Time-Dependent Cox Model

Question

Consider the attached (dummy) sample csv file where two methods (i.e. Method A and Method B) are used to evaluate time to progression (PFS) in cancer patients. For each patient we also have the overall survival (OS).

data available as CSV from here

What I´d like to investigate is whether the PFS with method A or B better predicts overall survival of the patient.

I thought about two Cox models where the PFS (of method A or B) is included as a time-dependent covariate (using coxph) and later compare the performance of both models e.g. with C-index or Brier scores (e.g. with the pec library). Is this approach reasonable?

Unfortunately I already struggle with setting up the required dataframe correctly (because the methodA or B column that are generated though tmerge contain NA values despite disease progression in the relevant columns which does not correspond to the underlying data):

library(survival)

df_test <- read.table(file = "https://www.dropbox.com/s/vqns04vheqt57nk/cox.csv?dl=1", header = TRUE, sep=";")

df_test_methodA<-tmerge(data1=df_test,data2=df_test,id=Patient_ID,
                endpt = event(OS_time, OS_event),
                methodA = tdc(Method_A_PFS_time,Method_A_PFS_event))

  df_test_methodB<-tmerge(data1=df_test,data2=df_test,id=Patient_ID,
                    endpt = event(OS_time, OS_event),
                    methodB = tdc(Method_B_PFS_time,Method_B_PFS_event))

View(df_test_methodA)
View(df_test_methodB)

Your help and input would be highly appreciated. Thank you.

I've always thought it was rather strange that "PFS" was being discussed in the same sentence as "overall survival" since in models where the endpoint is "progression", death from other causes raises a censoring flag. — IRTFM, Apr 20 '18 at 21:00
Thanks for your comment. I think its a valid question to investigate the potential of PFS as a surrogate for OS (i.e. in my case to look whether PFS defined through method A or B is a better surrogate). There are quite a few studies on this topic listed in PubMed: see this [link](https://www.ncbi.nlm.nih.gov/pubmed/?term=%22Progression-free+survival%22+AND+surrogate+AND+%22overall+survival%22) — user86533, Apr 20 '18 at 21:08
It's only going to be reliably so if the predictors of progression strongly overlap and correlate with predictors of overall survival. That's only going to be the case where recurrence is followed shortly by death. Comorbidity will be a strong confounder. It will not be true when that is not the case, as happens with breast cancer and prostate cancer to name two common cancers with long-term survival after recurrence. I'm finding it hard to understand how this data is arranged. And shouldn't there be an "ordering-of-event" variable that shows whether method A or B came first? — IRTFM, Apr 20 '18 at 21:24
They study is on brain tumors with a very low survival rate (median <2 years). Method A and B cannot be ordered because they are only based on different criterion (different thresholds on imaging that had to be met to qualify for pregression) — user86533, Apr 20 '18 at 21:30
But you have subjects where both occurred. Wouldn't sequence need to be taken into account, since you would not choose to apply the second method unless progression occurred? — IRTFM, Apr 20 '18 at 21:32
As I´ve already said, this is not the case. Method A and B should just be compared to identify which of them is a better surrogate for OS. Sequence doesn´t need to be taken into account (you wouldn´t use both methods in combination). — user86533, Apr 21 '18 at 16:13

Time-Dependent Cox Model

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