Collection Of Biostatistics Research Archive
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Random Genetic Mosaics I. Models and Moments
No full textA genetic mosaic is a genetically composite organism, within whose tissues two or more genetically distinct mosaic types of cells coexist. Subsequent to the onset of mosaicism in an individual, the mosaic type of a dividing cell is copied into the two new cells. Mosaic-composition data are measurements of the compositions of one or more tissues in one or more individuals in terms of the mosaic types of their constituent cells. Such data are widely used in studies of tissue development. Their analysis is generally based on assumptions to the effect that mosaic types are randomly assigned to the cells present at the onset of mosaicism, and that the differences between the mosaic types are developmentally unimportant. From precise interpretations of these assumptions, stochastic models of the mosaic composition of a system of tissues will be constructed (for an arbitrary number of mosaic types). The low-order cumulants of the joint distribution of the mosaic-composition variables will be shown to have a simple structure under the stronger models. The data of Nesbitt (1971) will be analyzed. These are measurements of the proportions of type-1 cells in five tissues in 34 mice, with measurement errors distributed as independent binomial proportions. Data-analytic models will be motivated and fitted in which the underlying tissue proportions are given a multivariate normal distribution over mice
Statistical Analysis of HIV Infectivity Based on Partner Studies
No full textPartner studies produce data on the infection status of partners of individuals known or assumed to be infected with the human immunodeficiency virus (HIV) after a known or estimated number of contacts. Previous studies have assumed a constant probability of transmission (infectivity) of the virus at each contact. Recently, interest has focused on the possibility of heterogeneity of infectivity across partnerships. This paper develops parametric and nonparametric procedures based on partner data in order to examine the risk of infection after a given number of contacts. Graphical methods and inference techniques are presented that allow the investigator to evaluate the constant infectivity model and consider the impact of heterogeneity of infectivity, error in measurement of the number of contacts, and regression effects of other covariates. The majority of the methods can be computationally implemented easily with use of software to fit generalized linear models. The concepts and techniques are closely related to ideas from discrete survival analysis. A data set on heterosexual transmisison is used to illustrate the methods
Hypothesis Testing of Regression Parameters in Semi-Parametric Generalized Linear Models for Cluster Correlated Data
No full textGeneralized and working Wald and score tests for regression coefficients in the class of semi-parametric marginal generalized linear models for cluster correlated data (Liang and Zeger, 1986) are proposed, and their asymptotic distribution examined. In addition, the asymptotic distribution of the naive likelihood ratio test, or deviance difference, is presented. Following Rao and Scott (12984), we propose simple adjustments to such working tests. The asymptotic distributions of the working tests allow us to explore theoretical bounds on the ratios of the robust variance of the regression parameter estimators and their naive variance counterparts computed assuming independent observations. In addition, the adequacy of a particular choice of working correlation structure is considered. We illustrate our results with a numerical example
Some Comments on Rosner\u27s Multiple Logistic Model for Clustered Data
No full textRosner (1984, Biometrics 41, 1025-1035) proposed a binary regression model for analyzing binary response data gathered in clusters or groups. This model is useful for understanding the degree of intracluster correlation among responses, adjusted for the potential confounding effects of other covariates. However, estimates of the effects of covariates on the binary outcome obtained using Rosner\u27s model can be misleading. For example, we show that the covariate effects given by Rosner\u27s model do not correspond to those measured by either of the two standard approaches for correlated binary data. We present an example which compares the regression coefficients arising from fits of Rosner\u27s model to other logistic models for clustered observations, using data from a study of breast disease
Estimating the Incubation Period of AIDS by Comparing Population Infection and Diagnosis Patterns
