Correlated Bivariate Normal Competing Risks—Structuring Estimation In An Ill-Posed Problem

Estimation of correlation between competing risks has long been known to be an ill-posed problem, due to lack of identifiablity, termed the identifiability crisis [Crowder, Scand J Stat 1991].Recently, many semi-parametric models and a fully parametric model have been used to permit estimation and assess sensitivity of results to degree of correlation [Jeong and Fine Biostatistics 2007; see also Tai et al, SIM 2008]. Parametric models are non-standard and calculations complex; Jeong and Fine’s parametric model employs a Gompertz distribution. For log-Normal data, complexity of calculations in a bivariate Normal (BVN) model is forbidding and direct optimization unstable.

We describe a parametric solution available in the BVN case. Our approach uses an EM algorithm for competing risks (generalising the Aitkin’s EM for univariate survival). Complex calculations are evaluated in closed form using a lemma of Stein [Liu, Statist Prob Letters 1994]. This probabilistic and statistical platform for exploring the ill-posedness is implemented within the **bnc** R-package (in preparation).

We introduce these various components in the talk.