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Title: NONLINEAR MODELS WITH REPEATED MEASURES FOR ANALYZING DISEASE PROGRESS

Author
item MACCHIAVELLI, R. - UNIV. OF PUERTO RICO
item ROBLES, W. - UNIV. OF PUERTO RICO
item ABREU, E - UNIV. OF PUERTO RICO
item Pantoja, Alberto

Submitted to: Applied Statistics In Agriculture Conference Proceedings
Publication Type: Abstract Only
Publication Acceptance Date: 4/25/2004
Publication Date: 4/25/2004
Citation: Macchiavelli, R., Robles, W., Abreu, E., Pantoja, A. 2004. Nonlinear models with repeated measures for analyzing disease progress. Applied Statistics In Agriculture Conference Proceedings. 16:255-269

Interpretive Summary:

Technical Abstract: Nonlinear models are commonly used in plant disease epidemiology to model temporal changes in the proportion of diseased plants (disease index). Most of the times they are fit using least squares, with linearizing transformations separately for each treatment. Sometimes they are directly fit using nonlinear least squares. These traditional approaches assume that the disease index has a normal distribution, that they are independent and that they have constant variance. These assumptions are clearly violated: the number of diseased plants has a binomial or beta-binomial distribution, the observations are taken repeatedly on the same units, and the variances are not constant as the index increases from 0 to 1. Furthermore, separate fitting for each treatment does not permit efficient treatment comparisons. In this paper we apply different strategies to model the progress of papaya ring spot virus in papaya under 4 different treatments. Models fit include monomolecular, logistic, Gompertz and exponential. By using lack of fit tests, the logistic model is chosen. With this model we compare the following methods using SAS: least squares with transformed data, nonlinear least squares assuming normal distribution, generalized linear model assuming binomial distribution with overdispersion, GEE assuming binomial distribution, and nonlinear mixed models assuming binomial distribution. Marginal (population average) and subject-specific interpretations of the models are discussed.