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I got contrary results from my log-rank (not significant) versus my cox regression (significant) regarding the effect of my treatment variable with the aim of hypothesis testing. That's no real wonder, considering that the cox regression adjusts for 6 covariates other than my treatment. However, I'm confused about the proposition I can make. Without putting too much emphasis on the statistical significance, is the proposition correct that the treatment has a significant effect on survival?

I know that the logrank test equals a univariate cox regression (only considering treatment) and that it's critized by experts (The logrank test statistic is equivalent to the score of a Cox regression. Is there an advantage of using a logrank test over a Cox regression?). Further, the statement made by the logrank test compares the survival curves while the cox regression models the relationship of the variables used to the survival time. But what is the implication if the aim is hypothesis testing?

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Your "not-significant" log-rank test could be due to imbalance between treatment groups in terms of other outcome-associated variables. Also, in a Cox model, omitting any outcome-associated variable will tend to bias the magnitudes of the coefficients for included predictors toward 0. The log-rank analysis does just that: the only predictor you include is treatment, so the log-rank test might be underestimating the true treatment effect. Thus you typically want to adjust in some way for as many outcome-related predictors as reasonable.

The Cox multiple regression model is one way to adjust for other predictors. There are other ways that might better assess the causal effect of the treatment. The treatment-effect tag on this site labels many useful pages.

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  • $\begingroup$ Dear EdM, thanks a lot for your helpful answers. I've got another two questions: First, regarding the difference between the results of log-rank and cox-regression, the contrary results could be a result of: 1) less power in logrank (due to no covariates) 2) covariate adjustment (imbalance between groups in outcome-associated variables) in cox, 3) the tendency of cox models to zero, if outcome-associated variables are omitted, i.e., non-collapsibility (see answers (stats.stackexchange.com/questions/605915/…). Does that sound right? $\endgroup$
    – Sebastian
    Commented Apr 22, 2023 at 13:45
  • $\begingroup$ Second, regarding the treatment-effect tag, I read the posts with this tag and "survival" but tbh, I didn't see any advice for better models than cox models to test for treatment effects in clinical RCTs. Could you drop some names so I can read about it? Do you mean parametric models (Weibull etc.) which make an assumption of the underlying distribution of the hazard function? $\endgroup$
    – Sebastian
    Commented Apr 22, 2023 at 13:47
  • $\begingroup$ @Sebastian your first comment is correct, although the 3 issues are somewhat related to each other. With respect to treatment-effect, what I have in mind are "counterfactual" approaches that evaluate things like what would be predicted to happen if all individuals had received the treatment. That's less of a problem in RCTs than in observational studies. This book is a good introduction. On this site, @Noah frequently provides helpful explanations. $\endgroup$
    – EdM
    Commented Apr 23, 2023 at 15:13
  • $\begingroup$ Thank you! That's really helpful. One more question would be: assuming i have two models with 5 covariates each (5 sociodemographic vs. 5 clinical) plus the treatment effect. I can rule out the possibility of option 1 (power) and 3 (collapsibliity) due to the same amount of covariates (I assume). One model shows a significant treatment effect, the other doesn't. This would suggest that option 2 is in place, i.e. the adjustment for covariates between the groups leads to significant effects in one model (say sociodemographic), but not the other (say clinical) due to imbalances in covariates $\endgroup$
    – Sebastian
    Commented Apr 28, 2023 at 9:55
  • $\begingroup$ Somehow I'm confused about this. In my models, the sociodemographic gets a highily significant effect for treatment (and an HR of 1.8 in favor of treatment 2), the clinical one gets no signfiicant effect of treatment (and an HR of 1.3 in favor of treatment 2). If we assume only 1 covariate, let's say age, this would mean: the age at baseline is imbalanced. It has a significant effect on survival. Thus, the group difference gets larger (higher HR and lower p) under adjustment of age, as age was HIGHER in treatment 2 group or LOWER in treatment 2 group? $\endgroup$
    – Sebastian
    Commented Apr 28, 2023 at 10:06

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