Hadrien Charvat and Aurelien Belot
Fit an (excess) hazard regression model using different shapes for the baseline hazard (Weibull, piecewise constant and B-splines), with the possibility to include time-dependent and/or non-linear effect(s) of variable(s) and a random effect defined at the cluster level. The time-dependent effect of a covariate is modelled by adding interaction terms between the covariate and a function of time of the same class as the one used for the baseline hazard (in particular, with the same knots for piecewise constant hazards; and with the same degree and the same knots for B-spline functions)”. The random effect is assumed to follow a normal distribution with mean 0 and standard deviation sigma. The optimisation process uses the adaptive Gaussian quadrature to calculate the cluster specific marginal likelihood. The full (log) marginal likelihood, defined as the sum of the (log) cluster-specific marginal likelihood, is then maximised using optimisation routine such as nlm or optim. Functions to compute and plot the predicted (excess) hazard and (net) survival are provided.
The new mexhaz R package 1.1 is now available in the CRAN website (https://cran.r-project.org/web/packages/mexhaz/index.html).
References and further reading
Charvat H, Remontet L, Bossard N, Roche L, Dejardin O, Rachet B, Launoy G, Belot A; and the CENSUR Working Survival Group. A multilevel excess hazard model to estimate net survival on hierarchical data allowing for non-linear and non-proportional effects of covariates. Statistics in Medicine 2016 (doi:10.1002/sim.6881)