5/2020: 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 older example models which use TreeAge Pro 2017 are no longer relevant, since July 2019 PartSA implementation of TreeAge uses differential equation solver for precise area under the curve calculations and Markov cycle concepts are actually detracting from the continuous nature of area and reward calculations. The new PartSA functionality does support number of event and state entry/exit rewards, which support various innovative extensions to building PartSA models. The fundamental concept to keep in mind in building PartSA models is the time unit used for expressing the survival/hazard functions and the appropriate reward per unit time. Please refer to TreeAge Pro help documentation and example models for detail explanations.

Only comments referring to the new PartSA functionality have been retained below.

## Comments

Tina CalentiHow would you incorporate a fixed palliative care cost for every death in a partitioned survival model (i.e., a fixed amount/same amount for every death regardless of length of time spent in PFS or progressed disease)? Thanks

Al ChrosnyThank you for an interesting question. Indeed the topic of Death cost or more generally State Entry or Exit costs within PartSA comes up. Mathematically speaking the Entry or Exit costs are not a direct function of the area under (or between) survival curve(s), they are a function of the derivative of the survival curve. In case of death cost it would be the derivative of the Overall Survival curve that determines how many people die per unit of time.

Surv(@T(n)) - Surv(@T(n+1)) => This gives you the number of people that die between time T(n) and T(n+1). So you could multiply that proportion of people dying in the time period by the fixed Death Cost.

An alternative approach might be to consider that PartSA method was really meant to be strictly an area under the curve method. However, it is morphing rapidly with all sorts of innovative additions, e.g. landmarking, state entry costs, etc.

Just a hypothetical question. For all other states the PartSA uses some sort of average per unit time costs that are then integrated over time. So actual cost is the function of the area under (between) curve(s). Isn't it a methodologically more consistent to treat Death costs on average bases and apply them to the area "above" the OS curve. I do not know the answer as to which approach is better, but it might be a good topic for research.

Finally, TreeAge Pro 2019 R2.0 scheduled for release in July will introduce a completely new support for building PartSA models, new PartSA node type and new PartSA analysis and reports. All of that will be integrated within the other capabilities of sensitivity analysis, etc. You will be able to convert a PartSA model to a Markov model structure. Also the Markov models will be able to generate PartSA like output (the survival curves).

Please reach out on e-mail to support@treeage.com if you would like to learn more about the TreeAge Pro 2019 R2.0 release.

Nataniel Lester-CollThanks for adding this- looks very useful. Tracking adverse events is integral to performing CEA for cancer treatments. Is there a way to do this in PartSA? E.g., many new cancer treatments how low rates (e.g., 1-3% range) of serious toxicities, but when they happen they are have serious health consequences and they are costly to manage. As far as I can tell, microsimulation is the best way to capture such events but could this be done in PartSA somehow? Thanks.

Andrew MunzerFirst, this model is no longer the best way to do PartSA. Our new PartSA feature handles the complex calculations internally without the need for difficult equations.

If there are important events required for a model, I don't think that PartSA is a good choice. Markov and simulation models include both health states and events while PartSA models only include health states. Both Markov and simulation models handle events well, but simulation models can store the event occurrence for each patient, providing more flexibility in a situation like you described.

In other words, I agree with you that a simulation model would likely be best for your situation.

Paul JuelicherWith the new PartSA feature, is there a way to use the area under the curve / time spend in the state as a reward variable in cost-effectiveness-PartSA models? Would be nice to see this in the CE rankings report.

Andrew MunzerNote that the Time report will already provide area under curve values by time unit.

If you also want this in the Rankings report for comparison by strategy, you can add an extra payoff for time in any specific state. Then enter a 1 for the continuous rewards for that payoff set for the appropriate survival curve node(s).

1. Tree Preferences > Payoffs

2. PartSA Info at appropriate Survival Curve nodes.

Tina CalentiWith regards to the question asked about modeling adverse events. With the new partitioned survival model abilities in TreeAge, can you not now incorporate the adverse effect by calculating probability of the event by survival time unit (so if your survival time unit is monthly, can you calculate a monthly probability of an adverse event and use that probability to incorporate the added monthly cost of the adverse effect when calculating monthly continuous costs, for instance)?

Al ChrosnyYes, you can do a lot of different things to represent costs and effectiveness of adverse events, but it does not mean that they will correctly represent the experience of the cohort. The whole point of using the area between the curves is to capture the proportions of people in those states and add up the average continuous costs over the period of the analysis. I think you will find that the area between survival curves is already computing the cumulative cost that is properly scaled by the proportion of remaining in the state. As long as you can express the costs as average per unit of time, you can use continuous costs.

The event costs can be added, but they occur at specific points in time, which may or may not be appropriate assumption for the entire cohort. Certainly, individual adverse events will happen at random times, which you cannot express as event costs at time x in PartSA. You can express them only as an average component of continuous cost.

For example STANDARD_AVERAGE_COST_PER_YEAR_IN_PostProgression + ADVERSE_EVENT_AVERAGE_COST_PER_YEAR_IN_PostProgreesion

Let's say 20% of post progression patients experience and adverse event and it costs 100K. Then ADVERSE_EVENT_AVERAGE_COST_PER_YEAR_IN_PostProgreesion = 0.2 * 100K

Obviously you can make these expressions time dependent and add more complex combinations of costs.

Tina CalentiThanks for your answer. I was wondering about adverse events related to chemotherapy given for 6 cycles and how you would incorporate those costs. For instance, if febrile neutropenia occurred in 15% of patients on chemo and each episode costs $7000 to treat, how do you incorporate this type of event?

Al ChrosnySince PartSA models make assumption of a common starting time and state membership defined by area between curves, you really have decide which simplification is more realistic for your model. I would suggest that you build a corresponding DES model and compare results to make sure that your implementation is correct.

If you are assigning Chemo costs as events already using Event cost schedule, you could add another component to those costs (1/6)*0.15*$7000.

If you are assigning cost of Chemo as part of average per unit time cost in a particular state, then add the a following component to your average costs 0.15*$7000.

I cannot say which one is a better for your particular case. I would recommend trying both approaches and validating them with a DES model and actual data.

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