Constructing confidence intervals for likelihood ratio test from clogit()

Question

I am working on a project for a professor, and I have been asked to construct a confidence interval for the likelihood ratio test from clogit() using R.

clogit(obesity_status ~ bmi + strata(pair), data = twindata)

It looks like clogit() returns 3 p-values for the likelihood ratio test, Wald test, and score test. More specifically, when I run summary(model), it returns:

Likelihood ratio test= 2.41  on 1 df,   p=0.02
Wald test            = 3.25  on 1 df,   p=0.06
Score (logrank) test = 4.42  on 1 df,   p=0.02

But, when I run confint(model), it gives me a confidence interval of:

0.7, 95

But how could this be if the p-value for the LRT is < 0.05? Is it because it's returning a CI based on the Wald test? If so, is there a way to get the confidence interval based on the likelihood ratio test with p = 0.02?

Thank you for your help.

Answer 1

It's a Wald confidence interval. There is no built-in support for likelihood or score confidence intervals for clogit, but it's fairly straightforward to get a likelihood interval by profiling in this single-parameter case. We can use the offset function to force a specific value of the coefficient and work out the resulting likelihood.

Example, from the survival package since you didn't supply one

> data(infert)
> clogit(case ~ spontaneous +  strata(stratum), data=infert)
Call:
clogit(case ~ spontaneous + strata(stratum), data = infert)

              coef exp(coef) se(coef)     z        p
spontaneous 1.1768    3.2441   0.2315 5.083 3.71e-07

Likelihood ratio test=33.76  on 1 df, p=6.228e-09
n= 248, number of events= 83 
> clogit(case ~ spontaneous +  strata(stratum), data=infert)$loglik
[1] -90.77935 -73.89824

Now

> threshold<- -73.89824 -qchisq(0.95,1)
> threshold
[1] -77.7397
> f<-function(beta) clogit(eval(bquote(case ~ offset(.(beta)*spontaneous) +  strata(stratum))), data=infert)$loglik-threshold
> f(1.176)
[1] 3.841457

We need a number above the true upper limit and a number below the true lower limit. I'll pick 2 and 0

> uniroot(f,lower=1.1768,upper=2)$root
[1] 1.890439
> uniroot(f,upper=1.1768,lower=0)$root
[1] 0.5850132

So, (0.585,1.89) is the confidence interval.