Model-based estimation of measures of association for time-to-event outcomes.

Federico Ambrogi,Elia Biganzoli,Patrizia Boracchi

doi:10.1186/1471-2288-14-97

Abstract

BackgroundHazard ratios are ubiquitously used in time to event applications to quantify adjusted covariate effects. Although hazard ratios are invaluable for hypothesis testing, other adjusted measures of association, both relative and absolute, should be provided to fully appreciate studies results. The corrected group prognosis method is generally used to estimate the absolute risk reduction and the number needed to be treated for categorical covariates.MethodsThe goal of this paper is to present transformation models for time-to-event outcomes to obtain, directly from estimated coefficients, the measures of association widely used in biostatistics together with their confidence interval. Pseudo-values are used for a practical estimation of transformation models.ResultsUsing the regression model estimated through pseudo-values with suitable link functions, relative risks, risk differences and the number needed to treat, are obtained together with their confidence intervals. One example based on literature data and one original application to the study of prognostic factors in primary retroperitoneal soft tissue sarcomas are presented. A simulation study is used to show some properties of the different estimation methods.ConclusionsClinically useful measures of treatment or exposure effect are widely available in epidemiology. When time to event outcomes are present, the analysis is performed generally resorting to predicted values from Cox regression model. It is now possible to resort to more general regression models, adopting suitable link functions and pseudo values for estimation, to obtain alternative measures of effect directly from regression coefficients together with their confidence interval. This may be especially useful when, in presence of time dependent covariate effects, it is not straightforward to specify the correct, if any, time dependent functional form. The method can easily be implemented with standard software.

Highlights

Hazard ratios are ubiquitously used in time to event applications to quantify adjusted covariate effects
The purpose of this paper is to provide an outline of the methods generally adopted to estimate adjusted summary measures of associations, different from the hazard ratio, in time-to-event studies and to present a new method based on transformation models
In randomized controlled trials (RCT) the use of adjusted estimates is suggested for example to account for potential covariate imbalances or since prognostically relevant covariates were considered for a stratified randomization [20,21,22]

Summary

Introduction

Hazard ratios are ubiquitously used in time to event applications to quantify adjusted covariate effects. Hazard ratios are invaluable for hypothesis testing, other adjusted measures of association, both relative and absolute, should be provided to fully appreciate studies results. The appropriateness of the use of a specific measure of association may depend on the study objectives and design. The use of specific measures of association depends on the statistical methods available for estimation. In epidemiology, a debated subject concerns the use of odds ratios, estimated through logistic regression, in cohort studies of common outcomes [1,2]. When time-to-event outcomes are analyzed, the presence of censoring calls for specific methods of analysis [3]. The measure of effect generally considered is the adjusted hazard ratio estimated by means of Cox proportional hazard model, ([4,5])

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