Can two Kaplan-Meier survival curves cross and still have proportional hazards?
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2.0 years ago
curious ▴ 530

The way I understand cox regression is that it works on the assumption that the hazard curves for groups are proportional and as such do not cross on a plot.

So I have this experiment that is looking at the effect of low or high expression levels of gene 1 and gene 2 on survival of cancer patients using cox regression.

I am using low expression of gene 1 and gene 2 as my reference level (red curve on plot below) to compare all the other curves against.

I make my plot:

There is extensive crossover between the red and blue curve, which make me worry I am breaking the proportional hazard assumption when comparing those curves with cox regression :(

I run the cox.zph function, which I understand to be a statistical test for proportional hazards. None of the p values for my groups are <0.5, which makes me think I am not breaking the assumption regardless of the visual crossover on the plot.

This is my general code approach:

res.cox <- coxph(Surv(new_death, death_event) ~ event_rna , data=all_clinical_df)
res.cox.extended <- summary(res.cox)
test_proportional_hazard <- cox.zph(res.cox)


This is the output of cox.zph:

                               rho  chisq     p
event_rna high_gene1_low_gene2  -0.1651 1.5135 0.219
event_rna low_gene1_high_gene2  -0.0422 0.0981 0.754
event_rna high_gene1_high_gene2 -0.1251 0.8244 0.364
GLOBAL                          NA 1.6660 0.645


This is the summary of the coxph output:

Call:
coxph(formula = Surv(new_death, death_event) ~ event_rna, data = all_clinical_df)

n= 170, number of events= 56

coef exp(coef) se(coef)     z Pr(>|z|)
event_rna high_gene1_low_gene2  1.217946  3.380239 0.440276 2.766  0.00567 **
event_rna low_gene1_high_gene2  0.008347  1.008382 0.571929 0.015  0.98836
event_rna high_gene1_high_gene2 1.237366  3.446522 0.404320 3.060  0.00221 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef) exp(-coef) lower .95 upper .95
event_rna high_gene1_low_gene2     3.380     0.2958    1.4262     8.011
event_rna low_gene1_high_gene2      1.008     0.9917    0.3287     3.094
event_rna high_gene1_high_gene2     3.447     0.2901    1.5604     7.613

Concordance= 0.648  (se = 0.035 )
Likelihood ratio test= 17.57  on 3 df,   p=5e-04
Wald test            = 14.8  on 3 df,   p=0.002
Score (logrank) test = 16.66  on 3 df,   p=8e-04


I have been on this for a while and would be extremely grateful for any suggestions.

cox regression survival • 2.1k views