No full textThe incidence of AIDS virus infections over time among gay men in San Francisco is nonparametrically estimated from interval-censored data by using the EM algorithm to maximize a roughness-penalized likelihood. Because the distribution of AIDS diagnoses is the convolution of the infection and incubation distributions, the incubation distribution can be estimated by comparing the estimated infection distribution and the observed pattern of diagnoses. This is again accomplished by nonparametrically maximizing a roughness-penalized likelihood using the EM algorithm. The optimal degree of smoothness for the estimates is chosen using external data and subjective assessments of plausibility. Three prospective studies of initially uninfected men produce comparable estimated infection rates and are merged to produce an overall estimate, which shows rates increasing until mid-1982 and then falling sharply. The estimated incubation period hazard function is near zero for two years following infection and then increases until it flattens out at about seven years after infection. Bootstrap simulations are used to gauge the variability of the estimates. Because infections were concentrated in the years 1980 to 1982, the incubation estimate is fairly accurate. Inclusion of the roughness penalty in the criteria to be optimized greatly reduces the variability of the estimates while also greatly speeding the convergence of the algorithms
An Annotated Bibliography of Quantitative Methodology Relating to the AIDS Epidemic
No full textThis paper provides an annotated bibliography of over 100 articles containing quantitative methodology relating to the AIDS epidemic. The majority of the work describes mathematical and statistical models of the growth and extent of the epidemic, and statistical procedures to estimate key components of the disease process. Among these components, attention has focused primarily on estimating the incubation distribution. It is hoped that the bibliography will not only interest those currently active in the field but also encourage other statisticians to become involved in AIDS research efforts. The general area of AIDS research appears to be a rich source of statistical problems of considerable interest and importance
Effects of Pituitary Stalk-transection and Type of Barrier on Pituitary and Luteal Function During the Estrous Cycle of the Ewe
Full text linkEffects of pituitary stalk-transection on plasma concentrations of luteinizing hormone (LH), follicle stimulating hormone (FSH) prolactin (PRL) and progesterone were investigated during the estrous cycle of ewes. Pituitary stalk (SS) or sham (SH) transection was performed on day 1 (estrus = day 0) of the estrous cycle. A Teflon or Silastic barrier was placed between the cut ends of the stalk to prevent reorganization of the portal vasculature. Immediately following surgery, pulsatile administration of gonadotropin releasing hormone (GnRH, 200 ng/hr) or .9% NaCl was initiated and continued for the duration of the experiment. Estradiol benzoate (EB, 50 μg im) was administered to all ewes on day 3. Mean concentrations of LH were greater in SS ewes than in SH ewes (P\u3c.05). There was a trend (P=.06) for the concentration of LH to be higher in ewes with Teflon compared with Silastic barriers between the cut ends of the stalk. Infusion of GnRH elevated concentrations of LH in both SS and SH ewes (P\u3c.05). Concentrations of progesterone were reduced (P\u3c.01) in saline-infused SS ewes while infusion of GnRH in SS ewes maintained concentrations of progesterone similar to saline-infused SH ewes. The concentrations of FSH or PRL were unaffected by SS, type of barrier or treatment with GnRH. Administration of EB failed to induce a surge of LH except in a SH ewe infused with GnRH. Ewes were more responsive to infusion of GnRH following SS than after SH as reflected by increased plasma concentrations of LH and progesterone
Sample Size Calculations and Optimal Followup Time in Health Services Research Using Utilization Rates
Full text linkIt is not always possible to estimate the sample sizes needed in health services research because special formulas are needed, and the necessary data may not be available to use in the formulas. We provide some useful formulas for the sample size required in comparing the means of two groups. These include the special case where the two groups are not of equal size either because one is known to have a higher variability or because one group has already been chosen and its size is thus fixed. We also explore the relationship of the mean to the standard deviation for utilization measures, so that the latter can be estimated from the former for use in the equations. In general, the coefficient of variation is on the order of 2, suggesting that the standard deviation may be crudely estimated as twice the mean. The optimal follow-up period is also calculated
Statistical Measures for Admission Rates
Full text linkHospital admission rates are often shown and interpreted without consideration of their inherent variability, which may lead to faulty conclusions. This may be because theoretically correct variance estimates are not known for the type of estimates usually used; i.e., total admissions divided by total person-months of observation. Here, correct methods for testing and estimation are shown for situations where they exist. For other types of data, approximate procedures are proposed and their properties examined theoretically and empirically, yielding recommendations for exact and approximate estimation and testing methods for admission rates in common situations