When is Log rank preferred over Univariable Cox regression?

Hi all,

This may sound like an amateur-ish question; but is there ever an advantage for log rank over univariable cox regression? The latter seems to do exactly the same thing log rank does + (a) quantify the relationship (HRs & CIs), and (b) accommodates continuous variables, which otherwise would have to be dichotomized (or categorized) for comparisons using Log rank/Breslow/Tarone-Ware…etc.

Thank you,
Eslam

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No advantage and even disadvantages:

  • log-rank test does not work for continuous exposures
  • it does not allow for covariate adjustment
  • the usual P-value from log-rank may not be as accurate as the likelihood ratio \chi^2 statistic from Cox PH

For the life of me I don’t know why we still teach log-rank and why it keeps appearing in medical and epidemiologic journals. It has all the assumptions of Cox and more. Glad you raised the issue.

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@f2harrell, another version I also see frequently used is the stratified log-rank which I think would also be inferior to the corresponding stratified Cox regression for the same reasons. A somewhat related question I have is what is the practical value of a stratified Cox model vs. the unstratified Cox model? Since the stratified Cox model estimates separate hazard functions for each stratum, would that lead to loss of precision compared with the unstratified model? In addition, I would assume that since a stratified Cox produces HRs that are weighted averages of the stratum-specific HRs, it makes the assumption that these weighted HRs are constant across strata, which is not necessarily a very plausible assumption?

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Good points. A stratified Cox model makes obsolete a stratified log-rank test. Stratification does not normally cause a loss of precision of the remaining \hat{\beta}, but it does cause a loss of precision of absolute survival probability estimates.

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Good to know - appreciate the insight!