adjsurv {mexhaz}

Computation of direct adjusted survival estimates based on a mexhaz model

Description

Function for computing direct adjusted survival estimates from a model fitted with the mexhaz. It can be used to obtain direct adjusted survival estimates for one or two populations. In the latter case, survival difference estimates are also computed. Corresponding variance estimates are based on the Delta Method (based on the assumption of multivariate normality of the model parameter estimates). 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

adjsurv(object, time.pts, data, data.0 = NULL, weights = NULL,
marginal = TRUE, quant.rdm = 0.5, cluster = NULL, quant.rdm.0 = 0.5,
cluster.0 = NULL, level = 0.95, 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 direct adjusted estimates are to be calculated.

data.0

an optional data.frame containing the values of the covariates of a second population for which direct adjusted estimates can also be calculated (and compared with those of the first population). The default value is set to NULL.

weights

optional argument specifying the weights to be associated with each row of data (and data.0). the default value is set to NULL which corresponds to attributing to each row of the dataset(s) a weight equal to one over the total number of rows.

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. The marginal hazard rate is obtained as the opposite of the marginal time derivative of the survival divided by the marginal survival. When FALSE (default value), cluster-specific posterior predictions or conditional predictions are calculated depending on the value of the cluster argument.

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).

level

a number in (0,1) specifying the level of confidence for computing the confidence intervals of the hazard and the survival. By default, level=0.95.

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 direct adjusted survival curve. It contains the following elements:

results

a data.frame consisting of: the time points at which the direct adjusted survival values have been calculated; the direct ajusted survival values with their confidence limits for population data; the direct ajusted survival values with their confidence limits for population data.0; the direct adjusted survival difference estimates with their confidence limits.

type

type of results returned by the function. The value is used by plot.resMexhaz and lines.resMexhaz, and set to "as" (adjusted survival).

multiobs

value used by plot.resMexhaz and lines.resMexhaz, and set to FALSE (computation of the adjusted survival at several time points for one vector of covariates).

ci.method

method used to compute confidence limits. Currently set to "delta" as only the Delta Method is implemented.

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)

## Direct adjusted survival for the simdatn1 population
DAS_Modbs1_2 <- adjsurv(Mod_bs1_2, time.pts=seq(1,10),
data=simdatn1)