Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and...

Area of Science:

• Quantitative microbial risk assessment
• Statistical modeling
• Experimental design

Background:

• Parameter identifiability is foundational for sound statistical modeling, often overlooked compared to goodness of fit.
• Nonidentifiability indicates a lack of objective information in data for parameter estimation, implying underinformativeness in mechanistic models.

Purpose of the Study:

• To explore structural nonidentifiability and its implications in mechanistic models.
• To demonstrate tools for detecting nonidentifiable parameters.
• To emphasize the importance of identifiability in experimental design and data interpretation.

Main Methods:

• Algebraic proof of structural nonidentifiability in selected examples.
• Application of profile likelihood analysis.
• Utilization of Bayesian Markov Chain Monte Carlo with uniform priors.

Main Results:

• Structural nonidentifiability was demonstrated in mechanistic models for microbial risk assessment.
• Profile likelihood and MCMC methods were shown to detect nonidentifiable parameters.
• Nonidentifiable models can fit data well but yield flawed inferences and predictions.

Conclusions:

• Identifiability must be considered during experimental design and ethics approval to ensure data provide objective information.
• Bayesian methods applied to nonidentifiable models can introduce subjective information via priors.
• Structural nonidentifiability can lead to spurious models and inappropriate predictions.