predMexhaz: Predictions based on a mexhaz model

Description

Function for predicting the (excess) hazard and the corresponding (net) survival from a model fitted with the `mexhaz` function for a particular vector of covariates. If the survival model was fitted with an expected hazard, the estimates obtained are excess hazard and net survival estimates. When the model includes a random effect, the predicted values are obtained for the value 0 of the random effect. Confidence limits can be obtained by Monte-Carlo simulation (for all types of baseline hazard) and by the Delta Method (not available for Weibull hazard). This function allows the computation of the hazard and the survival at one time point for several vectors of covariables or for one vector of covariables at several time points.

Usage

 ```1 2``` ```predMexhaz(model, time.pts, data.val = data.frame(.NotUsed=NA), conf.int=c("none","delta","simul"), nb.sim = 10000) ```

Arguments

 `model` an object of class `mexhaz`, corresponding to a survival 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.val` a `data.frame` containing the values of the covariables at which predictions should be calculated. `conf.int` method to be used to compute confidence limits. Selection can be made between the following options: `"none"` indicates absence of confidence limits estimation (default value); `"delta"` for the Delta Method (this option is not available for models using a Weibull hazard); `"simul"` for Monte Carlo simulations (can be time-consuming, especially for models using B-splines for the logarithm of the baseline hazard). `nb.sim` integer value representing the number of simulations used to estimate the 95% confidence limits for the (excess) hazard and the (net) survival. This argument is used only if `conf.int="simul"`.

Value

An object of class `predMexhaz` that can be used by the functions `plot.predMexhaz` and `points.predMexhaz` to produce graphics of the (excess) hazard and the (net) survival. It contains the following elements:

 `call` the `mexhaz` function call on which the model is based. `results` a `data.frame` consisting of: the time points at which the (excess) hazard and the (net) survival have been calculated; the values of the covariables used to estimate the (excess) hazard and the (net) survival; the (excess) hazard values with their confidence limits; and the (net) survival values with their confidence limits. `variances` a `data.frame` consisting of two columns: the variance of the logarithm of the (excess) hazard and the variance of the (excess) cumulative hazard for each time points or each vector of covariables. These variances can be used to estimate the population (net) survival. The object `variances` is produced only when B-splines are used to model the logarithm of the baseline (excess) hazard with the option `conf.int="delta"`. `type` the type of predictions produced. Can take the value `"multitime"` (computation of the hazard and the survival at at several time points for one vector of covariables) or `multiobs` (computation of the hazard and the survival at at one time point for several vectors of covariables). This value is used by `plot.predMexhaz` and `points.predMexhaz`. `ci.method` the method used to compute confidence limits. `nb.sim` number of simulations used to estimate the 95% confidence limits (set to `NA` if confidence limits were not requested or calculated with the Delta Method).

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)

`print.predMexhaz`, `plot.predMexhaz`, `points.predMexhaz`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```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) ## Prediction at several time points for one vector of covariates Pred_Modbs1_2A <- predMexhaz(Mod_bs1_2, time.pts=seq(0.1,10,by=0.1), data.val=data.frame(agecr=0,depindex=0.5,IsexH=1), conf.int="delta") ## Prediction for several vectors of covariates at one time point Pred_Modbs1_2B <- predMexhaz(Mod_bs1_2, time.pts=10, data.val=data.frame(agecr=c(-0.2,-0.1,0), depindex=c(0.5,0.5,0.5), IsexH=c(1,1,1)), conf.int="delta") ## Prediction for all individuals of the study population at one time point Pred_Modbs1_2C <- predMexhaz(Mod_bs1_2, time.pts=10, data.val=simdatn1, conf.int="delta") ```

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