bic.surv {BMA}

Bayesian Model Averaging for Survival models.

Description

Bayesian Model Averaging for Cox proportional hazards models for censored survival data. This accounts for the model uncertainty inherent in the variable selection problem by averaging over the best models in the model class according to approximate posterior model probability.

Usage

bic.surv(x, ...)

## S3 method for class 'matrix'
bic.surv(x, surv.t, cens, strict = FALSE, 
      OR = 20, maxCol = 30, prior.param = c(rep(0.5, ncol(x))), 
      OR.fix = 2, nbest = 150, factor.type = TRUE, 
      factor.prior.adjust = FALSE, call = NULL, ...)

## S3 method for class 'data.frame'
bic.surv(x, surv.t, cens, 
      strict = FALSE, OR = 20, maxCol = 30, 
      prior.param = c(rep(0.5, ncol(x))), OR.fix = 2, 
      nbest = 150, factor.type = TRUE, 
      factor.prior.adjust = FALSE, call = NULL, ...)

## S3 method for class 'formula'
bic.surv(f, data, strict = FALSE, 
     OR = 20, maxCol = 30, prior.param = c(rep(0.5, ncol(x))), 
     OR.fix = 2, nbest = 150, factor.type = TRUE, 
     factor.prior.adjust = FALSE, call = NULL, ...)

Arguments

x

a matrix or data frame of independent variables.

surv.t

a vector of values for the dependent variable.

cens

a vector of indicators of censoring (0=censored 1=uncensored)

f

a survival model formula

data

a data frame containing the variables in the model.

strict

logical indicating whether models with more likely submodels are eliminated. FALSE returns all models whose posterior model probability is within a factor of 1/OR of that of the best model.

OR

a number specifying the maximum ratio for excluding models in Occam's window

maxCol

a number specifying the maximum number of columns in design matrix (including intercept) to be kept.

prior.param

a vector of prior probabilities that parameters are non-zero. Default puts a prior of .5 on all parameters. Setting to 1 forces the variable into the model.

OR.fix

width of the window which keeps models after the leaps approximation is done. Because the leaps and bounds gives only an approximation to BIC, there is a need to increase the window at this first "cut" so as to ensure that no good models are deleted. The level of this cut is at 1/(OR^OR.fix); the default value for OR.fix is 2.

nbest

a value specifying the number of models of each size returned to bic.glm by the modified leaps algorithm.

factor.type

a logical value specifying how variables of class "factor" are handled. A factor variable with d levels is turned into (d-1) dummy variables using a treatment contrast. If factor.type = TRUE, models will contain either all or none of these dummy variables. If factor.type = FALSE, models are free to select the dummy variables independently. In this case, factor.prior.adjust determines the prior on these variables.

factor.prior.adjust

a logical value specifying if the prior distribution on dummy variables for factors should be adjusted when factor.type=FALSE. When factor.prior.adjust=FALSE, all dummy variables for variable i have prior equal to prior.param[i]. Note that this makes the prior probability of the union of these variables much higher than prior.param[i]. Setting factor.prior.adjust=T corrects for this so that the union of the dummies equals prior.param[i] (and hence the deletion of the factor has a prior of 1-prior.param[i]). This adjustment changes the individual priors on each dummy variable to 1-(1-pp[i])^(1/(k+1)).

call

used internally

...

unused

Details

Bayesian Model Averaging accounts for the model uncertainty inherent in the variable selection problem by averaging over the best models in the model class according to approximate posterior model probability. bic.surv averages of Cox regression models.

Value

bic.surv returns an object of class bic.surv

The function summary is used to print a summary of the results. The function plot is used to plot posterior distributions for the coefficients. The function imageplot generates an image of the models which were averaged over.

An object of class bic.glm is a list containing at least the following components:

postprob

the posterior probabilities of the models selected

label

labels identifying the models selected

bic

values of BIC for the models

size

the number of independent variables in each of the models

which

a logical matrix with one row per model and one column per variable indicating whether that variable is in the model

probne0

the posterior probability that each variable is non-zero (in percent)

postmean

the posterior mean of each coefficient (from model averaging)

postsd

the posterior standard deviation of each coefficient (from model averaging)

condpostmean

the posterior mean of each coefficient conditional on the variable being included in the model

condpostsd

the posterior standard deviation of each coefficient conditional on the variable being included in the model

mle

matrix with one row per model and one column per variable giving the maximum likelihood estimate of each coefficient for each model

se

matrix with one row per model and one column per variable giving the standard error of each coefficient for each model

reduced

a logical indicating whether any variables were dropped before model averaging

dropped

a vector containing the names of those variables dropped before model averaging

call

the matched call that created the bma.lm object

Note

If more than maxcol variables are supplied, then bic.surv does stepwise elimination of variables until maxcol variables are reached. Many thanks to Sanford Weisberg for making source code for leaps available.

Author(s)

Chris Volinsky [e-mail]; Adrian Raftery [e-mail]; Ian Painter [e-mail]

References

Volinsky, C.T., Madigan, D., Raftery, A.E. and Kronmal, R.A. (1997). "Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke." Applied Statistics 46: 433-448

See Also

summary.bic.surv, print.bic.surv, plot.bic.surv

Examples

## Not run: 
## veteran data
library(survival)
data(veteran)

test.bic.surv<- bic.surv(Surv(time,status) ~ ., data = veteran, 
                         factor.type = TRUE)
summary(test.bic.surv, conditional=FALSE, digits=2)
plot(test.bic.surv)

imageplot.bma(test.bic.surv)

## End(Not run)


## pbc data
data(pbc)
x<- pbc[1:312,]
surv.t<- x$time
cens<- as.numeric((x$status == 2))

x<- x[,c("age", "albumin", "alk.phos", "ascites", "bili", "edema", 
         "hepato", "platelet", "protime", "sex", "ast", "spiders", 
         "stage", "trt", "copper")]

## Not run: 
x$bili<- log(x$bili)
x$alb<- log(x$alb)
x$protime<- log(x$protime)
x$copper<- log(x$copper)
x$ast<- log(x$ast)

test.bic.surv<- bic.surv(x, surv.t, cens, 
                         factor.type=FALSE, strict=FALSE)
summary(test.bic.surv)

## End(Not run)