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An international effort is now underway to obtain the DNA sequence for the entire human genome (Watson and Jordan, 1989, Genomics 5, 654-656; Barnhart, 1989, Genomics 5, 657-660). This Human Genome Initiative will generate sequence data from several species other than humans, and will result in several copies per species of at least some regions of the genome. Although the project has generated much interest, it is but one aspect of the widespread effort to generate DNA sequence data. Published sequences are collected in common databases, and release 63 of GenBank in March 1990 contained 40,127,752 bases from 33,337 reported sequences (News from GenBank 3; Mountain View, California: Intelligenetics, Inc., 1990). Large though this database is, it is only about 1% of the number of bases in the human genome. Interpretations of data of such magnitude are going to require the collaborative efforts of biometricians and molecular biologists, and an aim of this paper is to show that there is also a role for readers of this journal in the design of surveys of DNA sequences. Discussion here will center on the use of sequence data in evolutionary studies, where some region of DNA is sequenced in several different species. The object is to infer the evolutionary history of that particular region, or of the species themselves. Statistical issues in the very important studies on sequences to locate and characterize regions responsible for human diseases will not be addressed here. We will discuss appropriate ways of measuring distances between DNA sequences and of predicting the sampling properties of the distances. There are procedures for inferring evolutionary histories for a set of elements that depend on a matrix of distances between each pair of elements, and the precision of resulting trees must be influenced by the precision of the distances. We will show that account needs to be taken of two sampling processes--the sampling of sequences by the investigator ("statistical sampling"), and the sampling of genetic material involved in the formation of offspring from a parental population ("genetic sampling").

In this paper the nature of the reasoning processes applied to the nature-nurture question is discussed in general and with particular reference to mental and behavioral traits. The nature of data analysis and analysis of variance is discussed. Necessarily, the nature of causation is considered. The notion that mere data analysis can establish "real" causation is attacked. Logic of quantitative genetic theory is reviewed briefly. The idea that heritability is meaningful in the human mental and behavioral arena is attacked. The conclusion is that the heredity-IQ controversy has been a "tale full of sound and fury, signifying nothing". To suppose that one can establish effects of an intervention process when it does not occur in the data is plainly ludicrous. Mere observational studies can easily lead to stupidities, and it is suggested that this has happened in the heredity-IQ arena. The idea that there are racial-genetic differences in mental abilities and behavioral traits of humans is, at best, no more than idle speculation.

The field of biostatistics is enjoying unparalleled developments. Never before have members of our profession been in such demand. Current applications are significantly influencing the direction of research in statistical methodology. It is not clear whether there is a discipline which can be termed 'biostatistics', but we are part of the emergence of a discipline which is termed 'biostatistical science'. It refers to the applications of statistics, probability, computing and mathematics to the life sciences, with the goal of advancing our knowledge of a subject-matter field in this area. This paper discusses the role of computing, some aspects of training, and future directions of biostatistical science. A special role is envisioned for the Biometric Society to be more active in problems associated with developing countries.

Panel members representing medical/statistical professionals involved in producing and evaluating medical research, i.e., practicing physicians, editors of refereed medical journals, and statisticians in federal regulatory agencies, private industry, and academic medical circles, identified several major problems with medical research papers and proposed a number of ways to improve their quality. Panelists and members of the audience then participated in an hour-long open discussion of the merits and feasibility of proposed solutions.

A prologue on science and statistics focuses attention on the role of statistics in science. Statisticians must be trained as scientists and to meet the needs of science. Those needs surely involve the formulation, modification and verification of stochastic models designed to represent natural phenomena. The method of paired comparisons provides a simple experimental technique but one with a literature rich in model development.

Timely and complete health, social and economic data can be obtained from samples, but usually only for snajor geographic areas and large subgroups of the population. Small domain estimates are available from censuses, but only infrequently and then only for a few variables. Efffiective planning of health services and other governmental activities cannot depend on traditional data sources, the data must be more current and more complete than these sources provide. Since estimates are needed for a great diversity of domains, a definition and classification of domains is presented to clarify the direction of this review. The existing small domain estimation techniques are split into several distinct approaches and reviewed separately. The basic methodologies of these techniques are presented together with their data requirements and limitations. The existing techniques are briefly assessed in regard to their performance and their potential for further application. Current research approaches are also reviewed and possible lines for future advances are indicated.

The increasing influence of multicenter clinical trials in medicine since World War II, and the contributions of statistical methods to the success of such trials, are uncontested. The burgeoning interest in the methodology of clinical trials has been followed by the establishment of formal mechanisms for exchange of ideas, such as the Annual Symposium on Coordinating Clinical Trials and the newly founded Society for Clinical Trials. Nevertheless, as recently as February 1978, Robert S. Gordon, Jr wrote the following words in an editorial (Gordon, 1978)

A variety of statistical issues which arise in the analysis of tumorigenesis assay data are reviewed. Tumor acceleration appeared as a possibility in the Red Dye 40 situation and that phenomenon is discussed. Experimental design considerations covered include sex, cage locations, and whether there is complete randomization, or whether littermates are stratified across doses, or whether, as in multigeneration studies, all littermates are treated alike. Whichever, the statistical analysis should be appropriate. Statistical techniques must take into account the time-to-response aspect in the detection of palpable tumors along with the complication of censored observation due to interim mortality. A logrank technique for accomplishing this must be further adjusted so as to handle tumors detectable only on necropsy. Dosage effects may be sought in a variety of ways, including alternative procedures for identifying progressive dosage effects. Separate analyses may be conducted for separate tumor sites or types, introducing a multiple-testing aspect. Because of the sparseness of data for many individual tumor sites, the usual multiple-testing procedures have to be modified. Statistical analysis, however, is only a guide to the careful interpretation of results, and the need to take action as a result of that interpretation remains.

