Asymptotic behavior of the scaled mutation rate estimators

Important aspects of population evolution have been investigated using nucleotide sequences. Under the neutral Wright–Fisher model, the scaled mutation rate represents twice the average number of new mutations per generations and it is one of the key parameters in population genetics. In this study, we present various methods of estimation of this parameter, analytical studies of their asymptotic behavior as well as comparisons of the distribution's behavior of these estimators through simulations. As knowledge of the genealogy is needed to estimate the maximum likelihood estimator (MLE), an application with real data is also presented, using jackknife to correct the bias of the MLE, which can be generated by the estimation of the tree. We proved analytically that the Waterson's estimator and the MLE are asymptotically equivalent with the same rate of convergence to normality. Furthermore, we showed that the MLE has a better rate of convergence than Waterson's estimator for values of the parameter greater than one and this relationship is reversed when the parameter is less than one.     

Estimation and Testing of Tumor Incidence Rates in Experiments Lacking Cause-of-Death Data

Approximate nonparametric maximum likelihood estimation of the tumor incidence rate and comparison of tumor incidence rates between treatment groups are examined in the context of animal carcinogenicity experiments that have interval sacrifice data but lack cause-of-death information. The estimation procedure introduced by MALANI and VAN RYZIN (1988), which can result in a negative estimate of the tumor incidence rate, is modified by employing a numerical method to maximize the likelihood function iteratively, under the constraint that the tumor incidence rate is nonnegative. With the new procedure, estimates can be obtained even if sacrifices occur anywhere within an interval. The resulting estimates have reduced standard error and give more power to the test of two heterogeneous groups. Furthermore, a linear contrast of more than two groups can be tested using our procedure. The proposed estimation and testing methods are illustrated with an experimental data set.     

On the use of historical control information for trend test in carcinogenesis

In this article a new non-model-based significance test for detecting dose-response relationship with the incorporation of historical control data is proposed. This non-model-based test is considered simpler from a regulatory perspective because it does not require validating any modeling assumptions. Moreover, our test is especially appropriate to those studies in which the intravenous doses for the investigational chemical are labeled as, e.g., low, medium and high or the dose labels do not suggest any obvious choices of dose scores. This test can be easily adopted for detecting general dose-response shape, such as an umbrella pattern. Simple adjustments will be proposed for better control of the actual Type I error. Data sets from two carcinogenesis studies will be used to illustrate our method. We also evaluate the performance of the proposed test and the famous model-based Tarone's trend test with respect to size and power.     

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.