Abstract
BACKGROUND: Laplacian-P-splines (LPS) has been recently shown to deliver a fast
and accurate Bayesian inference in (generalized) additive models, epidemic models, additive proportional odds models,
and proportional survival models.
OBJECTIVES: This project aims at extending the LPS toolbox in survival models to build a method that makes explicit use
of the gradient and the Hessian information resulting from Laplace approximations. In particular, it is applied to
Gamma Shared Frailty survival model.
METHODS: Two algorithms were developed: a sampling-free LPS algorithm, and Metropolis-Adjusted Langevin Algorithm
(MALA) within Gibbs Sampler. The two methods were derived algebraically, implemented R,
tested on 300 simulated datasets with different right-censoring ratios, compared to available frequentist
function (emfrail), and applied on a real-life dataset from a randomized clinical trial of Interferon Gamma (IG)
in Chronic Granulomatous Disease (CGD) in children.
RESULTS: The estimated B-spline coefficients and the regression parameters turned out to be reasonably precise
and to have negligible bias on the simulated datasets. Also the estimates of the frailty variance were virtually
identical to those of the frequentist method, though some discrepancies were observed in datasets with
clusters of small sizes. In the CGD study, the two algorithms developed in this project and the
emfrail function resulted in very similar point estimates and the 95% confidence/credible intervals of the treatment
effect: −1.163 [−1.867; −0.460], −1.190 [−1.879; −0.484],
and −1.052 [−1.660; −0.444], respectively, leading to the same conclusion of substantial effect
of IG treatment on reducing hazard of recurrent serious infections.
Similarly, very close point estimates and the intervals were obtained for female sex (−0.250 [−1.142; 0.642],
−0.249 [−1.185; 0.623], and −0.227 [−1.003; 0.548], respectively), with no hazard-altering effect.
CONCLUSIONS: The two algorithms developed in this project reliably extend LPS methodology to Gamma Shared Frailty
survival models.