Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Partial proportional odds model for analyzing pedestrian crashes,threshold heterogeneity by scale and proportional odds factor

Despite low traffic in Wyoming,pedestrian crash severity accounts for a high number of fatalities in the state.Thus this study was conducted to highlights factors contributing to those crashes.The results highlighted that drivers under influence,type of vehicle,location of crashes,estimated speed of vehicles,driving over the recommended speed are some of factors contributing to the severity of crashes.In this study,we used proportional odds model which assumes that the impact of each attribute is consistent or proportional across various threshold values.However,it has been argued that this assumption might be unrealistic,especially at the presence of extreme values.Thus,the assumption was relaxed in this study by shifting the thresholds based on some explanatory attributes,or proportional odds effects.In addition,we accounted for the spread rate,or scale,of the model’s latent distribution of pedestrian crashes.The results highlighted that the partial proportional odds model through proportional odds factor and scale effects result in a significant improvement in model fit compared with the standard proportional odds model.Comparisons were also made across standard normal,simple partial ordinal model,and partial ordinal accounting for scale heterogeneity.In addition,various potential threshold structures such as symmetric and flexible were considered,but similar goodness of fits were observed across all those models.Extensive discussion has been made regarding the formulation of the implemented methodology,and its implications.

Transformation Models for Survival Data Analysis with Applications

When the event of interest never occurs for a proportion of subjects during the study period, survival models with a cure fraction are more appropriate in analyzing this type of data. Considering the non-linear relationship between response variable and covariates, we propose a class of generalized transformation models motivated by Zeng et al. [1] transformed proportional time cure model, in which fractional polynomials are used instead of the simple linear combination of the covariates. Statistical properties of the proposed models are investigated, including identifiability of the parameters, asymptotic consistency, and asymptotic normality of the estimated regression coefficients. A simulation study is carried out to examine the performance of the power selection procedure. The generalized transformation cure rate models are applied to the First National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the purpose of examining the relationship between survival time of patients and several risk factors.