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I am wondering whether and how can I back-calculate the log-likelihood ratio statistic from a Cox proportional hazard analysis with 1 degree of freedom.

For instance, if I have an hazard ratio (HR) of 0.1327, with standard error of the ln(HR) of 0.0584, what computations should I perform and which would eventually be the log-likelihood ratio statistic?

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You can calculate the Wald statistic by logHR/SE(logHR). The square of this Wald statistic is typically very close to the likelihood ratio test statistic, since they are asymptotically equivalent.

I don't think you can calculate the likelihood ratio statistic given only the estimated log HR and the standard error.

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  • $\begingroup$ I tried it a couple of times but I am not convinced. For instance, using Stata -> 'webuse drugtr' -> 'stcox age', I get HR=0.1328, lnHR=-2.0189, SE=0.0584 (thus Wald statistic=34.5703), whereas, according to the output, Log likelihood=-88.00 and LR chi2=23.82. Am I doing it wrong? $\endgroup$
    – Giuseppe Biondi-Zoccai
    Commented Feb 2, 2017 at 14:54
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    $\begingroup$ Indeed, I now recognize we cannot back calculate the LR statistic given only log HR and SE. $\endgroup$
    – Giuseppe Biondi-Zoccai
    Commented Mar 5, 2017 at 19:25

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