riskfunc {mexhaz}

Computation of hazard ratio and risk ratio estimates based on a mexhaz model

Description

Function for computing hazard ratio and risk ratio (ratio of cumulative probabilities of failure) estimates from a model fitted with the mexhaz function. Corresponding confidence intervals are based on the Delta Method or Monte Carlo simulation (based on the assumption of multivariate normality of the model parameter estimates). This function allows the computation of estimates at one time point for several vectors of covariates or for one vector of covariates at several time points. When the model includes a random effect, three types of predictions can be made: (i) marginal predictions (obtained by integration over the random effect distribution), (ii) cluster-specific posterior predictions for an existing cluster, or (iii) conditional predictions for a given quantile of the random effect distribution (by default, for the median value, that is, 0).

Usage

riskfunc(object, time.pts, data, data.0, marginal = TRUE, quant.rdm = 0.5,
cluster = NULL, quant.rdm.0 = 0.5, cluster.0 = NULL, type = c("hr", "rr"),
conf.int = c("delta", "simul"), level = 0.95, nb.sim = 10000, seed = NULL,
dataset = NULL)

Arguments

object

an object of class mexhaz, corresponding to a hazard-based regression model fitted with the mexhaz function.

time.pts

a vector of numerical values representing the time points at which predictions are requested. Time values greater than the maximum follow-up time on which the model estimation was based are discarded.

data

a data.frame containing the values of the covariates of the population for which hazard ratios or risk ratios are to be calculated.

data.0

a data.frame containing the values of the covariates of the reference population. Each row of data.0 is used as the reference for the corresponding row of data.

marginal

logical value controlling the type of predictions returned by the function when the model includes a random intercept. When TRUE, marginal predictions are computed. The marginal survival is obtained by integrating the predicted survival over the distribution of the random effect. When FALSE (default value), conditional predictions depending on the value of the cluster argument are calculated.

quant.rdm

numerical value (between 0 and 1) specifying the quantile of the random effect distribution that should be used when requesting conditional predictions. The default value is set to 0.5 (corresponding to the median, that is a value of the random effect of 0). This argument is ignored if the model is a fixed effect model, when the marginal argument is set to TRUE, or the cluster argument is not NULL.

cluster

a single value corresponding to the name of the cluster for which posterior predictions should be calculated. These predictions are obtained by integrating over the cluster-specific posterior distribution of the random effect and thus require the original dataset. The dataset can either be provided as part of the mexhaz object given as argument or by specifying the name of the dataset in the dataset argument (see below). The cluster argument is not used if the model is a fixed effect model. The default value is NULL: this corresponds to marginal predictions (if marginal is set to TRUE, the preferred option), or to conditional predictions for a given quantile (by default, the median) of the distribution of the random effect (if marginal is set to FALSE).

quant.rdm.0

random effect distribution quantile value to be used with data.0 (see argument quant.rdm for details).

cluster.0

cluster value to be used with data.0 (see argument cluster for details).

type

argument specifying the type of predictions to be calculated. Selection can be made between "hr" (hazard ratio) and "rr" (risk ratio, i.e., ratio of cumulative failure probabilities).

conf.int

method to be used to compute confidence limits. Selection can be made between the following options: "delta" for the Delta Method (default value); "simul" for Monte Carlo simulations (can be time-consuming, especially for models using B-splines for the logarithm of the baseline hazard).

level

a number in (0,1) specifying the level of confidence for computing the confidence intervals of the hazard and the survival. By default, this argument is set to 0.95.

nb.sim

integer value representing the number of simulations used to estimate the confidence limits for the (excess) hazard and the (net) survival. This argument is used only if conf.int is set to "simul".

seed

argument allowing the user to set a random seed for simulations (only relevant when conf.int is set to "simul"). The default value is set to NULL in which case a random seed is automatically generated inside the function.

dataset

original dataset used to fit the mexhaz object given as argument to the function. This argument is only necessary if cluster-specific posterior predictions are requested (and if the dataset is not already provided in the mexhaz object). The default value is set to NULL.

Value

An object of class resMexhaz that can be used by the function plot.resMexhaz to produce graphics of the hazard ratio or risk ratio curve. It contains the following elements:

results

a data.frame consisting of: the time points at which values have been calculated; the hazard ratio / risk ratio values with their confidence limits.

type

type of results returned by the function. The value is used by plot.resMexhaz and lines.resMexhaz, and can take the values "hr" (hazard ratio) or "rr" (risk ratio).

multiobs

value used by plot.resMexhaz and lines.resMexhaz, and set to FALSE when estimates are computed at several time points for one vector of covariates.

ci.method

method used to compute confidence limits.

level

level of confidence used to compute confidence limits.

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;35:3066-3084 (doi: 10.1002/sim.6881)

Skrondal A, Rabe-Hesketh S. Prediction in multilevel generalized linear models. J R Stat Soc A Stat Soc 2009;172(3):659-687 (doi: 10.1111/j.1467-985X.2009.00587.x).

See Also

plot.resMexhaz, lines.resMexhaz

Examples

data(simdatn1)

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

Mod_bs1_2 <- mexhaz(formula=Surv(time=timesurv,
event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="exp.bs",
degree=1, knots=c(1,5), verbose=0)

## Risk ratio along time for agecr=0.2 compared to agecr=0.1

RR_Modbs1_2 <- riskfunc(Mod_bs1_2, time.pts=seq(0,10,le=101),
data=data.frame(agecr=0.2,depindex=0,IsexH=1),
data.0=data.frame(agecr=0.1,depindex=0,IsexH=1),type="rr",
conf.int="delta")

plot(RR_Modbs1_2)