Optimized Piecewise Exponential Modeling Using Dynamic Programming: An Illustration From Treatment-Naïve Advanced Melanoma
Author(s)
Oguzhan Alagoz, PhD1, Murat Kurt, BS, MS, PhD2.
1University of Wisconsin-Madison, Middleton, WI, USA, 2Director, Iovance Biotherapaeutics, Inc., Philadelphia, PA, USA.
1University of Wisconsin-Madison, Middleton, WI, USA, 2Director, Iovance Biotherapaeutics, Inc., Philadelphia, PA, USA.
OBJECTIVES: Spline-based and non-parametric piecewise survival models are used as flexible alternatives to standard parametric models in capturing sophisticated hazard trends manisfested by the mechanisms of action of modern oncology treatments. However, locations of knots in these models are often decided in an unsystematic fashion with limited methodological guidance. We devised a dynamic programming approach to optimize the placement of knots for piecewise exponential survival modeling.
METHODS: The approach partitioned smoothed, cumulative hazard function into a prespecified limit number of linear segments. The objective was to minimize the cumulative Bayesian Information Criteria (BIC) associated with all segments. BIC score for each candidate segment was indirectly estimated by minimizing sum of squared-errors for the corresponding linear fit. Locations of knots were optimized in a backward recursion using estimated BIC scores of adjacent candidate segments and penalties associated with each knot. The approach was illustrated using published progression-free survival (PFS) and overall survival (OS) data with 10-year follow-up from the CheckMate-067 trial in treatment-naive advanced melanoma. To avoid overfitting, for each endpoint, up to 2 knots were used and tail segments were required to cover at least 20% and 10% of the total number of corresponding events in primary and sensitivity analyses, respectively.
RESULTS: Across all arms, first and second knots were placed between months 21-24 and months 32-38, respectively, for OS and between months 3-9 and months 6-16, respectively, for PFS. In the sensitivity analysis, across all arms and endpoints, optimized locations of knots were no earlier than their counterparts in the primary analysis. For each endpoint, optimized locations of knots and fractions of events covered in each segment showed high similarity between nivolumab-containing arms.
CONCLUSIONS: Our modeling approach offers a scalable and flexible framework optimizing knot locations to assist long-term survival projections as well as sample size and power calculations in clinical trial design.
METHODS: The approach partitioned smoothed, cumulative hazard function into a prespecified limit number of linear segments. The objective was to minimize the cumulative Bayesian Information Criteria (BIC) associated with all segments. BIC score for each candidate segment was indirectly estimated by minimizing sum of squared-errors for the corresponding linear fit. Locations of knots were optimized in a backward recursion using estimated BIC scores of adjacent candidate segments and penalties associated with each knot. The approach was illustrated using published progression-free survival (PFS) and overall survival (OS) data with 10-year follow-up from the CheckMate-067 trial in treatment-naive advanced melanoma. To avoid overfitting, for each endpoint, up to 2 knots were used and tail segments were required to cover at least 20% and 10% of the total number of corresponding events in primary and sensitivity analyses, respectively.
RESULTS: Across all arms, first and second knots were placed between months 21-24 and months 32-38, respectively, for OS and between months 3-9 and months 6-16, respectively, for PFS. In the sensitivity analysis, across all arms and endpoints, optimized locations of knots were no earlier than their counterparts in the primary analysis. For each endpoint, optimized locations of knots and fractions of events covered in each segment showed high similarity between nivolumab-containing arms.
CONCLUSIONS: Our modeling approach offers a scalable and flexible framework optimizing knot locations to assist long-term survival projections as well as sample size and power calculations in clinical trial design.
Conference/Value in Health Info
2025-11, ISPOR Europe 2025, Glasgow, Scotland
Value in Health, Volume 28, Issue S2
Code
MSR157
Topic
Economic Evaluation, Health Technology Assessment, Methodological & Statistical Research
Disease
Oncology