ON PIECE-WISE MODELLING OF SURVIVAL DATA WITH TIME CHANGING COVARIATE FUNCTION

Survival analysis involve the set of statistical techniques or procedures used to study time until an event occurs, these techniques are not without some conditions. One of the basic assumptions is that, to enable a straight forward interpretation of hazard rates of subject’s covariate(s) on some reference categories or in situations where variables are continuous in nature, the hazard rates must be constant through time “also known as the proportional hazard assumption” for cox regression. This assumption is often violated in medical practice where subject’s vital statistics or measures are often time varying, as their medical situations changes with time. This paper under study a modification of Piece wise survival model, where three levels of Weibull distribution were assumed for baseline hazards, the sensitivity of the baselines were assessed under four (4) censoring percentages (0%, 25%, 50%, & 75%) and sample sizes (n=100, n=500 & n=1000), for when models were Single parametric (SPM) and when partitioned – Piece wise Parametric Model (PPM). A Piece-wise Bayesian hazard model with structured additive predictors in which the functional form of time varying covariate was incorporated in a non-proportional hazards framework was developed, capable of incorporating complex situations in a more flexible framework. Analysis was done utilizing MCMC simulation technique. Results revealed on comparison that the PPM outperformed the SPM with smaller DIC values and larger predictive powers with the LPML criterion and consistently so throughout all simulations.

Uji Asumsi Proportional Hazard pada Faktor yang Mempengaruhi Waktu Tahan Hidup Pasien Kanker Paru

<p>Lung cancer is the disease that its death risk always increase, because of that the survival time of its patient is interesting to be researched. One of the method that can be used to research survival time of lung cancer patient is Cox regression. It has an assumption that called proportional hazard assumption. Proportional hazard assumption can be tested by graph method that is log-log graph, but the result is only used as temporary suspicion<em>.</em> For a better result, the goodness of fit test can be used by calculate the correlation between rank of survival time and schoenfeld residual. The result is age variabel doesn’t satisfy proportional hazard assumption.</p><p> </p><strong>Keywords : </strong>cox regression; proportional hazard assumption; log-log graph; goodness of fit test.

The Average Hazard Ratio – A Good Effect Measure for Time-to-event Endpoints when the Proportional Hazard Assumption is Violated?

Summary Background: In many clinical trial applications, the endpoint of interest corresponds to a time-to-event endpoint. In this case, group differences are usually expressed by the hazard ratio. Group differences are commonly assessed by the logrank test, which is optimal under the proportional hazard assumption. However, there are many situations in which this assumption is violated. Especially in applications were a full population and several subgroups or a composite time-to-first-event endpoint and several components are considered, the proportional hazard assumption usually does not simultaneously hold true for all test problems under investigation. As an alternative effect measure, Kalbfleisch and Prentice proposed the so-called ‘average hazard ratio’. The average hazard ratio is based on a flexible weighting function to modify the influence of time and has a meaningful interpretation even in the case of non-proportional hazards. Despite this favorable property, it is hardly ever used in practice, whereas the standard hazard ratio is commonly reported in clinical trials regardless of whether the proportional hazard assumption holds true or not. Objectives: There exist two main approaches to construct corresponding estimators and tests for the average hazard ratio where the first relies on weighted Cox regression and the second on a simple plug-in estimator. The aim of this work is to give a systematic comparison of these two approaches and the standard logrank test for different time-toevent settings with proportional and nonproportional hazards and to illustrate the pros and cons in application. Methods: We conduct a systematic comparative study based on Monte-Carlo simulations and by a real clinical trial example. Results: Our results suggest that the properties of the average hazard ratio depend on the underlying weighting function. The two approaches to construct estimators and related tests show very similar performance for adequately chosen weights. In general, the average hazard ratio defines a more valid effect measure than the standard hazard ratio under non-proportional hazards and the corresponding tests provide a power advantage over the common logrank test. Conclusions: As non-proportional hazards are often met in clinical practice and the average hazard ratio tests often outperform the common logrank test, this approach should be used more routinely in applications.

Performance of two formal tests based on martingales residuals to check the proportional hazard assumption and the functional form of the prognostic factors in flexible parametric excess hazard models

Summary Net survival, the one that would be observed if the disease under study was the only cause of death, is an important, useful, and increasingly used indicator in public health, especially in population-based studies. Estimates of net survival and effects of prognostic factor can be obtained by excess hazard regression modeling. Whereas various diagnostic tools were developed for overall survival analysis, few methods are available to check the assumptions of excess hazard models. We propose here two formal tests to check the proportional hazard assumption and the validity of the functional form of the covariate effects in the context of flexible parametric excess hazard modeling. These tests were adapted from martingale residual-based tests for parametric modeling of overall survival to allow adding to the model a necessary element for net survival analysis: the population mortality hazard. We studied the size and the power of these tests through an extensive simulation study based on complex but realistic data. The new tests showed sizes close to the nominal values and satisfactory powers. The power of the proportionality test was similar or greater than that of other tests already available in the field of net survival. We illustrate the use of these tests with real data from French cancer registries.