Can two Kaplan-Meier survival curves cross and still have proportional hazards?
0
1
Entering edit mode
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:

enter image description here

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
ADD COMMENT

Login before adding your answer.

Traffic: 1624 users visited in the last hour
Help About
FAQ
Access RSS
API
Stats

Use of this site constitutes acceptance of our User Agreement and Privacy Policy.

Powered by the version 2.3.6