MixtureLogitAFT: Fit Logistic-AFT Location-Scale Mixture Regression Models

In MixtureRegLTIC: Mixture Regression Models for Left-Truncated and Interval-Censored Data

Description

A function to fit parametric logistic-AFT location-scale mixture regression models with nonsusceptibility for LTIC data.

Usage

MixtureLogitAFT(formula, eventprobreg = ~1, locationreg = ~1, scalereg = ~1,
var.entry, var.mixturetype = NULL, var.weight = NULL,
data, time.origin = 0, shape = NULL)

Arguments

formula	A formula object specifies the regression response using a survival object of the same form as from the Surv function. The status indicator is 0=right censored, 1=event at time, 2=left censored, and 3=interval censored.
eventprobreg	The formula for covariates of the logistic regression part for the event (susceptibility/non-cure) probability in the mixture model. The eventprobreg = NULL corresponds to the one-component model.
locationreg	The formula for covariates of the location regression part in the AFT submodel.
scalereg	The formula for covariates of the scale regression part in the AFT submodel.
var.entry	A variable specifies each study subject's left-truncated time at the entry in the follow-up study. The var.entry = NULL corresponds to no left-truncation.
var.mixturetype	A variable specifies the number of fitted component(s) in the mixture regression model for each study subject. The defined value of 1 is for "1-component", and the value of 2 is for <e2><80><9c>2-component with cure<e2><80><9d>. All subjects in the same stratum must have the same defined values. If all strata have either one-component or two-component models, then var.mixturetype needs not to be included in the data.frame by setting var.mixturetype = NULL.
var.weight	A numeric variable specifies the weight for each observation contributed differently to the log-likelihood. The default var.weight = NULL corresponds to equal contributions.
data	A data.frame contains the variables named in the formula, eventprobreg, locationreg, scalereg, var.entry, var.mixturetype and var.weight.
time.origin	A numeric value specifies the time origin in the AFT submodel. The default time.origin = 0.
shape	The default shape = NULL indicates the shape parameter of the generalized log-gamma distribution to be estimated from the data. Otherwise, a numeric value assigns the fixed shape parameter of a specified generalized log-gamma distribution of the error variate to be fitted in the AFT submodel, or a character string "logistic" stands for the logistic distribution of the error variate to be fitted in the AFT submodel.

Details

This function fits the logistic-AFT location-scale mixture regression models with nonsusceptibility/cure for LTIC data. The event time is assumed following either a generalized gamma distribution or a log-logistic distribution, i.e., the error variate in the AFT submodel has a generalized log-gamma distribution or a logistic distribution. The family of generalized gamma distributions for the event time includes many important distributions as its special cases: Weibull (shape = 1), lognormal (shape = 0), and reciprocal Weibull (shape = -1) distributions. Ordinarily, the shape parameter of the generalized gamma distribution is estimated jointly with the logistic, location and scale regression parameters. If a special error distribution is preferred, then the argument shape should be specified.

To obtain the maximum likelihood estimators of the parameters in the logistic-AFT location-scale mixture regression model, R function optim() is applied using the negative log-likelihood function and its first and second derivatives.

As indicated in the scenario (e) of Figure 1 in Chen et al. (2013), some strata may present with nonsusceptibility/cure and the other strata without that. This function can simultaneously handle situations in which both one-component and two-component location-scale regression models jointly emerge as in the above-mentioned scenario. The usage of var.mixturetype facilitates this kind of analysis. However, a consideration of the joint one-component and two-component mixture regression models needs special caution in selecting the covariates and interpreting the corresponding parameter estimates in the logistic regression part.

Note

To obtain the standard errors and confidence intervals of the estimated regression parameters, formulas of the associated first and second derivatives were given in Appendix A of Chen et al. (2013) by the chain rule and the Leibnitz rule. An unexported R function HGNlogL() calculates the negative log-likelihood and the corresponding first and second derivatives with several unexported R functions. In addition, a FORTRAN program with algorithm and codes in Moore (1982) were used to compute the incomplete gamma integral.

References

Chen CH, Tsay YC, Wu YC and Horng CF. Logistic-AFT location-scale mixture regression models with nonsusceptibility for left-truncated and general interval-censored data. Statistics in Medicine, 2013; 32:4285<e2><80><93>4305.

Moore RJ. Algorithm AS. 187: derivatives of the incomplete gamma integral. Applied Statistics - Journal of the Royal Statistical Society, Series C, 1982; 31:330<e2><80><93>333.

See Also

NPMLEsurv, plotMixture, plotNPMLEsurv, plotResidual, printMixture

Examples

data(simLTICdataA)

##### fit the logistic-AFT location-scale model for LTIC data
fit=MixtureLogitAFT(formula=Surv(time1,time2,status)~1,
    eventprobreg=~X1,locationreg=~X1,scalereg=~X1,
    var.entry="entry",data=simLTICdataA)

##### print regression results of the fitted regression model
printMixture(fit)

##### plot estimated survival curves
#win.graph(width=18,height=10)
#par(mfrow=c(1,2))
plot.fit=plotMixture(fit)
legend(20,0.4,legend=plot.fit$legend,col=plot.fit$col,lty=plot.fit$lty,
       title=" Strata (Case / Total)")

plotD.fit=plotMixture(fit,dist="cond")
legend(3,0.4,legend=plotD.fit$legend,col=plotD.fit$col,lty=plotD.fit$lty,
       title=" Strata (Case / Total)")

##### estimate the NPMLE
est=NPMLEsurv(formula=Surv(time1,time2,status)~X1,var.entry="entry",data=simLTICdataA)

##### plot estimated event curves with both the regression model and NPMLE
#win.graph(width=18,height=10)
#par(mfrow=c(1,2))
plot.fit=plotMixture(fit,curve="event",col=c("red","blue"))
legend(20,1,legend=plot.fit$legend,col=plot.fit$col,lty=plot.fit$lty,
       title=" Strata (Case / Total)")
par(new=TRUE)
plot.NPMLE=plotNPMLEsurv(est,curve="event",lty=c(2,2),col=c("red","blue"))

plotD.fit=plotMixture(fit,curve="event",dist="cond",col=c("red","blue"))
legend(3,1,legend=plotD.fit$legend,col=plotD.fit$col,lty=plotD.fit$lty,
       title=" Strata (Case / Total)")
par(new=TRUE)
plotD.NPMLE=plotNPMLEsurv(est,dist="cond",curve="event",lty=c(2,2),col=c("red","blue"))

MixtureRegLTIC documentation built on May 1, 2019, 9:21 p.m.