# Distribution of the partial likelihood ratio test in Cox model?

If I replace the partial likelihood of the Cox model

https://en.wikipedia.org/wiki/Proportional_hazards_model#The_Cox_model

instead of the likelihood in the likelihood ratio test

https://en.wikipedia.org/wiki/Likelihood-ratio_test

What is the distribution of this test statistic? Is it still $$\chi^2_q$$?

The partial likelihood ratio test is asymptotically $$\chi^2_q$$ as well, under conditions that guarantee consistency and asymptotic normality of the partial maximum likelihood estimators. This is a standard result in several textbooks.