Gregg E. Dinse

Nonparametric estimation of lifetime and disease onset distributions from incomplete observations.

In this paper we derive and investigate nonparametric estimators of the distributions of lifetime and time until onset associated with an irreversible disease that is detectable only at death. The nonparametric maximum likelihood solution requires an iterative algorithm. An alternative though closely related pair of estimators for the lifetime and onset distributions exists in closed form. These estimators are the familiar Kaplan-Meier estimator and an isotonic regression estimator, respectively. First-order approximations provide variance estimators. The proposed methods generalize and shed additional light on the constrained estimators presented by Kodell, Shaw and Johnson (1982, Biometrics 38, 43-58). Data from an animal experiment illustrate the techniques.

A Mixture Model for the Regression Analysis of Competing Risks Data

SUMMARY A parametric mixture model provides a regression framework for analysing failure-time data that are subject to censoring and multiple modes of failure. The regression context allows us to adjust for concomitant variables and to assess their effects on the joint distribution of time and type of failure. The mixing parameters correspond to the marginal probabilities of the various failure types and are modelled as logistic functions of the covariates. The hazard rate for each conditional distribution of time to failure, given type of failure, is modelled as the product of a piece-wise exponential function of time and a log-linear function of the covariates. An EM algorithm facilitates the maximum likelihood analysis and illuminates the contributions of the censored observations. The methods are illustrated with data from a heart transplant study and are compared with a cause-specific hazard analysis. The proposed mixture model can also be used to analyse multivariate failure-time data.

Nonparametric Estimation for Partially-Complete Time and Type of Failure Data

Many statistical models focus on a random variable that represents time until failure and an indicator variable that denotes type of failure. When censoring mechanisms are introduced, an incomplete observation on the failure time often precludes observation of the indicator. In addition to conventional outcomes, for which observations on the time until failure and the type of failure are both complete or both incomplete, this paper considers partially-complete outcomes, for which only one of the random variables if fully observed. An iterative algorithm yields distribution-free estimates of the joint law governing this random pair; these estimates converge to the maximum likelihood solution. Recent developments permit approximations to the information and covariance matrices. Several special cases lead to closed-form estimates of the underlying distribution. Data from two recent clinical trials are used to illustrate the proposed techniques.

Nonparametric Prevalence and Mortality Estimators for Animal Experiments with Incomplete Cause-of-Death Data

Abstract Age-specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity. Nonparametric maximum likelihood estimators for the prevalence and mortality functions are available for the case in which incidental and fatal occurrences of a disease can always be distinguished. This article generalizes these methods to allow the role of a disease in causing death to be uncertain for a subset of the animals dying with the disease. The proposed analysis makes no assumptions about the degree of disease lethality. Data from sacrificed animals can be incorporated easily, although sacrifices are not necessary if a certain representativeness assumption holds. No restrictions are imposed on the distribution of survival times, but the prevalence function is held constant over time intervals for stabilization purposes. Variances are estimated by inverting the observed information matrix. An EM algorithm simplifies the analysis when the ...

Logistic Regression Analysis of Incidental-Tumor Data from Animal Carcinogenicity Experiments

Survival differences can have a substantial impact on the statistical comparison of tumor development in control and treated animals and thus should be taken into account routinely in the analysis of carcinogenicity data from laboratory experiments. However, the appropriate survival adjustment depends on whether the tumor of interest is fatal or incidental. The usual analysis of incidental tumors, which adjusts for survival by stratifying the animals according to age at death, has various shortcomings. Alternatively, logistic regression methods allow a continuous survival adjustment and furnish a convenient framework for solving many of the problems associated with the age-stratified approach of grouping the data into time intervals. Logistic regression substitutes modeling the prevalence function for the arbitrary choice of time intervals, providing a survival adjustment (when the model holds) even when differential mortality might increase the bias or decrease the sensitivity of interval-based methods. The logistic analysis also can incorporate covariables which, if ignored, might confound the interpretation of the data. Several examples illustrate these potential advantages of basing the analysis of incidental tumors on logistic regression techniques.

Comparison of NTP historical control tumor incidence rates in female Harlan Sprague Dawley and Fischer 344/N Rats.

