Showing papers in "Biometrics in 1981"

Time Series: Data Analysis and Theory.

Abstract: This book will be most useful to applied mathematicians, communication engineers, signal processors, statisticians, and time series researchers, both applied and theoretical. Readers should have some background in complex function theory and matrix algebra and should have successfully completed the equivalent of an upper division course in statistics.

Modification of estimates of parameters in the construction of genetic selection indices ("bending")

Abstract: A method, termed 'bending', is proposed for the modification of the estimates of genetic (G) and phenotypic (P) covariance matrices, that are used in the construction of genetic selection indices for two or more traits. If P and G are estimated from the betweenand within-class covariance matrices, B and W respectively, in a one-way multivariate analysis of variance, then the method consists of contracting all the eigenvalues of the matrix product W-1B towards their mean but with the corresponding eigenvectors unchanged. The usefulness of the modification procedure is investigated by Monte Carlo simulation and Taylor series approximation methods. In general, the modification procedure improves the achieved response to selection, with the amount of improvement dependent on the (unknown) population parameters and the size of sample for estimation. In practice, there is some difficulty in selecting the value of the 'bending' factor; some very simple methods of doing this are proposed. If some of the parameter estimates are known to be defective (outside their valid limits), a simple and effective method for the selection of the 'bending' factor is to contract the eigenvalues so that they are all nonnegative.

Building Multiple Regression Models Interactively

Abstract: Automated multiple regression model-building techniques often hide important aspects of data from the data analyst. Such features as nonlinearity, collinearity, outliers, and points with high leverage can profoundly affect automated analyses, yet remain undetected. An alternative technique uses interactive computing and exploratory methods to discover unexpected features of the data. One important advantage of this approach is that the data analyst can use knowledge of the subject matter in the resolution of difficulties. The methods are illustrated with reanalyses of the two data sets used by Hocking (1976, Biometrics 32, 1-44) to illustrate the use of automated regression methods.

General relative-risk models for survival time and matched case-control analysis

Abstract: A general likelihood is derived for survival time and matched case-control analysis. It allows alternatives to the usual exponential dependence of relative risk on exposure variables; instead this dependence can be modelled in terms of any specific parametric function. These general relative risk models are particularly useful for study of forms of dose-response relationships with a single continuous exposure variable and forms of interactions between multiple exposure variables (continuous or discrete). Illustrative applications to data [for Quebec] on the risks of lung cancer in relation to smoking and asbestos exposure are presented. (summary in FRE) (EXCERPT)

Capture-Recapture Models Allowing for Age-Dependent Survival and Capture Rates

Abstract: A K-sample capture-recapture model for an open population of animals, which allows for different identifiable age categories to have different survival and capture probabilities, is developed. Explicit maximum likelihood estimators of population size and survival rates, together with their asymptotic variances and covariances, are given. A test of whether survival and capture rates are independent of age is shown to be of simple hypergeometric form. An illustrative example based on resighting data of neck-collared giant Canada geese (Branta canadergsis maxima) is presented. The relationship of this model to other capture-recapture and band-recovery models is discussed.

Comparison of different methods for decision-making in bioequivalence assessment.

Abstract: If the regulatory requirements are symmetrical, the use of symmetrical confidence intervals as a decision rule for bioequivalence assessment leads, as shown by simulations, to better level properties and an inferior power compared to a rule based on shortest confidence intervals. A choice between these two approaches will have to depend on a loss function. For asymmetric regulatory requirements, symmetrical confidence intervals should not be used; however, a decision can still be based on posterior probabilities, pr (theta epsilon [r1, r2]/x), or shortest confidence intervals. For purposes of inference, presentation and interpretation of results, we think that the use of symmetrical confidence intervals alone can be misleading and we therefore recommend that the posterior probabilities and densities, or at least the shortest confidence intervals, be given.

An index of tracking for longitudinal data

Abstract: Longitudinal studies provide the opportunity to relate chronic disease risk factors in children to the same risk factors in adults. The epidemiologic concept of tracking allows the quantification of that relationship. Tracking of a risk factor is defined as the maintenance of relative rank over a given time span. A U statistic is defined, which is based on a set of individual growth curves and which estimates the degree of tracking observed. The properties of this estimator are discussed, and applications presented.

Evaluating Diagnostic Tests

Abstract: Diagnostic tests, regarded as methods of classification, are rarely perfect. Classification error and competing technologies require careful evaluation of diagnostic tests, usually by comparison to some standard. Conditional probabilities of correct classification, called 'sensitivity' and 'specificity', are typically used as evaluative measures. In this paper we consider misclassification as nonsampling error, evaluating its effect on the observed sensitivity and specificity.

A variance components approach to categorical data models with heterogeneous cell populations: analysis of spatial gradients in lung cancer mortality rates in North Carolina counties

Abstract: A mixed categorical-continuous variable model is proposed for the analysis of mortality rates. This model differs from other available models, such as weighted least squares and loglinear models, in that the within-cell populations are assumed to be heterogeneous in their levels of mortality risk. Heterogeneity implies that, in addition to the sampling variance considered in other available models, there will be a second component of variance due solely to within-cell heterogeneity. Maximum likelihood procedures are presented for the estimation of the model parameters. These procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function. This assumption is shown to be equivalent to assuming a mixture of Poisson processes with the differential risk levels among individuals within each cell being governed by a two-parameter gamma distribution. The model is applied to data on lung cancer mortality for 1970-1975 for the 100 counties of North Carolina. The analysis shows that, though a gradient in lung cancer mortality rates exist in space, the gradient is restricted to specific demographic categories identified by race, age and sex.

Matching in epidemiologic studies: validity and efficiency considerations.

