Unusual analysis of survival outcomes

[Matt Williams]

Dear List,

I was wondering if people could give me their thoughts on a question I
was asked at work. It concerns a published randomised clinical trial.
The PMID is 19171716 and the full text is availiable at:

http://jco.ascopubs.org/content/27/7/1007.full.pdf+html

My specific question is about analysis of OS in the study. The Log-
rank test showed no statistically significant improvement in OS.
However, an they undertook an analysis at a fixed time point:

"and there was a significant increase in the 5-year OS by the
log( log(.)) transformation"

I am a little troubled by this - analysing OS at a single timepoint
seems problematic, and if we look at the curves, we see that the
"better" treatment, has a higher mortality rate initially.

I would be grateful if anyone else had any experience or advice on
similar matters.

Thanks,
Matt

[BXC (Bendix Carstensen)]

Basically, the log-rank test is a test of whether there is any difference between the groups UNDER the proportional hazards assumption.

What the authors apparently observe (I did not read the paper only your mail) is some sort of non-proportionality, or in plains statistical terms an interaction between group and time with respect to the mortality outcome.

As always, NEVER do a test.
ALWAYS fit a model, stating your assumptions.

So they should have said:

"We fitted a PH-model, and estimated the RR in the to be xx(aa-bb).
Since we suspected mortality to vary differently by time between the groups we realized that the PH-assumption was pretty goofy, so instead we fitted a model with separate time-effect in the two groups. Figure 1 shows the mortality in each group as a function of time, along with the estimated RR as a function of time since... It is clear that..."

Formally, they are not addressing the interaction on the mortality scale, but on the survival scale, but then why use the log-rank test?

The major problem for most non-statisticians is not the fitting of the interaction model (which for some odd reason has acquired a particular name of its own, "the stratified Cox-model"), it is the graphing of the underlying mortalities and the RR as a function of time. Graphs of the cumulative hazards/survival are not very informative.

A hint as to how this sort of analysis is done in practise and how to produce the graphs can be found in the paper:

@article{Carstensen:Plummer:2010:JSSOBK:v38i06,
author = "Bendix Carstensen and Martyn Plummer",
title = "Using Lexis Objects for Multi-State Models in R",
journal = "Journal of Statistical Software",
volume = "38",
number = "6",
pages = "1--18",
day = "4",
month = "1",
year = "2011",
CODEN = "JSSOBK",
ISSN = "1548-7660",
bibdate = "2010-09-16",
URL = "http://www.jstatsoft.org/v38/i06",
accepted = "2010-09-16",
acknowledgement = "",
keywords = "",
submitted = "2010-02-09" }

an applied work using this approach to mortality is:

@Article{pmid18815769,
Author="Carstensen, B. and Kristensen, J. K. and Ottosen, P. and Borch-Johnsen, K. ",
Title="{{T}he {D}anish {N}ational {D}iabetes {R}egister: trends in incidence, prevalence and mortality}",
Journal="Diabetologia",
Year="2008",
Volume="51",
Number="12",
Pages="2187--2196",
Month="Dec"
}
______________________________________________

Bendix Carstensen
Senior Statistician
Epidemiology
Steno Diabetes Center A/S
Niels Steensens Vej 2-4
DK-2820 Gentofte
Denmark
+45 44 43 87 38 (direct)
+45 30 75 87 38 (mobile)
b...@steno.dk http://BendixCarstensen.com
www.steno.dk

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