8/2019: Note that the original article from 2017 described how to create a Partitioned Survival Analysis (PartSA) model within the existing Markov structure. This is no longer necessary as we now support PartSA models as a new model type. For more information, go to the Partitioned Survival Analysis page on our website.
Partitioned Survival Analysis (PartSA) has been used often in the context of evaluating oncology treatments. PartSA models differ from state progression models in an important way. For detail description of PartSA you can refer to the following article:
The following model built in TreeAgePro (PartSA_2Markov_1DES v1.trex) can be used to see how State Transition models (both Markov and DES) differ from PartSA model. The "PartSA Markov" strategy still uses Markov node but simply iterates through single state for the duration of the analysis. The calulcations of areas under the curves and between the curves is implemented through Event Rewards. The same Overall Survival and Progression Free Survival (Exponential distributions with 2 different lambda parameters) are used in all three models to draw Time - To - Event samples for DES, to calculate Transition Probabilities for Markov State Transition Model and to calculate the partitions of the cohort in Progression Free (PFS) Area, Post Progression (PP) Area under these curves.
The models use 2 different costs and 2 different utilities for PFS and PP areas. These values can be changed to represent different scenario. The model can be evaluated with microsimulation or samping+microsimulation. It is possible to run Cohort Analyses on the individual Markov nodes (DES nodes require microsimulation).
You can change the values of the distribution parameters to see how the results generated by the models change. When Lambda for OS (e.g. 0.04) is small and Lambda for PFS (e.g. 0.7) is order of magnitude or more larger than Lambda OS than the results between State Transition Models (Markov and DES) and the Partitioned Survival Analysis model are relatively close. However, when LambdaPFS and LambdaOS get close to each other, you will get results that are quite different between PartSA model and the State Transition models (DES and Markov). Try LambdaOS of 0.4 and LambdaPFS of 0.7 and you will see that results between PartSA and Transition model are diverging.
In case of Exponential survival curves the exact calculations for the area's under the curve are possible with closed form formulas. Refer to the attached Excel document which calculates the areas under the exponential curves and the corresponding costs and utilities for reference.
For further background on the mathematical formulas behind the PartSA refer to:
In conclusion the PartSA is a different technique for estimating Costs and Utilities of treatment. It makes different simplifying assumptions about the patient histories in Post Progression state(s). In particular using the same Survival Curves for PartSA and State Transition Models will lead to increasingly different results, where OS and PFS curves converge close to each other.
PartSA models with different survival curves can be easily accommodated in TreeAgePro using either tables (using the empirical Kaplan-Meier curves) or other parametric distributions (e.g. Weibull, etc.). Additional survival curves could be used to partition the cohort into additional groups using analogous area under the curve calculations.