Design considerations for small experiments and simple logistic regression

• Published in: Journal of statistical computation and simulation Vol. 79; no. 1; pp. 81 - 91
• Main Authors: Russell, K. G., Eccleston, J. A., Lewis, S. M., Woods, D. C.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.01.2009; Taylor & Francis Ltd
• Subjects: Approximation; Asymptotic methods; Bias; Design of experiments; Generalized linear models; Integrated mean square error; Maximum penalized likelihood; Optimality; Regression analysis; Statistical methods
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949650701609006

Inference for a generalized linear model is generally performed using asymptotic approximations for the bias and the covariance matrix of the parameter estimators. For small experiments, these approximations can be poor and result in estimators with considerable bias. We investigate the properties of designs for small experiments when the response is described by a simple logistic regression model and parameter estimators are to be obtained by the maximum penalized likelihood method of Firth [Firth, D., 1993, Bias reduction of maximum likelihood estimates. Biometrika, 80, 27-38]. Although this method achieves a reduction in bias, we illustrate that the remaining bias may be substantial for small experiments, and propose minimization of the integrated mean square error, based on Firth's estimates, as a suitable criterion for design selection. This approach is used to find locally optimal designs for two support points.