Mixed effect parametric excess hazard models

Description

Fit an (excess) hazard regression model using different shapes for the baseline hazard (Weibull, piecewise constant and exponential of a B-spline), 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 be normally distributed with mean 0 and standard deviation sigma. The optimisation process uses adaptive Gaussian quadrature to calculate the cluster-specific marginal likelihoods. The logarithm of the full marginal likelihood, defined as the sum of the logarithms of the cluster-specific marginal likelihoods, is then maximised using optimisation routines such as nlm or optim. Functions to compute and plot the predicted (excess) hazard and (net) survival are provided.

Details

Author(s)

Hadrien Charvat, Aurelien Belot

References

Charvat H, Remontet L, Bossard N, Roche L, Dejardin O, Rachet B, Launoy G, Belot A; 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. Stat Med 2016. (doi: 10.1002/sim.6881)

Examples

data(simdatn1)

## Fit of a mixed-effect excess hazard model, with the baseline hazard
## described by a Weibull distribution (without covariables)

Mod_weib_mix <- mexhaz(formula=Surv(time=timesurv,
event=vstat)~1, data=simdatn1, base="weibull",
expected="popmrate", verbose=0, random="clust")


## Examples of syntax for various models (not run) 

## Fit of a fixed-effect excess hazard model, with the baseline hazard
## described by a Weibull distribution and with effects of age (agecr),
## deprivation index (depindex) and sex (IsexH) using the optim
## procedure and the BFGS method (see help of optim).

# Mod_weib <- mexhaz(formula=Surv(time=timesurv,
# event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="weibull",
# expected="popmrate", verbose=1000, fnoptim="optim",
# method="BFGS")


## Fit of a mixed-effect excess hazard model, with the baseline hazard
## described by a cubic B-spline with two knots at 1 and 5 year and with
## effects of age (agecr), deprivation index (depindex) and sex (IsexH)

# Mod_bs3_2mix <- mexhaz(formula=Surv(time=timesurv,
# event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="exp.bs",
# degree=3, knots=c(1,5), expected="popmrate", random="clust",
# verbose=1000)


## Fit of a fixed-effect overall hazard model, with the baseline hazard
## described by a piecewise constant function with the following vector
## of knots (defining the endpoints of the intervals on which the hazard
## is constant): (1,3,5,8), and with effects of age (agecr), deprivation
## index (depindex) and sex (IsexH)

# Mod_pw <- mexhaz(formula=Surv(time=timesurv, event=vstat)~
# agecr+depindex+IsexH, data= simdatn1, base="pw.cst", knots=c(1,3,5,8),
# verbose=1000)


## Fit of a fixed-effect excess hazard model, with the baseline hazard
## described by a cubic B-spline with two knots at 1 and 5 year and with
## effects of age (agecr), deprivation index (depindex) and sex (IsexH)

# Mod_bs3_2 <- mexhaz(formula=Surv(time=timesurv,
# event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="exp.bs",
# egree=3, knots=c(1,5), expected="popmrate", verbose=1000)


## Fit of a mixed-effect excess hazard model, with the baseline hazard
## described by a cubic B-spline with two knots at 1 and 5 year and with
## effects of age (agecr), deprivation index (depindex) and sex (IsexH)

# Mod_bs3_2mix <- mexhaz(formula=Surv(time=timesurv,
# event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="exp.bs",
# degree=3, knots=c(1,5), expected="popmrate", random="clust",
# verbose=1000)


## Fit of a mixed-effect excess hazard model, with the baseline hazard
## described by a cubic B-spline with two knots at 1 and 5 year, with
## effects of age (agecr), deprivation index (depindex) and sex (IsexH)
## and with a time-dependent effect for age (agecr) and sex (IsexH).

# Mod_bs3_2mixnph <- mexhaz(formula=Surv(time=timesurv,
# event=vstat)~agecr+depindex+IsexH + nph(agecr+IsexH), data=simdatn1,
# base="exp.bs", degree=3, knots=c(1,5), expected="popmrate",
# random="clust", verbose=1000)

Results