Sigmoid curves have found broad applicability in biological sciences and biopharmaceutical research during the last decades. A well planned experiment design is essential to accurately estimate the parameters of the model. In contrast to a large literature and extensive results on optimal designs for linear models, research on the design for nonlinear, including sigmoid curve, models has not kept pace. Furthermore, most of the work in the optimal design literature for nonlinear models concerns the characterization of minimally supported designs. These minimal, optimal designs are frequently criticized for their inability to check goodness of fit, as there are no additional degrees of freedom for the testing. This design issue can be a serious problem, since checking the model adequacy is of particular importance when the model is selected without complete certainty. To assess for lack of fit, we must add at least one extra distinct design point to the experiment. The goal of this dissertation is to identify optimal or highly efficient designs capable of checking the fit for sigmoid curve models. In this dissertation, we consider some commonly used sigmoid curves, including logistic, probit and Gompertz models with two, three, or four parameters. We use D-optimality as our design criterion. We first consider adding one extra point to the design, and consider five alternative designs and discuss their suitability to test for lack of fit. Then we extend the results to include one more additional point to better understand the compromise among the need of detecting lack of fit, maintaining high efficiency and the practical convenience for the practitioners. We then focus on the two-parameter Gompertz model, which is widely used in fitting growth curves yet less studied in literature, and explore three-point designs for testing lack of fit under various error variance structures. One reason that nonlinear design problems are so challenging is that, with nonlinear models, information matrices and optimal designs depend on the unknown model parameters. We propose a strategy to bypass the obstacle of parameter dependence for the theoretical derivation. This dissertation also successfully characterizes many commonly studied sigmoid curves in a generalized way by imposing unified parameterization conditions, which can be generalized and applied in the studies of other sigmoid curves. We also discuss Gompertz model with different error structures in finding an extra point for testing lack of fit. / Statistics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/2476 |
| Date | January 2012 |
| Creators | Su, Ying |
| Contributors | Raghavarao, Damaraju, Iglewicz, Boris, Chitturi, Pallavi, Chan, Ivan S. F. |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 102 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/2458, Theses and Dissertations |
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