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Sensitivity of Weibull Model Parameter Estimates to Variation in Simulated Disease Progression Data. Wayne M. Thal, Graduate assistant, Department of Plant Pathology, North Carolina State University, Raleigh 27650; C. Lee Campbell(2), and L. V. Madden(3). (2)Assistant professor, Department of Plant Pathology, North Carolina State University, Raleigh 27650; (3)Assistant professor, Department of Plant Pathology, Ohio State University, Wooster 44691. Phytopathology 74:1425-1430. Accepted for publication 8 August 1984. Copyright 1984 The American Phytopathological Society. DOI: 10.1094/Phyto-74-1425.

Sensitivity of estimates of Weibull parameters (a, b, c) to alterations in factors controlled or not controlled by investigators was examined by using simulated disease progression data generated from the monomolecular, Bertalanffy-Richards (with shape parameter m fixed at 0.5), Gompertz, and logistic models. Data were generated using six levels of initial disease proportion (y0 = 0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01); ten levels of rho- a common weighted mean rate parameter (rho = 0.008, 0.017, 0.025, 0.033, 0.041, 0.050, 0.058, 0.067, 0.075, 0.083); four data point spacings; and four final disease levels. The effect of a fixed a-parameter on estimated c-parameter values was examined. Weibull model parameters were estimated using nonlinear regression techniques; the Marquardt and Gauss-Newton methods proved most suitable. Estimates of a were sensitive to values of rho when data were generated using the Gompertz and logistic models and when values of y0 were high. Estimates of b were inversely related to rho and estimates of c were insensitive to changes in rho. Estimated parameter values for models other than the monomolecular were sensitive to changes in y0. Reducing the final level of y affected estimates of c; the magnitude of the effect increased as the inflection point of the generating disease progress model increased. Estimates of c were insensitive to changes in data point spacing but increased as values of a decreased in the two-parameter model. Estimates of a, b, and c were generally highly correlated which may indicate overparameterization of the model.

Additional keywords: disease progression models, quantitative epidemiology.