# Based on Hoyel et algorithm method, how to use HR in sensitivity analysis

Recently, Transition Probability troubled a lot, espicially in K-M curvers (PFS and OS curves). HR played a important role in sensitivity analysis, but i still can reconginezed the relationship between them, i read the Hoyel et algorithm method, the details were not mentioned.

## Comments

Andrew MunzerThank you for the links to the articles. Both describe methods to fit distributions to survival data. This type of best fit can be done in regression analysis software like R, STATA, SASS. This best-fit function is not supported by TreeAge Pro, which is a predictive tool.

However, once you have the best fit distributions for progression, you can use the distribution directly within TreeAge Pro to derive Markov transition probabilities by cycle based on that underlying distribution.

Please refer to the following TreeAge Knowledge Base article that we just published last night.

Generating Probabilities from Kaplan-Meier Survival Data

Andrew MunzerI would like to help, but I don't understand what you are asking. Please clarify.

GSHPChinaIn some situation, we can't obtain transition probability (TP) directly. espicially in survival analysis, K-M curves that help a lot, in three health state markov model (figure below), how to calculate TP ? Hoyel and Vakaramoko Diaby provide two method, but i still confoused with HR role in both method. In sensitivity analysis HR played important role, but i can't understand it.

GSHPChinaIt‘s very great a example for new learner

GSHPChinait's very kind of you, for more thing, in three state markov mode （Progression free state, Progression state , Death）, PFS curves calculate which two state transition probability? So as to OS ?

Andrew MunzerThere is no direct link between the PFS and OS curves and a Markov model. The PFS and OS curves can suggest transition probabilities for the Markov model, but this is not a perfect match. You may be able to use the reverse of the PFS curve for progression probabilities, but the other downstream transitions don't match perfectly with those underlying curves. I'm sorry I cannot provide a direct set of steps to use that data.

Vanessa MirskyHello, I also wanted to share a resource that might help. Below is a link to a 2015 HTA report done by the Norway government in assessment of several therapies for inoperable or metastatic malignant melanoma. If you go to pages 62- 97 it has details on the economic assessment and the methodology used to derive transition probabilities from alive to death and from progression free survival to progressed disease. The model was built using TreeAge Pro as well so could be helpful for you with answering your specific question.

https://www.fhi.no/globalassets/dokumenterfiler/rapporter/2015/rapport_2015_22_malignt_melanom_v3.pdf

I hope this helps!

Sincerely,

Vanessa

GSHPChinaMany paper estimated the transition probiblity with Pseudo-individual patient data were generated using the algorithm derived by Hoyle et al ( Hoyle MW, Henley W. Improved curve fits to summary survival data: application to economic evaluation of health technologies. BMC Med Res Methodol. 2011;11:139. doi:10.1186/1471-2288-11-139), All authors did not mention the relationship between PFS or OS and the transition probability in two tanslated states.

GSHPChinaGSHPChinaIn below picture, it gives details of Transition Probability calculation method.

GSHPChinaProgression to death, It is hard to understand. The clinical data is the CLL-8 trial

Andrew MunzerI don't see any reason you can't add formulas like you have presented in the table above into a TreeAge Pro model. However, you will need to work through the detailed calculations required for your model.

RaynaHello! Have you figured out the calculation of progression to death?

I guess that if it could be calculated as"1-S(t)/S(t-u)-Background mortality rate", is it right? What do you think?

Al ChrosnyDepending on the magnitude of the rates involved the "1-S(t)/S(t-u)-Background mortality rate" will lead to biases. It may be acceptable level of bias, but it should be explored with some sensitivity analysis.

Probabilites do not add. Classical way to combine independent probabilities is to use (1 - (1 - P1) * (1 - P2)). If P1 and P2 are dependent a Bayes formula should be used. It is very likely that S(t) and background mortality are dependent, since some background mortality may actually be captured by the S(t).

I would recommend using two different probability derivations in two versions of the model and see what is the impact on the results.

Another approach might be to assume certain distributions for transition probabilities and then calibrate the Markov model to observed progressions of the cohort. Some new calibration capabilities are coming in January 2020 release of TreeAge Pro.

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