Nonidentifiability in Model Calibration and Implications for Medical Decision Making

Area of Science:

• Mathematical Modeling
• Biostatistics
• Cancer Research

Background:

• Model calibration estimates parameters by matching model outputs to targets.
• Nonidentifiability occurs when multiple parameter sets solve calibration problems, impacting decision-making.
• This study addresses the implications of nonidentifiability in model calibration and proposes methods to detect it.

Purpose of the Study:

• To evaluate the implications of nonidentifiability on optimal strategies in model calibration.
• To provide methods for checking the presence of nonidentifiability.
• To demonstrate how nonidentifiability affects treatment effectiveness estimates.

Main Methods:

• Calibrated a 3-state Markov model of cancer relative survival (RS).
• Performed calibration with and without an additional target (ratio between nondeath states).
• Utilized Nelder-Mead algorithm, collinearity, and likelihood profile analyses to assess nonidentifiability.

Main Results:

• Nonidentifiability was present when only RS was used, indicated by high collinearity and bimodal profiles.
• Different, equally fitting parameter sets yielded varying treatment effectiveness estimates (0.67 vs. 0.31 years).
• Adding an extra target improved identifiability, evidenced by a lower collinearity index and unimodal profile.

Conclusions:

• Equally likely parameter estimates from nonidentifiable models can lead to divergent conclusions.
• Incorporating checks for nonidentifiability and its implications is essential for standard model calibration.
• Addressing nonidentifiability ensures more robust and reliable outcomes in model-based decision-making.