convertmtol {PHInfiniteEstimates}

Convert a polytomous regression to a conditional logistic regression.

Description

Convert a polytomous regression to a conditional logistic regression.

Usage

convertmtol(xmat, str, yvec, subjects)

Arguments

xmat

regression matrix

str

stratum label

yvec

vector of responses

subjects

vector of subject labels passed directly to the output.

Details

Implements version of (Kolassa 2016). The multinomial regression is converted to a conditional logistic regression, and methods of (Kolassa 1997) may be applied. This function differs from convertbaselineltolr of this package in that the former treats the richer data structure of package mlogit, and this function treats a less complicated structure. Data in the example is the breast cancer data set breast of package coxphf.

Value

a data set on which to apply conditional logistic regression, corresponding to the multinomial regression model.

References

Kolassa JE (1997). “Infinite Parameter Estimates in Logistic Regression.” Scandinavian Journal of Statistics, 24, 523–530. doi:10.1111/1467-9469.00078.

Kolassa JE (2016). “Inference in the Presence of Likelihood Monotonicity for Polytomous and Logistic Regression.” Advances in Pure Mathematics, 6, 331-341. doi:10.4236/apm.2016.65024.

Examples

#Uses data set breast from package coxphf.
data(breast)
out<-convertstoml(Surv(breast$TIME,breast$CENS),breast[,c("T","N","G","CD")])
out1<-convertmtol(out[,c("T","N","G","CD")],out[,"chid"],out[,"choice"],
   out[,"patients"])
glmout<-glm.fit(out1$xmat,out1$y,family=binomial())
#In many practice examples, the following line shows which observations to retain
#in the logistic regression example.
moderate<-(fitted(glmout)<1-1.0e-8)&(fitted(glmout)>1.0e-8)
# Proportional hazards fit illustrating infinite estimates.
coxph(Surv(TIME,CENS)~ T+ N+ G+ CD,data=breast)
# Wrong analysis naively removing covariate with infinite estimate
coxph(Surv(TIME,CENS)~ T+ N+ CD,data=breast)
summary(glm((CENS>22)~T+N+G+CD,family=binomial,data=breast))

out2<-reduceLR(out1$xmat,yvec=out1$y,keep="CD")
bestcoxout<-coxph(Surv(TIME,CENS)~ T+ N+ G+ CD,data=breast,
   subset=as.numeric(unique(out1$subjects[out2$moderate])))