computer methods and programs in biomedicine 101 ( 2 0 1 1 ) 62–71 journal homepage: www.intl.elsevierhealth.com/journals/cmpb ODMixed: A tool to obtain optimal designs for heterogeneous longitudinal studies with dropout Shirley Ortega ∗ , Frans E.S. Tan, Martijn P.F. Berger University of Maastricht, Department of Methodology and Statistics, P.O. Box 616, 6200 MD Maastricht, The Netherlands article info Article history: Received 5 March 2009 Received in revised form 2 April 2010 Accepted 14 April 2010 Keywords: D-optimal designs Dropout Heterogeneous autocorrelation Linear mixed models Longitudinal data Relative efficiency abstract ODMixed is a computer program to obtain optimal designs for linear mixed models of lon- gitudinal studies. These designs account for heterogeneous correlated errors and for data with dropout. Designs are compared by using relative efficiencies, e.g., between a D-optimal design for homogeneous data and another for heterogeneous data or between a D-optimal design for complete data against another that optimizes designs when data is missing at random. Two examples are worked out to illustrate how researchers could use this computer program to profit of optimal design theory at the planning stage of longitudinal studies. © 2011 Elsevier Ireland Ltd. All rights reserved. 1. Introduction At the planning stage of longitudinal studies, the allocation of the resources (time, subjects and/or money) is a critical issue. To collect longitudinal data, it is common practice to use equally spaced designs since these designs are model-free. However, these designs can be suboptimal when compared with their optimal counterparts [1] or when data is missing [2]. Both studies showed that at the planning stage of longitu- dinal data, researchers may profit, substantially, from optimal design theory. Optimal design of experiments give the lowest estimators variance such that the estimators have high precision. How- ever, these designs are model-dependent, i.e., the researcher must have prior knowledge about the underlying model fit- ting the longitudinal data. These data are usually correlated, can have heterogeneous variances and/or can be affected by ∗ Corresponding author. Tel.: +31 070 3352072. E-mail addresses: shortegaazurduy@yahoo.com, sota@cbs.nl (S. Ortega). dropout. The most suitable model to fit data with correlated and unbalanced data structures is the linear mixed models [3]. In this paper, we present a computer program ODMixed that computes optimal designs for complete data, for data suf- fering from dropout and for data having heterogeneous error structures. ODMixed is made in Matlab. Matlab is chosen because of its flexible plotting capabilities, robust optimiza- tion algorithms and steadily growing number of toolboxes, not to mention the fact that it is been steadily introduced in biomedical and health sciences applications. To our knowledge this is the first program that computes optimal designs for heterogeneous longitudinal data and data missing at random. Notice that the optimal designs with com- plete data and homogenous error structure can be matched with those obtained for one-cohort using the Program for Optimal design of Longitudinal Studies (POLS) which is an interactive program implemented in Matlab that allows to compute D-optimal designs for different polynomial models 0169-2607/$ – see front matter © 2011 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2010.04.004