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I am not sure how to interpret the results given from the Cox PH model and the Kaplan-Meier curves. The analyses are conducted in R.

In an observational study, 172 patients are categorized based on tumor profileration status (Ki67): 0-2%, 3-4%, 5-10% and >10% (an index of tumor activity).

I am investigating the correlation between Ki67-status and the event of tumor recurrence.

library(survival) library(survminer)

Call:
coxph(formula = Surv(time.to.recurrence, event.recurrence) ~ 1 + 
    factor(ki67), data=p)

  n= 172, number of events= 30 
   (4 observations deleted due to missingness)

                  coef exp(coef) se(coef)     z Pr(>|z|)   
factor(p$ki67)1 0.1109    1.1172   0.5781 0.192  0.84793   
factor(p$ki67)2 0.7136    2.0412   0.6065 1.176  0.23942   
factor(p$ki67)3 1.8830    6.5731   0.6774 2.780  0.00544 **

I want to test if the proportional hazard assumption is violated:

                   rho chisq     p
factor(p$ki67)1  0.064 0.123 0.726
factor(p$ki67)2 -0.151 0.702 0.402
factor(p$ki67)3 -0.222 1.450 0.229
GLOBAL              NA 4.686 0.196

By using ggcoxzph(), I have the following print:

Shoenfeld residuals

Interpretation

1) Each covariate is non-significant correlated to time - thus, time independent supporting that the proportional hazard assumption is valid and the model is fit for use

2) The graphic visualizes a non-random pattern further supporting the PH assumption

The Kaplan-Meier analysis was subsequently conducted

Call: survfit(formula = Surv(time.to.recurrence, event.recurrence) ~ 1 + 
    factor(ki67), data = p, conf.type = "log")

   4 observations deleted due to missingness 
                  n events median 0.95LCL 0.95UCL
factor(p$ki67)=0 30      4     NA      NA      NA
factor(p$ki67)=1 86     12     NA     124      NA
factor(p$ki67)=2 44      9     NA     118      NA
factor(p$ki67)=3 12      5     56       7      NA

The Kaplan-Meier curves were then computed:

Kaplan-Meier Curves

1) How can this graph be interpreted? Intuitively, that curves should not be crossed if the PH assumption is valid?

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The only crossings of survival curves in your data are between the first 2 groups (0-2% and 3-4% Ki67+), between which there is no significant difference in survival (HR 1.1, p-value 0.85). This is not of concern with respect to the proportional hazard assumption. If you took the 116 cases initially at risk in those 2 groups and randomly broke them into groups of the sizes of those two groups (30 and 86) I suspect that you would find similar "crossings" in Kaplan-Meier curves, as one or another group randomly has higher survival fractions at different times. That is, what you see is normally expected variability between essentially identical survival curves.

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