Semiparametric Modeling for Multivariate Survival Data via Copulas

TL;DR

This paper introduces a flexible semiparametric multivariate survival model using copulas and the YP model for margins, capable of handling crossing survival curves and encompassing PH and PO models, with demonstrated effectiveness through simulations and ovarian cancer data.

Contribution

It presents a novel class of multivariate survival models combining copulas with semiparametric margins, enhancing flexibility and interpretability over existing models.

Findings

Model effectively captures crossing survival curves.

Closed-form likelihood simplifies inference.

Demonstrated versatility on ovarian cancer data.

Abstract

We propose a new class of multivariate survival models based on archimedean copulas with margins modeled by the Yang and Prentice (YP) model. The Ali-Mikhail-Haq (AMH), Clayton, Frank, Gumbel-Hougaard (GH), and Joe copulas are employed to accommodate the dependency among marginal distributions. Baseline distributions are modeled semiparametrically by the piecewise exponential (PE) distribution and the Bernstein polynomials. The new class of models possesses some attractive features: i) the ability to take into account survival data with crossing survival curves; ii) the inclusion of the well-known proportional hazards (PH) and proportional odds (PO) models as particular cases; iii) greater flexibility provided by the semiparametric modeling of the marginal baseline distributions; iv) the availability of closed-form expressions for the likelihood functions, leading to more straightforward inferential procedures. We conducted an extensive Monte Carlo simulation study to evaluate the performance of the proposed model. Finally, we demonstrate the versatility of our new class of models through the analysis of survival data involving patients diagnosed with ovarian cancer.