Boot_CI {pARccs}R Documentation

Bootstrap confidence intervals for partial attributable risks (PAR) from case-control data

Description

With Boot_CI you can determine confidence intervals for partial atributable risks from case-control data. Therefor the nonparametric bootstrap is used with whose bootstrap replications eighter percentile confidence intervals or BCa confidence intervals are developed (or both, if you want to).

Usage

Boot_CI(D, E, C = NULL, model, stepwise = FALSE, scope = NULL, 
        nboot = 1000, alpha = 0.025, original, 
        type = c("perc", "bca", "both"), strat_boot = TRUE)

Arguments

D a vector which holds the case-control state ("1" = case, "0"=control)
E a matrix of the exposure factor/s (all of them have to be dichotomous!)
C a matrix of the confounder/s (all of them have to be categorical!)
model a model formula or an object of class "glm"
stepwise a logical value indicating whether a stepwise-selected model should be used in the computation, default is FALSE
scope a description of the variables which should be taken into account in the stepwise selection (upper model) and which variables are necessarily part of the model (lower model)
nboot number of (bootstrap-)replication, default is 250
alpha left- and right-hand error (default is 0.025), so you will get a 100*(1-2*alpha)% confidence interval
original a vector of the computed partial attributable risks from the original data
type a description of the type of confidence intervals which should be computed, "perc" stands for the percentile confidence interval, "bca" for the BCa confidence interval. You should choose "both" if you want to have calculated both types of confidence intervals. type="perc" is the default.
strat_boot a logical value indicating whether a stratified or a non-stratified bootstrap should be executed, default is TRUE

Details

The computation of the partial attributable risks from the data set does not take place in this function. You have to estimate them separately and pass the results through original to the function Boot_CI.

To generate the bootstrap sample in every replication step one may use eighter the stratified or the non- stratified method. If strat_boot=TRUE the sampling occurs separately from case-data and control-data, otherwise the sampling occurs from the complete data set.

If stepwise=TRUE the logistic regression model fitting the data from the bootstrap sample is choosen in a stepwise algorithm by the AIC. Therefor the argument scope is needed (look ?step for more information). Note, that at least the main effects of the exposure factors (and confounders) have to be part of the lower model, so that the stepwise algorithm is only used to identify the most significant interactions. If stepwise=FALSE the formula of the argument model is used to build a model fitting the data of the bootstrap sample.

The bootstrap replications for the partial attributable risks are used to build confidence intervals (as default 95% confidence intervals are computed). Therefor two methods are implemented: the percentile method (type="perc") and the bias-corrected and accelerated (BCa) method (type="bca"). In conjunction with the choice between these two methods you should take note of the great computational effort by using the BCa method.

Value

Boot_CI returns a named matrix with two columns: the first contains the lower endpoint, the second the upper endpoint.

Note

Also if there are only a single exposure factor/confounder you have to enter a matrix, so this will be a matrix with only one column.

The names of the variables (outcome, exposure factors, confounders) in the argument model have to be identically to the (column-)names of the entered data. Furthermore all given exposure factors and confounders have to be part of the argument model.

It is also important that the given variables in D, E and C are not defined as factors.

Validity of the interval estimation can only be taken for granted for data with simple random sampling, stratified random sampling or frequency-matching of controls.

Author(s)

Christiane Raemsch

References

Efron, B.; Tibshirani, R. (1986) Bootstrap methods for standard errors, confidence intervals, and other measure of statistical accuracy Statistical Science 1, 54-75

Efron, B.; Tibshirani, R. (1993) An Introduction to the Bootstrap Chapman & Hall (Monographs on Statistics and Applied Probability 57)

See Also

PAR

Examples


###### Computation of BCa confidence intervals #######
###### for the PAR if there are no confounders #######

set.seed(2007)
dicho           <- c(0,1)
cc_state        <- sample(dicho, 100, replace=TRUE)
exposure1       <- sample(dicho, 100, replace=TRUE, prob=c(0.7, 0.3))
exposure2       <- sample(dicho, 100, replace=TRUE, prob=c(0.4, 0.6))
relation        <- as.formula(cc_state~exposure1+exposure2)
data_exp        <- cbind(exposure1, exposure2)
PAR_exposures   <- PAR(cc_state, data_exp, model=relation)
CI_95           <- Boot_CI(D=cc_state, E=data_exp, model=relation, 
                           nboot=70,original=PAR_exposures, type="bca")

###### Computation of percentile confidence intervals #######
###### for the PAR if there are confounders           #######

set.seed(2008)
dicho           <- c(0,1)
cc_state        <- sample(dicho, 100, replace=TRUE)
exposure1       <- sample(dicho, 100, replace=TRUE, prob=c(0.7, 0.3))
exposure2       <- sample(dicho, 100, replace=TRUE, prob=c(0.4, 0.6))
cat_confounder  <- c(0,1,2,3)
confounder1     <- sample(cat_confounder, 100, replace=TRUE)
relation        <- as.formula(cc_state~exposure1+exposure2+confounder1)
data_exp        <- cbind(exposure1, exposure2)
conf            <- matrix(confounder1, ncol=1)
colnames(conf)  <- c("confounder1")
PAR_exposures   <- PAR(cc_state, data_exp, conf, model=relation)
CI_95           <- Boot_CI(D=cc_state, E=data_exp, C=conf, model=relation, 
                           nboot=70,original=PAR_exposures)


[Package pARccs version 0.1-1 Index]