simexaft {simexaft}

SIMEX Algorithm for Accelerated Failure Time Model with Covariates Subject to Measurement Error

Description

Implementation of the SIMEX algorithm for Accelerated Failure Time model with covariates subject to measurement error.

Usage

simexaft(formula = formula(data), data = parent.frame(), 
        SIMEXvariable, repeated = FALSE, repind = list(), 
        err.mat = err.mat, B = 50, lambda = seq(0, 2, 0.1), 
        extrapolation = "quadratic", dist = "weibull")

Arguments

formula

specifies the model to be fitted, with the variables coming with data. This argument has the same format as the formula argument in the existing R function "survreg".

data

optional data frame in which to interpret the varialbes occurring in the formula.

SIMEXvariable

the index of the covariate variables that are subject to measurement error.

repeated

set to TRUE or FALSE to indicate if there are repeated measurements for the mis-measured variables.

repind

the index of the repeated measurement variables for each mis-measured variable. It has an R list form. If repeated = TRUE, repind must be specify.

err.mat

specifies the variables with measurement error, If repeated = FALSE, err.mat must be specify.

B

the number of simulated samples for the simulation step. The default is set to be 50.

lambda

the vector of lambdas, the grids for the extrapolation step.

extrapolation

specifies the function form for the extrapolation step. The options are linear, quadratic and both. The default is set to be quadratic.(first 4 letters are enough)

dist

specifies a parametric distribution that is assumed in AFT model. This argument is the same as the dist option in the existing R function "survreg". These include "weibull", "exponential", "gaussian", "logistic", "lognormal", and "loglogistic".

Details

If the SIMEXvariable is repeated measured then you only need to use arguments repeated and repind without mention err.mat. The summary.simex will contain repind.

Value

coefficient

the corrected coefficients of the AFT model

se

the standard deviation of each coefficient

pvalue

the p-value for the hypothesis of that coefficient equal zero

scalreg

the estimate of the scale

theta

the estimates for every B and lambda

lambda

the vector of lambdas for which the simulation step should be done

B

the number of simulated samples for the simulation step.

formula

the model to be fitted in the survreg function

err.mat

the covariance matrix of the variables with measurement error

repind

the list contiains the names of the repeat measument variables

extrapolation

the extrapolation method: linear ,quadratic are implemented (first 4 letters are enough)

SIMEXvariable

the vector contains the names of the variables with meansurement error

Author(s)

Juan Xiong, Wenqing He and Grace Y. Yi

References

Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F. and Hothorn, T. (2011). mvtnorm: Multivariate Normal and t Distributions. R package version 0.9-9991, URL http://CRAN. R-project.org/package=mvtnorm.

He, W., Yi, G. Y. and Xiong, J. (2007). Accelerated Failure Time Models with Covariates Subject to Measurement Error. Statistics in Medicine, 26, 4817-4832.

Therneau, T. and Lumley, T. (2011). survival: Survival Analysis, Including Penalised Likelihood. R package version 2.36-10, URL http://CRAN.R-project.org/package=survival.

See Also

survreg, plotsimexaft

Examples

library("simexaft")
library("survival")
data("BHS")

dataset <- BHS

dataset$SBP <- log(dataset$SBP - 50)

###Naive AFT approach
formula <- Surv(SURVTIME,DTHCENS) ~ SBP + CHOL + AGE + BMI + SMOKE1 + SMOKE2

out1 <- survreg(formula = formula, data = dataset, dist = "weibull")

summary(out1)


###fit a AFT model with quadratic extrapolation
set.seed(120)

ind <- c("SBP", "CHOL")

err.mat <- diag(rep(0.5625, 2))

out2 <- simexaft(formula = formula, data = dataset, SIMEXvariable = ind, 
        repeated = FALSE, repind = list(), err.mat = err.mat, B = 50,
        lambda = seq(0, 2, 0.1),extrapolation = "quadratic", dist = "weibull")

summary(out2)







    #################### repeated measurements #################################
    data("rhDNase")

    ###true model
    rhDNase$fev.ave <- (rhDNase$fev + rhDNase$fev2)/2

    output1 <- survreg(Surv(time2, status) ~ trt + fev.ave, data = rhDNase, 
                    dist = "weibull")

    summary(output1)


    ####sensitive analysis#####
    set.seed(120)

    fev.error <- rhDNase$fev + rnorm(length(rhDNase$fev), mean = 0, 
                                    sd = 0.15 * sd(rhDNase$fev))

    fev.error2 <- rhDNase$fev2 + rnorm(length(rhDNase$fev2),mean = 0, 
                                    sd = 0.15 * sd(rhDNase$fev2))

    dataset2 <- cbind(rhDNase[, c("time2", "status", "trt")], fev.error, fev.error2)

    formula <- Surv(time2, status) ~ trt + fev.error

    ind <- "fev.error"


    ########naive model using the average FEV value####################
    fev.error.c <- (fev.error + fev.error2)/2

    output2 <- survreg(Surv(time2, status) ~ trt + fev.error.c, data = rhDNase, 
                    dist = "weibull")

    summary(output2)


    ######use simexaft and apply the quadratic extrapolation######
    formula <- Surv(time2, status) ~ trt + fev.error

    output3 <- simexaft(formula = formula, data = dataset2, SIMEXvariable = ind, 
            repeated=TRUE,repind=list(c("fev.error", "fev.error2")), err.mat=NULL, 
            B=50, lambda=seq(0,2, 0.1), extrapolation="quadratic", dist="weibull")
            
    summary(output3)