Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

A coalescent analysis for modeling the mutation process in colorectal cancer

Colorectal cancer is the forth most common diagnosed cancer in the United States. Every year about a hundred forty-seven thousand people will be diagnosed with colorectal cancer and fifty-six thousand people lose their lives due to this disease. Most of the hereditary nonpolyposis colorectal cancer (HNPCC) and 12% of the sporadic colorectal cancer show microsatellite instability. Colorectal cancer is a multistep progressive disease. It starts from a mutation in a normal colorectal cell and grows into a clone of cells that further accumulates mutations and finally develops into a malignant tumor. In terms of molecular evolution, the process of colorectal tumor progression represents the acquisition of sequential mutations. ^ Clinical studies use biomarkers such as microsatellite or single nucleotide polymorphisms (SNPs) to study mutation frequencies in colorectal cancer. Microsatellite data obtained from single genome equivalent PCR or small pool PCR can be used to infer tumor progression. Since tumor progression is similar to population evolution, we used an approach known as coalescent, which is well established in population genetics, to analyze this type of data. Coalescent theory has been known to infer the sample's evolutionary path through the analysis of microsatellite data. ^ The simulation results indicate that the constant population size pattern and the rapid tumor growth pattern have different genetic polymorphic patterns. The simulation results were compared with experimental data collected from HNPCC patients. The preliminary result shows the mutation rate in 6 HNPCC patients range from 0.001 to 0.01. The patients' polymorphic patterns are similar to the constant population size pattern which implies the tumor progression is through multilineage persistence instead of clonal sequential evolution. The results should be further verified using a larger dataset. ^

An analysis of the revenue policy -making process of the Texas Legislature

The purpose of this dissertation was to develop a conceptual framework which can be used to account for policy decisions made by the House Ways and Means Committee (HW&MC) of the Texas House of Representatives. This analysis will examine the actions of the committee over a ten-year period with the goal of explaining and predicting the success of failure of certain efforts to raise revenue.^ The basis framework for modelling the revenue decision-making process includes three major components--the decision alternatives, the external factors and two competing contingency theories. The decision alternatives encompass the particular options available to increase tax revenue. The options were classified as non-innovative or innovative. The non-innovative options included the sales, franchise, property and severance taxes. The innovative options were principally the personal and corporate income taxes.^ The external factors included political and economic constraints that affected the actions of the HW&MC. Several key political constraints on committee decision-making were addressed--including public attitudes, interest groups, political party strength and tradition and precedents. The economic constraints that affected revenue decisions included court mandates, federal mandates and the fiscal condition of the nation and the state.^ The third component of the revenue decision-making framework included two alternative contingency theories. The first alternative theory postulated that the committee structure, including the individual member roles and the overall committee style, resulted in distinctive revenue decisions. This theory will be favored if evidence points to the committee acting autonomously with less concern for the policies of the Speaker of the House. The Speaker assignment theory, postulated that the assignment of committee members shaped or changed the course of committee decision-making. This theory will be favored if there was evidence that the committee was strictly a vehicle for the Speaker to institute his preferred tax policies.^ The ultimate goal of this analysis is to develop an explanation for legislative decision-making about tax policy. This explanation will be based on the linkages across various tax options, political and economic constraints, member roles and committee style and the patterns of committee assignment. ^