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Analysis of proportional hazards models fitting with parametric bootstrap

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Authors: J. Casellas, J. Tarrés, J. Piedrafita, L. Varona
Issue: 102-2 (103-109)
Topic: Animal Production
Keywords: Model fitting, Parametric bootstrap, Longevity, Proportional hazards, Survival

It is difficult to test the fitting of proportional hazards models because the available tests, mainly graphical tests, suffer from a substantial degree of subjectivity. In this sense, we developed a parametric bootstrap procedure to test de fitting of survival models based on the simulation of data set replicates through Monte Carlo simulation and taking as starting point the estimates previously obtained for the parameters of each model. Bootstrap intervals for the Kaplan-Meier survival estimate were established along the parametric space analyzed. Significant fitting deficiencies were revealed when the observed survival was not included within the bootstrapped interval. This approach was tested on a survival data set of Bruna dels Pirineus beef calves, assuming four different parametric baseline hazard functions (exponential, Weibull, exponential time-dependent and Weibull timedependent) and the Cox’s semiparametric model. Within this context, exponential time-dependent and Cox’s models did not show significant deviations, whereas the remaining ones suffered from important over and underestimations of the reference statistic. Given the lower computational requirements of parametric models, the exponential time-dependent one seemed preferable for the analysis of Bruna dels Pirineus calves survival.

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