The National Toxicology Program (NTP) has historically used Fischer 344/N (F344/N) rats for the majority of its bioassays. Recently the NTP began using the Harlan Sprague Dawley (SD) as the primary rat model for NTP studies. The NTP had previously used female SD rats in nine bioassays. This article compares historical control (HC) tumor incidence rates from these nine SD rat studies with HC tumor rates from matched NTP F344/N rat bioassays to identify similarities and differences. Matching on sex, laboratory, diet, and route led to nine comparable F344/N rat studies. Our analyses revealed statistically significant strain differences, with female SD rats having lower incidence rates for clitoral gland adenoma (0.2% vs. 5.8%) and mononuclear cell leukemia (0.9% vs. 16.7%) and higher incidence rates for mammary gland fibroadenoma (67.4% vs. 48.4%), mammary gland carcinoma (10.2% vs. 2.4%), and thyroid gland C cell adenoma (25.4% vs. 13.6%) relative to female F344/N rats. These represent five of the seven most common tumor types among female SD and F344/N rats in the NTP HC database. When vehicle was included as an additional matching criterion, the number of comparable F344/N rat studies dropped to four, but similar results were obtained.

An Investigation of the Effects of Late-Onset Dietary Restriction on Prostate Cancer Development in the TRAMP Mouse

In our previous work we showed that dietary restriction initiated at puberty reduced prostate cancer development in the TRAMP mouse model. The current study was conducted to ascertain whether a dietary restriction regime would similarly reduce lesion development if imposed once tumor development was well established. Male TRAMP mice were maintained on an ad libitum diet until 20 weeks of age when proliferative prostate lesions are clearly evident. Mice were then subjected to a 20% restriction in dietary calories compared to matched controls, which were continued on ad libitum feeding. Mice were sacrificed at 20, 24, 32, and 39 weeks of age and proliferative epithelial lesions of the prostate were assessed using an established grading scheme. In this study, although dietary restriction reduced mean sex pluck weight (prostate and seminal vesicles), and mean grade of epithelial proliferative lesions in the dorsal and lateral lobes of the prostate, the effect was not as pronounced as was the case with dietary restriction from puberty. There was no relationship between serum insulin like growth factor (IGF-1) and prostate lesion grade. Additionally, we also report the relationship between lobe specific lesion development and SV40 immunostaining and, the occurance of neuroendocrine tumors (NETs) in the ventral prostate and urethra of the TRAMP mouse. NETs stained with high specificity and sensitivity for the neuroendocrine markers, synaptophysin and neuron-specific enolase (NSE), less for serotonin, but not for chromogranin A. NETs did not stain for cyclo-oxygenase-2 (COX-2) nor androgen receptor (AR). SV40 positive tubulo-acinar tumors seen occasionally in the kidney, did not stain for synaptophysin nor NSE.

Constant risk differences in the analysis of animal tumorigenicity data.

In a typical tumorigenicity study, most tumors are not observable in live animals and only a single (terminal) sacrifice is performed. This paper proposes a nonparametric, survival-adjusted analysis for these data that focuses on tumor incidence and yet does not require data on cause of death or assumptions about the tumors lethality. The tumor onset/death process is most naturally characterized in terms of the tumor incidence rate and the death rates for tumor-free and tumor-bearing animals. The proposed approach, however, reparameterizes the problem in terms of the incidence rate, the death rate for tumor-free animals, and the difference between the death rates for tumor-free and tumor-bearing animals (i.e., the risk difference). The advantage of this alternative formulation is that a full likelihood analysis is possible with as few as one sacrifice time if the risk difference is assumed to be constant with respect to time. Data from the large ED01 study suggest that reasonable results can be obtained under the assumption of constant risk differences.

Birth weight, early weight gain and pubertal maturation: a longitudinal study

To investigate the effect of birth weight and early weight gain on the timing of various measures of puberty in both girls and boys.

Semiparametric analysis of tumor incidence rates in survival/sacrifice experiments.

This paper addresses the problem of comparing treatment groups with respect to the rate of tumor development for animals in a survival experiment with some serial sacrifices. The analysis specifies a parametric model for the tumor incidence function, but places no parametric restrictions on the death rates. The procedure is feasible with as few as two sacrifice times and requires no individual data on cause of death. Other diseases need not act independently of the tumor of interest, nor are any restrictions imposed on tumor lethality or the relationship between the onset and death times for tumor-bearing animals. The proposed methods are illustrated with some survival/sacrifice data.