Validating Partitioned Survival Analysis models in Excel using TreeAge Pro

We were recently asked how to validate an Partitioned Survival Analysis (PartSA) Excel model using TreeAge Pro. The two models had different time cycles and so this made validating harder. This short article explains how to change to custom time cycles in TreeAge Pro to quickly validate your other models.

PartSA in TreeAge Pro

PartSA models in TreeAge Pro typically have annual or monthly time units. This article will show you how to convert the monthly or annual time units to a custom unit - such as weeks, day etc. 

The attached model compares different time scales and time reporting units. PartSA Different Time Scales.trex

Method to change time cycle

The model has two strategies, both use the same Exponential survival function with rate1 as the lambda parameter for the survival function. The top strategy uses a built in distribution and the bottom one uses an explicit expression for the survival function.

The variable CustomUnitsPerYear can be set to any desired value for the time unit such as 12 (monthly), 52 (weekly), (52/3) (three weekly), 365 (daily), (365.25/21) (three weekly), …  The model parameters of: _time; Time Horizon and Payoffs, need to be appropriately scaled.

See the picture below for how the CustomUnitsPerYear is used.  You may want to open the model in TreeAge Pro, as it may be easier to see the actual expressions within the application. Select the upper PartSA node and open PartSA View as below (your PartSA View, may be in the bottom tray, or you may drag it to the right tray as shown below).

In order to scale the payoffs by the custom time unit, select the terminal node and then in the PartSA View edit the Continuous cost by dividing it by CustomUnitsPerYear.  You would need to divide Interval costs, but not the others as they are “instantaneous” and should not be integrated over time.

Running Roll Back shows the two strategies are equivalent up to at least 4 decimal places.  You can increase the number of decimal places in Tree Preferences > Numeric Formatting to investigate further.

To review the results of both Strategies side by side, run Analysis > PartSA> Time Report on each of the PartSA nodes (top and bottom).

To confirm that the results are equivalent and consistent with their time units, scroll down on both reports to the very bottom and examine the Total Time and Payoffs: