| The work in this dissertation links a general continuous time Markov model for the progression of a disease through a number of disease states to a model for screening at fixed points in time. The main technical contribution is to show how symbolic mathematical systems such as Mathematica(TM) and Maple(TM) can be used to find closed form solutions for the expected cost of a screening program.;Using this general approach, expected total cost for a sequence of specific disease models were examined. The first goal was to compare the performance of screening designs with constant time intervals between screens under different disease models. The models paid particular attention to the disease process in the pre-clinical state where disease detection by screening is of value. Three specific pre-clinical disease sub-models were examined, single-stage, mixed-disease and two-stage. In general, when expected sojourn time in the pre-clinical state or states is held constant across all three models, the designs are robust to model choice.;It has been suggested that complex screening models can be approximated using screening points that occur as a random Poisson process, Parmigiani (1997). The second goal was to compare thew random screening models with the fixed model using our exact expected cost calculations. In general, the random screening model has higher health costs for fixed expected number of screens.;The third goal of this thesis was to optimize the cost of a screening program with respect to the screening intervals and the sensitivity of the screen. For this, we consider a disease with a screen test for which the sensitivity can be adjusted. Under this model, all positive screens were then confirmed by an expensive diagnostic procedure, which has sensitivity and specificity of one. All three pre-clinical submodels (single-stage, mixed-disease and two-stage models) were investigated.;The screening design models developed in this thesis were applied to colon cancer screening program. In this case the screen is an inexpensive fecal blood occult test and the diagnostic procedure, colonoscopy, is relatively expensive. |
