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Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant classification errors. We present a novel method that leverages optimal decision theory to address this problem. As a preliminary step, we develop an analysis that uses an assumed prevalence and conditional probability models of diagnostic measurement outcomes to define optimal (in the sense of minimizing rates of false positives and false negatives) classification domains. Critically, we demonstrate how this strategy can be generalized to a setting in which the prevalence is unknown by either (i) defining a third class of hold-out samples that require further testing or (ii) using an adaptive algorithm to estimate prevalence prior to defining classification domains. We also provide examples for a recently published SARS-CoV-2 serology test and discuss how measurement uncertainty (e.g. associated with instrumentation) can be incorporated into the analysis. We find that our new strategy decreases classification error by up to a decade relative to more traditional methods based on confidence intervals. Moreover, it establishes a theoretical foundation for generalizing techniques such as receiver operating characteristics by connecting them to the broader field of optimization. [ABSTRACT FROM AUTHOR]

This paper presents a practical numerical method for separating and estimating growth and mortality coefficients in stage- or size-structured populations using only observations of the relative or absolute abundance of each stage. The method involves writing a system of linear ordinary differential equations (ODEs) modelling the rate of change of abundance. The solution of the differential system can be numerically approximated using standard (e.g. sixth-order Runge-Kutta-Felhberg) methods. An optimization problem whose solutions yield ‘optimal’ coefficients for a given model is formulated. The ODE numerical integration technique can then be employed to furnish required function and gradient information to the optimization algorithm. The data-fitting software package ODRPACK is then successfully employed to estimate optimal coefficients for the ODE population model. Simulation experiments with four- and eight-stage model populations illustrate that the method results in the successful estimation of coefficients of mortality and growth from abundance data. [ABSTRACT FROM PUBLISHER]