Inference for the Dependent Competing Risks Model with Masked Causes of Failure

Abstract

The competing risks model is useful in settings in which individuals/units may die/fail for different reasons. The cause specific hazard rates are taken to be piecewise constant functions. A complication arises when some of the failures are masked within a group of possible causes. Traditionally, statistical inference is performed under the assumption that the failure causes act independently on each item. In this paper we propose an EM-based approach which allows for dependent competing risks and produces estimators for the sub-distribution functions. We also discuss identifiability of parameters if none of the masked items have their cause of failure clarified in a second stage analysis (e.g. autopsy). The procedures proposed are illustrated with two datasets.

Modeling multiple risks in the presence of double censoring

“…As noted by Craiu & Reiser (2006), Lawless (2003) shows that the variance of the cause-specific CIF is a linear function of V, where V is the asymptotic covariance matrix which can be calculated using the supplemented EM algorithm of Meng & Rubin (1991). However, Craiu & Reiser (2006) go on to state that this result is not applicable with masked data, since the varianceÁcovariance matrix V will not be diagonal due to the correlations between the various estimators induced by the EM algorithm. In short, viable expressions (or matrices) to quantify the standard errors of the CIF point estimators are not available for the SC-CR context as presented thus far.…”

“…Some recent research has focused on developing dependent competing risks models (cf. Escarela & Carriere (2003) and Craiu & Reiser (2006)). The complication of mutually dependent failure modes will not be considered in the ensuing theory.…”

Random partition masking model for censored and masked competing risks data

“…It has been argued that the symmetry assumption is misleading (see Lin and Guess 1994;Guttman et al 1995). Thus some people try to make MLE or Bayesian inferences based on the likelihood c in (1) assuming only S2, S3 and S1b without S1a (see, e.g., Flehinger et al 2001, p.502-504;Mukhopadhyay and Basu 2007, p. 333;Kuo and Yang 2000;Craiu and Duchesne 2004;Lawless 2003, andReiser 2006). Likelihoods (1) and c , together with the assumptions S1b, S2 and S3 actually form the second model for RMCR data.…”

“…Since F T,C is of main interest, it is better to consider the family of F T,C directly, though as noticed by Kalbfleisch and Prentice (2002) a parametric model for the dependency is hard to specify. Craiu and Duchesne (2004), Lawless (2003), and Craiu and Reiser (2006) propose a special parametric model in such case, where the cause specific hazard functions λ c (t)( de f = f T,C (t, c)/S T (t−)) are piecewise constant. We propose a more general and more convenient way to specify parametric models and apply them to analyze some real data.…”

Bayesian Analysis of Competing Risks Models with Masked Causes of Failure and Incomplete Failure Times

“…In contrast, based on a cause-specific formulation, Flehinger et al (2002) proposed an approach of completely parametric cause-specific hazards using stage 1 and stage 2 information when the failure times for the competing risks have a Weibull distribution. Craiu & Reiser (2006) developed an EM-based method that allowed dependent competing risks and produced estimators for the sub-distribution functions. Moreover, Lu & Tsiatis (2001) presented parametric models to estimate the regression coefficients where by the cause-specific hazard for the cause of interest is associated with the covariates through a proportional hazards relationship.…”