an important type of failure time regression model which relates the occurrence probability of critical failures to influential factors. However, little research work has been done on detecting changes in the PH models fitted based on different sets of reliability data. This paper develops the methods for change detection in the Cox PH models, also known as Semiparametric PH model, for reliability prediction and/or assessment of the time-to-failure data collected from different subjects. The effectiveness of the developed methods is illustrated through numerical studies and real-world data analysis. The developed technique possesses wide applicability to the systems and processes where the Cox PH model fits the reliability data well. Copyright © 2010 John Wiley & Sons, Ltd.
A maximum-mean-discrepancy goodness-of-fit test for censored data
2019
We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to compute, as is the test threshold, and we establish consistency under the null. Unlike earlier approaches such as the Log-rank test, we make no assumptions as to how the data distribution might differ from the null, and our test has power against a very rich class of alternatives. In experiments, our test outperforms competing approaches for periodic and Weibull hazard functions (where risks are time dependent), and does not show the failure modes of tests that rely on user-defined features. Moreover, in cases where classical tests are provably most powerful, our test performs almost as well, while being more general.
Computational and Mathematical Methods in Medicine, 2013
The Cox proportional hazards regression model has become the traditional choice for modeling survival data in medical studies. To introduce flexibility into the Cox model, several smoothing methods may be applied, and approaches based on splines are the most frequently considered in this context. To better understand the effects that each continuous covariate has on the outcome, results can be expressed in terms of splines-based hazard ratio (HR) curves, taking a specific covariate value as reference. Despite the potential advantages of using spline smoothing methods in survival analysis, there is currently no analytical method in the R software to choose the optimal degrees of freedom in multivariable Cox models (with two or more nonlinear covariate effects). This paper describes an R package, called smoothHR, that allows the computation of pointwise estimates of the HRs-and their corresponding confidence limits-of continuous predictors introduced nonlinearly. In addition the package provides functions for choosing automatically the degrees of freedom in multivariable Cox models. The package is available from the R homepage. We illustrate the use of the key functions of the smoothHR package using data from a study on breast cancer and data on acute coronary syndrome, from Galicia, Spain.