extension of Firth's logistic regression to cox regression model

Question

[ycding]

for a 2 by 2 table, if one entry has value of zero, we can run Firth's Logistic regression using "logistf" R package. what about the outcome or dependent variable is survival time, is there a corresponding R package for running Cox regression model for rare variants or copy number alterations?

thanks you,

Ding

Answer 1

[Kevin Blighe]

I believe that you are looking for the Cox proportional hazards regression model:

• Fit Proportional Hazards Regression Model

By a strange coincidence of statistics, the log likelihoods of a conditional logistic regression model are also equivalent to those of the Cox model. So, you can additionally fit a conditional logistic regression model if you have a matching stratum:

• Conditional Logistic Regression

Kevin

[ycding]

no, I worry that proportional hazards regression model does not fit well to data set with rare variants as predictor variables. for example, for a marker or gene, 3 of 100 patients carry a mutations (1) and all those three patients show long survival time (> 5 years, with no recurrence) compared to the other 97 patients (< 5 years) who do not carry the specific mutation. if considering survival time as a categorical dependent variable, 0 for < five years and 1 for > five years, one would use Firth's logistic regression model instead of regular logistic regression model for those sparse data. However, If one wants to consider survival time as continuous variable and fit a Cox proportional hazard regression model, the hazard ratio would be large or estimated inaccurately. I would think someone has already develop a modified Cox regression model to deal with those data set with rare variant variable as independent variable.

Answer 2

[ycding]

OK, "coxphf" R package is what I was looking for, which Implements Firth’s penalized maximum likelihood bias reduction method for Cox regression.It has been shown to provide a solution in case of monotone likelihood (nonconvergence of likelihood function). The program fits profile penalized likelihood confidence intervals which were proved to outperform Wald confidence intervals.

[Kevin Blighe]

Great - I will note this for future myself.