Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models

• Published in: Journal of statistical planning and inference Vol. 138; no. 9; pp. 2595 - 2606
• Main Author: Atkinson, Anthony C.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.09.2008; New York,NY Elsevier Science; Amsterdam
• Subjects: Combinatorics; Combinatorics. Ordered structures; D-optimum designs; Designs and configurations; Equivalence theorem; Exact sciences and technology; Experimental design; General topics; Mathematical analysis; Mathematics; Mixed model; Multivariate response; Probability and statistics; Schedule of observations; Sciences and techniques of general use; Sequences, series, summability; Simulated covariance matrix; Statistics; Time series; Mixed model; Schedule of observations; Time series; Equivalence theorem; D-optimum designs; Multivariate response; Simulated covariance matrix; Inclusion theorem; Non linear regression; D optimality; Statistical decision; Statistical method; Statistical regression; Covariance; Simulation; Correlation analysis; Regression model; Experimental design; Non linear model; Random effect; Optimal design(statistics); Analytical function
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2008.03.002

The problem considered is that of finding an optimum measurement schedule to estimate population parameters in a nonlinear model when the patient effects are random. The paper presents examples of the use of sensitivity functions, derived from the General Equivalence Theorem for D-optimality, in the construction of optimum population designs for such schedules. With independent observations, the theorem applies to the potential inclusion of a single observation. However, in population designs the observations are correlated and the theorem applies to the inclusion of an additional measurement schedule. In one example, three groups of patients of differing size are subject to distinct schedules. Numerical, as opposed to analytical, calculation of the sensitivity function is advocated. The required covariances of the observations are found by simulation.