Non-parametric estimation of survival in age-dependent genetic disease and application to the transthyretin-related hereditary amyloidosis

Abstract

In genetic diseases with variable age of onset, survival function estimation for the mutation carriers as well as estimation of the modifying factors effects are essential to provide individual risk assessment, both for mutation carriers management and prevention strategies. In practice, this survival function is classically estimated from pedigrees data where most genotypes are unobserved. In this article, we present a unifying Expectation-Maximization (EM) framework combining probabilistic computations in Bayesian networks with standard statistical survival procedures in order to provide mutation carrier survival estimates. The proposed approach allows to obtain previously published parametric estimates (e.g. Weibull survival) as particular cases as well as more general Kaplan-Meier non-parametric estimates, which is the main contribution. Note that covariates can also be taken into account using a proportional hazard model. The whole methodology is both validated on simulated data and applied to family samples with transthyretin-related hereditary amyloidosis (a rare autosomal dominant disease with highly variable age of onset), showing very promising results.

Fig 1. Simulated dataset.

Reference and estimation of the survival function S(t) for carriers with 95% point-wise confidence intervals (dashed lines). A total of n = 3,285 (1,641 males and 1,644 females) individuals including 441 affected and 319 genotyped. Left: simulation and estimation without gender effect. Right: simulation and estimation with a proportional protective effect for females (gender = 2).

Fig 2. Survival estimates.

Top-Left: French dataset with a gender PH effect (RH 1.7, Cox’s p-value 0.030); Top-Right: Portugese dataset with a gender PH effect (RH 1.57, Cox’s p-value 0.033); Bottom-Left: Swedish dataset with a non-significant gender PH effect (Cox’s p-value 0.42). Bottom-Right: Swedish dataset without any gender PH effect. 95% point-wise confidence intervals are given by the colored regions.