Parameter Estimation of Type-I and Type-II Hybrid Censored Data from the Log-Logistic Distribution

In experiments on product lifetime and reliability testing, there are many practical situations in which researchers terminate the experiment and report the results before all items of the experiment fail because of time or cost consideration. The most common and popular censoring schemes are type-I and type-II censoring. In type-I censoring scheme, the termination time is pre-fixed, but the number of observed failures is a random variable. However, if the mean lifetime of experimental units is somewhat larger than the pre-fixed termination time, then far fewer failures would be observed and this is a significant disadvantage on the efficiency of inferential procedures. In type-II censoring scheme, however, the number of observed failures is pre-fixed, but the experiment time is a random variable. In this case, at least pre-specified number of failure are obtained, but the termination time is clearly a disadvantage from the experimenter’s point of view. To overcome some of the drawbacks in those schemes, the hybrid censoring scheme, which is a mixture of the conventional type-I and type-II censoring schemes, has received much attention in recent years. In this paper, we consider the analysis of type-I and type-II hybrid censored data where the lifetimes of items follow two-parameter log-logistic distribution. We present the maximum likelihood estimators of unknown parameters and asymptotic confidence intervals, and a simulation study is conducted to evaluate the proposed methods

Confidence bands for the difference of two survival functions under the additive risk model

In many clinical studies, a commonly encountered problem is to compare the survival probabilities of two treatments for a given patient with a certain set of covariates, and there is often a need to make adjustments for other covariates that may affect outcomes. One approach is to plot the difference between the two subject-specific predicted survival estimates with a simultaneous confidence band. Such a band will provide useful information about when these two treatments differ and which treatment has a better survival probability. In this paper, we show how to construct such a band based on the additive risk model and we use the martingale central limit theorem to derive its asymptotic distribution. The proposed method is evaluated from a simulation study and is illustrated with two real examples.

Constant-Stress Partially Accelerated Life Testing for Log-Logistic Distribution with Censored Data

In order to quantify the life characteristics of a product, partially accelerated life tests are used when the data obtained from accelerated conditions cannot be extrapolated to normal use conditions. This study considers constant-stress partially accelerated life tests for censored lifetime data, where the lifetime distribution is assumed to follow log-logistic distribution. The maximum likelihood estimates are obtained for the distribution parameters and acceleration factor. Simulation studies are conducted to illustrate the statistical properties of the estimates and evaluate the performance of confidence intervals

Hypotheses Tests of Strain-specific Vaccine Efficacy Adjusted for Covariate Effects

In the evaluation of efficacy of a vaccine to protect against disease caused by finitely many diverse infectious pathogens, it is often important to assess if vaccine protection depends on variations of the exposing pathogen. This problem can be formulated under a competing risks model where the endpoint event is the infection and the cause of failure is the infecting strain type determined after the infection is diagnosed. The strain-specific vaccine efficacy is defined as one minus the cause-specific hazard ratio (vaccine/placebo). This paper develops some simple procedures for testing if the vaccine affords protection against various strains and if and how the strain-specific vaccine efficacy depends on the type of exposing strain, adjusting for covariate effects. The Cox proportional hazards model is used to relate the cause-specific outcomes to explanatory variables. The finite sample properties of proposed tests are studied through simulations and are shown to have good performances. The tests developed are applied to the data collected from an oral cholera vaccine trial.Competing risks model, cause-specific hazard function, Cox proportional hazards model,

Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana

Cancer Mortality, State Mean Elevations, and Other Selected Predictors

This ecological inquiry compares cancer mortality rates in the U.S. to the predictor of natural background radiation (via land elevation means) along with eight other predictors thought to be associated with cancer mortality. Age-adjusted cancer mortality in 2006 was compared to the predictors of mean land elevation, percent of smokers, educational attainment, percent of population without health insurance, income, obesity, health perception, physical activity, and diet. Among the six predictors considered appropriate for multiple linear regression, three were found to be statistically significant; from strongest to weakest, these three were: smoking, land elevation, and educational attainment. The predictors of smoking and educational attainment have long been considered associated with cancer mortality. The finding that the predictor of land elevation / natural background radiation is inversely related to cancer mortality is another piece of evidence supporting the theory of radiation hormesis. In this study, land elevation / natural background radiation ranked second in predictive strength regarding cancer mortality, behind smoking and ahead of educational attainment. Since this is an ecological inquiry, no causal inferences can be made

Oak Park Energy Efficiency & Carbon Reduction (Semester Unknown) IPRO 329: OakParkEnergyEfficiencyAndCarbonReductionIPRO329ProjectPlantF10_redacted

The overall purpose of the IPRO 329 team is to work with the Village of Oak Park in order to implement a strategic plan to educate Oak Park residents in making their homes more efficient and work toward a community wide reduction of energy and water usage. In doing so, we also hope to gain valuable experience in working in a team with members with varying degrees of experience and skills.Sponsorship: Oak ParkDeliverable

Oak Park Energy Efficiency & Carbon Reduction (Semester Unknown) IPRO 329: OakParkEnergyEfficiencyAndCarbonReductionIPRO329MidTermPresentationF10

The overall purpose of the IPRO 329 team is to work with the Village of Oak Park in order to implement a strategic plan to educate Oak Park residents in making their homes more efficient and work toward a community wide reduction of energy and water usage. In doing so, we also hope to gain valuable experience in working in a team with members with varying degrees of experience and skills.Sponsorship: Oak ParkDeliverable

Oak Park Energy Efficiency & Carbon Reduction (Semester Unknown) IPRO 329: OakParkEnergyEfficiencyAndCarbonReductionIPRO329PosterF10

The overall purpose of the IPRO 329 team is to work with the Village of Oak Park in order to implement a strategic plan to educate Oak Park residents in making their homes more efficient and work toward a community wide reduction of energy and water usage. In doing so, we also hope to gain valuable experience in working in a team with members with varying degrees of experience and skills.Sponsorship: Oak ParkDeliverable

Oak Park Energy Efficiency & Carbon Reduction (Semester Unknown) IPRO 329

The overall purpose of the IPRO 329 team is to work with the Village of Oak Park in order to implement a strategic plan to educate Oak Park residents in making their homes more efficient and work toward a community wide reduction of energy and water usage. In doing so, we also hope to gain valuable experience in working in a team with members with varying degrees of experience and skills.Sponsorship: Oak ParkDeliverable