Over the past year, the majority of my research on this project was performed in two areas: (1) censored failure-time analysis when some censoring indicators are missing and (2) analysis of historical control data in rodent carcinogenicity experiments.  These two areas of research are described in more detail below.  Area 1: Failure-time data are typically subject to censoring, such as when a study ends before all participants fail.  Additionally, when multiple causes of failure are operating, the time to failure from one cause can be censored by a failure from another cause.  In some situations, the censoring indicator is missing for a subset of individuals, such as in a carcinogenicity study when the pathologist is not able to determine the role of a tumor in causing death or in a clinical trial when some records are incomplete.  The analysis of failure-time data typically focuses on hazard functions.  In separate research efforts, we developed hazard analyses under two different models: an accelerated failure-time model and an additive hazards model.  Under an accelerated failure-time model, we derived three nonparametric hazard estimators that are appropriate when some failure times are right censored and some censoring indicators are missing.  Specifically, we developed a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator.  All three estimators use kernel smoothing techniques and enjoy certain large-sample properties such as uniform strong consistency and asymptotic normality.  A simulation study showed that the proposed hazard estimators also performed well in small samples.  Under the same accelerated failure-time model, we also developed a regression analysis, which allows us to evaluate the effects of various explanatory variables on the hazard functions.  Alternatively, under an additive hazards model, we derived two types of inverse probability weighted estimators.  The simple weighted estimator uses only individuals with known censoring indicators and the fully augmented weighted estimator uses all individuals.  Under a missing at random assumption, however, both estimators are consistent and have the same asymptotic normal distribution.  Also, both estimators are based on nonparametric kernel smoothers and have relatively simple closed forms.  A simulation study showed that the proposed hazard estimators performed well, even when the missing at random assumption was relaxed, as long as the censoring rate was not too high.  We wrote three manuscripts to summarize the work in this area.  For the homogeneous estimation problem under the accelerated failure-time model, we submitted a paper to the Journal of Statistical Planning and Inference and we are still awaiting a response from the journal.  For the regression analysis under the accelerated failure-time model, we submitted a paper to Lifetime Data Analysis.  Our paper was reviewed and we were invited to resubmit after making some modifications;we resubmitted the paper and we are awaiting the final decision.  Regarding the additive hazards research, we submitted a paper to the Canadian Journal of Statistics.  This paper was reviewed and we were invited to resubmit after making a few changes;we resubmitted the paper and we are awaiting the final decision.  Area 2: When evaluating the carcinogenicity of a chemical, toxicologists and pathologists often assess tumor incidence rates from the current rodent bioassay within the context of a historical database of control tumor rates from similar studies using animals of the same species, strain, and sex.  If the tumor rate in the control group of the current study is outside the range of historical control rates, there may be concern about the validity of the conclusions drawn from the current study.  When comparing tumor rates in current and historical control groups, our research demonstrated that a decision rule based on the historical range does not maintain the Type I error rate at the usual 5% signi&#64257;cance level and can, in fact, be as high as 67% in some real-world situations.  In other cases, the power can go to zero.  We developed a simple alternative procedure that controls Type I errors, adjusts for animal survival, and accounts for extra variability between studies.  Extensive simulations showed that our test operated at or below the nominal level, whereas the range-based test often resulted in extremely high Type I error rates.  In other research related to historical control data, we compared tumor incidence rates in two strains of rats used in NTP studies.  Specifically, in 2008 the NTP switched from using Fischer 344/N (F344/N) rats to using Harlan Sprague Dawley (SD) rats in its carcinogenicity, reproductive and immunotoxicity bioassays.  The NTP had previously used female SD rats in nine chronic bioassays.  We compared historical control tumor data from these nine SD studies with historical control tumor data from matched NTP chronic bioassays that used F344/N rats.  Our goal was to identify similarities and differences in tumor incidence rates across the two strains.  Matching on sex, diet, route, and laboratory led to nine comparable F344/N studies.  All tumor types with fewer than 3 occurrences in the entire historical control database were excluded, as were metastases and combinations of tumors, leaving a total of 82 tumor types.  Statistically significant strain differences in incidence rates were identified for several tumor types, including clitoral gland adenoma, mammary gland fibroadenoma, mammary gland carcinoma, thyroid gland C-Cell adenoma, and mononuclear cell leukemia.  When vehicle was included as an additional matching criterion, the number of comparable F344/N studies dropped to four, but similar results were obtained.  With respect to the comparison of current and historical control tumor rates, we submitted a paper to Biometrics and we are still awaiting a response from the journal.  Regarding the comparison of control tumor rates in SD and F344/N rats, the analyses are complete but the manuscript is still in preparation.  This research was conducted in collaboration with Dr. Shyamal Peddada and is also mentioned in the report for his project entitled 'Statistical Methods with Applications to Toxicology and Microarray Data'(Z01-ES-101744).