How to conclude univariate results if not significant but cox model Likelihood is < .05?

Question

Hi supposed I have the results below from a cox multivariate model using the coxph function in R.

Is it fair to conclude that the overall model is significant and that sex, being Male is protective? that is holding drug constant and being Male reduces the hazard by a factor of 0.2 or 80%? can I conclude this even if the univariate itself is not significant but the overall mode ( likelihood < .05) is?

                 coef   exp(coef) se(coef)      z Pr(>|z|)  
sexM            -1.6032    0.2012   1.0516 -1.525   0.1354  
drugY           1.1922    3.2943   0.6275  1.900   0.0545 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

              exp(coef) exp(-coef) lower .95 upper .95
sexM    0.2012     4.9690   0.02562     1.581
drugY           3.2943     0.3036   0.96294    11.270

Concordance= 0.692  (se = 0.072 )
Likelihood ratio test= 6.96  on 2 df,   p=0.023
Wald test            = 5.74  on 2 df,   p=0.06
Score (logrank) test = 6.55  on 2 df,   p=0.038

Answer 1

You seem to have a very small data set, so you should be reluctant to interpret much from this model.

The Wald test for the overall model, at p = 0.06, was not "significant" by the usual p < 0.05 criterion. The individual coefficient p-values, both greater than 0.05, are based on Wald tests, also. So technically they wouldn't be considered "significant," either.

Admittedly, with small data samples, the likelihood-ratio test is considered more reliable. You could consider evaluating corresponding profile-likelihood confidence intervals for the regression coefficients, as illustrated in Section 3.4 of Therneau and Grambsch.

But when I see hazard ratios like these, on the order of 3 (drug Y/N) and 5 (female/male), I worry that perhaps the model is overfit and unreliable, as such extreme values aren't typical of clinical data. With 2 predictors in your model, I would worry about overfitting if you have fewer than 30 events or so in your data or if there is imbalance in drug status between the sexes.

To evaluate "holding drug constant and being Male" you might consider including an interaction term between sex and drug, to allow for different effects of the drug depending on sex. That would probably require more cases, however.

I think that the safest thing to conclude is that there is some evidence supporting associations of drug or sex with outcome, but that the details can't be reliably distinguished from these data. These could be considered pilot data to inform further study.