mpl {bhm}

Joint models for clustered data with binary and survival outcomes.

Description

{mpl} is a function to fit a joint model for clustered binary and survival data using maximum penalized likelihood (MPL) method with Jackknife variance.

Usage

mpl(formula, ...)

## S3 method for class 'formula'
mpl(formula, formula.glm, formula.cluster, data, weights=NULL,
    subset = NULL, max.iter=100, tol = 0.005, jackknife=TRUE, ...)
#
# Use:
#
# fit = mpl(Surv(time, status)~w+z, y~x1+x2, ~cluster, data=data)
#

Arguments

formula

an object of class "formula"(or one that can be coerced to that class): a symbolic description of the Cox proportiobal hazards model to be fitted for survival data.

formula.glm

an object of class "formula"(or one that can be coerced to that class): a symbolic description of the generalized linear model to be fitted for binary data.

formula.cluster

an object of class "formula"(or one that can be coerced to that class): a symbolic description of the cluster variable.

data

an optional data frame, list or environment (or object coercible by 'as.data.frame' to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the enviro nment from which mpl is called.

weights

an optional vector of weights to be used in the fitting process. Should be 'NULL' or a numeric vector. If non-NULL, weights options in the glm model and the coxph model will be assinged with the supplied weights.

subset

only a subset of data will be used for model fitting.

max.iter

Maximum number of iterations, default is max.iter = 100

tol

Tolrance for convergence, default is tol = 0.005

jackknife

Jackknife method for variance, default is jackknife = TRUE

...

additional arguments to be passed to the low level regression fitting functions (see below).

Details

mpl(Surv(time, event)~w+z, y~x1+x2, ~cluster) will fit penalized likelihood for binary and survival data with cluster effect. Function print(x) can be used to print a summary of mpl results.

Value

mpl returns an object of class inheriting from "mpl". When jackknife = TRUE, an object of class "mpl" is a list containing the following components:

theta

the maximum estimate of the regression coefficients and varaince component

OR_HR

Odds ratios (OR) and hazard ratios (HR) for binary and survival outcomes, respectively

ase

Asymptotic standard error for theta, which is usually understimated

jse

Jackknife standard error of theta based on resampling, this is considered to be more robust

Note

Based on code from J. Wang.

Author(s)

Bingshu E. Chen ([e-mail])

References

Chen, B. E. and Wang, J. (2020). Joint modelling of binary response and survival for clustered data in clinical trials. Statistics in Medicine. Vol 39. 326-339.

See Also

coxph, glm, print.

Examples

##
### No run
# 
# fit = mpl(Surv(time, event)~trt+ki67, resp~trt+age, ~center.id) 
#