Hi everyone,
I'm trying to do a partitioned survival analysis (PartSA) to model a cohort of patients directly from survival data in the trial and evaluate cost-effectiveness of two different treatments. There are Kaplan-Meier OS and PFS curves published for one of these trials, so I have fitted both curves separately with Weibull distribution and extrapolated them to the time horizon of interest (15 years). However, the extrapolated PFS curve turned out to be higher than extrapolated OS curve, which obviously does not make sense for the analysis.
I'm sure this is happening quite a lot because the fact that correlation between time-to-event outcomes is not considered is one of the major limitations of this model. I was wondering if there any practical solutions on how to troubleshoot this. Is it possible to transform the data in any way to overcome this problem?
Many thanks,
Eugenia
Eugenia, is the extrapolated PFS curve higher than extrapolated OS curve during all the survival time? Or only in the end of the survival time? Could you show the kaplan meier curves?
Not just at the end of the survival time, but pretty much for the whole extrapolation. Please see the chart below. As you can see they diverge right where KM curves end.
Hi Eugenia,
From visual inspection, it seems that the extrapolated survival curve has not fitted very well. It would be worth checking other parametric survival functions and evaluate their goodness of fit by AIC-BIC relative to each other and then select the best fit. Have you read NICE DSU guidance ( http://nicedsu.org.uk/wp-content/uploads/2016/03/NICE-DSU-TSD-Survival-analysis.updated-March-2013.v2.pdf )? Maybe you might not have this problem (PFS > OS) later on.
All the best,
Masnoon.
I agree. Other parametric model could be better. In reality at the beginning the weilbull model worked well.
The main problem is that we usually have a small informative period to extrapolate to a much longer time.
Thanks for your help. I've seen these recommendations on using the distribution that has the lowest AIC before. Based on AIC, lognormal distribution would be the best fit for my data. But I'm really struggling to fit it on. I was using Hoyle & Henley method here:Article Improved curve fits to summary survival data: Application to...
There is an R code that provides you with an output for different types of distribution. So I've got the values for intercept and log_scale for lognormal distribution. But I'm struggling to find out the formulas for the shape and scale parameters that I need in order to build the graph.
As far as I understand, the survivor function for lognormal is 𝑆(𝑡)=1−Φ((𝑙𝑜𝑔(𝑡)−𝜇)/𝜎). So I need to estimate the parameters 𝜇 and 𝜎, but I'm not entirely sure how they are related to intercept and log_scale.
mean=exp(intercept +log_scale/2)
var=exp(2*intercept+log_scale)*(exp(log_scale)-1)
sd= square root(var)
let me know if it works well
Thank you very much for your help! I've managed to do the calculations and the lognormal distribution fitted much better indeed.
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