Abstract: SUMMARY Validity and efficiency issues are considered with regard to the use of matching and random sampling as alternative methods of subject selection in follow-up and case-control studies. We discuss the simple situation involving dichotomous disease and exposure variables and a single dichotomous matching factor, and we consider the influence on efiiciency of a possible loss of subjects due to matching constraints. The decision to match or not should be motivated by efficiency considerations. An efficiency criterion based on a comparison of confidence intervals under matching and random sampling for the effect measure of interest (the risk ratio and risk difference in follow-up studies, and the odds ratio in case-control studies) leads to the following conclusions when the sampling method does not influence the size of the comparison group. In follow-up studies, matching on a confounder is expected to lead to a gain in efficiency over random sampling, while matching on a nonconfounder is not expected to result in a loss of efficiency. In case-control studies, the same conclusions hold, except that matching is not as advantageous as in follow-up studies and can lead to a loss of efliciency in some situations (usually of little practical importance). When matching reduces the size of the comparison group, there is likely to be a meaningful gain in efficiency due to random sampling only when the matched comparison group is at most 40-50% the size of the randomlysampled comparison group in a follow-up study, and at most 50-65% the size in a case-control study.

Binary Mosaics and the Spatial Pattern of Heather

Abstract: An idealized model for the spatial pattern of heather in a planar region is proposed; in this model the subregiorl occupied by heather is represented by the union of randomly located discs of randomly varying radii. Some previous applications of the model are noted. Techniques for parameter estimation and for testing goodness of fit are suggested; these techniques are applied to data showing the incidence of heather in a lOmX20m rectangle at Jadraas, Sweden, thereby demonstrating the extension to binary mosaics of methodology previously illustrated with spatial point processes.

Tracking: Prediction of Future Values from Serial Measurements

Abstract: Repeated measurements of the same characteristic, obtained over time from each of a cohort of individuals, often show systematic change that facilitates prediction of future values. Several investigators have called this regular behavior 'tracking'. Most definitions of the term are related to the idea that a single individual's repeated measurements have expectations equal to a constant percentile of the population distribution asit changes over time. This paper investigates the relationship between this concept and the pattern of change implicit in growth-curve models. Growth-curve models are shown to be more general in some ways, more restrictive in others. We illustrate prediction of future values by growth techniques with an analysis of serial blood pressure measurements from the Framingham Heart Study. We also compare growth-curve analysis with recent work by McMahan (1981, Biometrics 37, 447-455) and suggest a more general class of random-effects models that may be useful in the study of tracking.

Evaluating serial cancer marker studies in patients at risk of recurrent disease.

Abstract: The proportional hazards model of Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187--220), with a time-dependent covariate, is used to analyze serial cancer marker data. A particular advantage of this method is the case with which missing marker data are handled. Analysis of a real data set shows that high levels of the cancer marker carcinoembryonic antigen (CEA) are associated with increased risk of death in patients with resected colorectal cancer. Several aspects of CEA marker history are analyzed, including CEA level at death time t, CEA level 200 days prior to time t, and whether or not CEA exceeded 5 ng/ml prior to t. Methods to test the hypothesis of no marker effect and to give estimates and confidence intervals for model parameters are outlined both for continuous and for grouped time-to-response data. For grouped data a likelihood ratio test of the proportional hazards assumption is suggested.

A Bayesian Approach to Bioequivalence for the 2 x 2 Changeover Design

Abstract: Bioequivalence trials are carried out to compare two or more formulations of a drug containing the same active ingredient, in order to determine whether the different formulation give rise to comparable blood levels. We consider the 2 x 2 changeover experiment the compares two formulations, one of which is considered the standard. For a single univariate characteristic of the plasma concentration--time curve, a criterion for bioequivalence is proposed based on the posterior probability that the difference in formulation means is less than a specific percentage of the mean of the standard. The sensitivity of this posterior probability to alternative priors is investigated. Differences in carry-over effects can be incorporated within the Bayesian framework without restoring to the "all-or-nothing" approach implied by a preliminary test. The use of sequential experimentation is discussed.

Carcinogenic risk assessment: a guide to the literature.

Abstract: An overview of the problems involved in assessing the carcinogenic potential of environmental chemicals is presented. Statistical aspects of the safety evaluation process are noted and appropriate references to the literature are provided. 1. Introducffon As a result of the increasing awareness of the potential health hazards of environmental chemicals, considerable effort is being devoted to the identification and regulation of those chemicals which are carcinogenic. While the primary concern of this research is ultimately human health, information on the carcinogenic potential of chemical substances is necessarily derived mainly from bioassays conducted with animal models. The carcinogenicity of a substance is established when the administration of it to test animals in an adequately designed and conducted laboratory experiment results in an increased incidence or decreased latent period of one or more types of neoplasia, when compared to control animals maintained under identical conditions but not exposed to the compound under study. In this paper, a guide to the statistical literature on carcinogenic risk assessment using animal models is presented. Included are sections on the general principles of carcinogen bioassay, statistical analysis of screening bioassays, quantitative risk assessment, and regulatory considerations. Some references have been included in more than one section, where appropriate. The practical aspects of conducting an adequate and valid carcinogen bioassay are discussed in the references in §2. Statistical procedures for the analysis of screening bioassays designed to detect carcinogenic compounds may be found in the references in §3. Although simple binomial comparisons of the tumor incidence rates observed in the control and test groups may be appropriate for conventional bioassay designs (§3.1), other procedures are required for two-generation studies where the litter rather than the individual animal may be the appropriate experimental unit for purposes of statistical analysis (§3.2). Time-adjusted analysis may be used whenever it is desirable to take into account the time at which lesions were observed (§3.3). Such an analysis may be