Open Access Open Badges Research article

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

Federico Ambrogi1*, Elia Biganzoli12 and Patrizia Boracchi1

Author Affiliations

1 Department of Clinical Sciences and Community Health, University of Milan, Via Venezian 1, 20133 Milan, Italy

2 Fondazione IRCCS Istituto Nazionale Tumori, Via Venezian 1, 20133 Milan, Italy

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BMC Medical Research Methodology 2014, 14:97  doi:10.1186/1471-2288-14-97

Published: 9 August 2014



Hazard 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.


The 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.


Using 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.


Clinically 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.

Survival analysis; Transformation models; Pseudo-values; Link functions; Numbers needed to treat