A review is presented of the post-war development of three theories in factor analysis which together form a basis for further development of methodology of the subject. They are the formulation of the factor-analysis model as a special type of second-order stochastic process, the maximum-likelihood theory of estimation of variables in the factor-analysis model when response variates are normally distributed, and the theory of analytic rotation based on optimization of an objective function.

An account from first principles is given of a number of aspects of analysis of covariance. Six different meanings of analysis of covariance are outlined and the history of this technique is sketched briefly. The development of the key formulae from the method of least squares is described, and generalizations to other distributions in the exponential family are mentioned. Special problems of application in randomized experiments and in observational studies are discussed. Finally, the decomposition of regression relations is considered along with components of covariance.

The first concern of this work is the development of approximations to the distributions of crude mortality rates age-specific mortality rates age-standardized rates standardized mortality ratios and the like for the case of a closed population or period study. It is found that assuming Poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate Poisson distribution....It is...suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic Poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories. Such a model is fit to mortality data for Canadian females classified by age and year. A dynamic variant of the model is further fit to the time series of total female deaths alone by year. The models with extra-Poisson variation are found to lead to substantially improved fits. (EXCERPT)

The statistical methodology for carcinogenic safety testing here developed has the following advantages: (1) Rather than making possibly unwarranted assumptions about a minimum slope in a dose response relationship, the present method represents an objective data based method of estimating "safe" doses. It is applicable to any specified permissible risk (of exceeding the spontaneous rate) and the latter must of course be specified by F.D.A. (2) Although the model which is used for the estimation of safe doses and their lower confidence points is parametric it comprises an adequately large number of parameters to allow for differences in the idiosyncracies of suspected carcinogens, host species and to a limited degree for variations in the experimental protocols. (3) The same computer program will cover the analysis of an experiments in which times to tumor have been recorded as well as experiments in which only tumor incidence rates have been recorded or mixtures of the two. "Better experimentation" is "rewarded" in that the lower confidence limits for the "safe doses" should be higher and more closely approach the true safe dose as the experimental effort increases. (4) The maximum likelihood estimation procedure is sophisticated and has asymptotic optimality properties. It utilizes the latest techniques of "convex programming" and the computer algorithm is straightforward and fast. The methodology proposed here also has the following shortcomings: (1) The model is (multi)parametric. However, it is of the form of the product model for age specific hazard rates which is now widely accepted. (2) Robustness studies on the effect of model breakdown on the estimated safe doses are as yet limited and should be followed up with more extensive studies. (3) Obviously no estimates of "safe doses" can be made if the spontaneous incidence rate is zero and the experimental dose levels have been chosen too small and no tumors have been observed. Similarly if the experimental doses are too small and the tumor incidence rates are all comparable with the spontaneous rate the estimation procedure is afflicted by extremely large errors. The situation improves slightly if the incidence for the highest dose level is higher than that of the lower dose levels which are all approximately equal. In such situations more satisfactory experimental data are needed. Some general recommendations are as follows: (1) Whenever possible it is preferable to record times to tumor and not just incidence rates. However, for experiments of sufficiently long duration necropsies following the varying times of death will provide adequate information on the time dependence of tumor incidence. It may also be advisable to deliberately vary the times of sacrifice to two or three different times. (2) Other considerations being equal it is preferable to have a large number of dose levels rather than more animals per dose level...

This paper considers a technique for estimating the size of caribou herds using radio-collared animals. It relies on a particular caribou behavior, i.e., in the summer, caribou aggregate in large, compact groups that afford protection against blood-sucking insects. During this aggregation period, biologists in aircraft search the caribou summer range trying to detect signals emitted by radio-collared animals and to locate the groups. Unfortunately, some radio-collared animals and their associated groups are missed. The groups that are found are photographed and enumerated, but the total number of photographed caribou underestimates the herd population since groups having no collared animals and some groups with collared animals are missed. This paper proposes a stochastic model to correct the abundance estimator for group undercoverage. An estimator for the size of the population is proposed with an associated variance estimate. The analysis of the July 1993 postcalving photographic inventory of the Riviere George herd is presented as an illustration.

SUMMARY Multidimensional longitudinal data result when researchers measure an outcome through time that is quantified by many different response variables. These response variables are often defined on different numerical scales. The objective of this paper is to present a method to summarize and estimate an overall treatment effect from this type of longitudinal data. A regression model is proposed that assumes the treatment effect can be parameterized as an acceleration or deceleration of the time scale of each response variable's trajectory. Generalized estimating equations are used to estimate the model parameters. Cognitive and functional ability data from Alzheimer's disease patients and quality of life data from an AIDS clinical trial are used to illustrate the model. Researchers often attempt to quantify outcomes, such as cognitive ability, quality of life, or physical functioning, for which no single measure exists. To effectively capture all aspects of the outcome, a number of measurements are commonly used. For example, cognitive ability in Alzheimer's disease patients is typically measured with a battery of performance-based tests. Quality of life in AIDS patients is often measured with a multi-item self-report questionnaire. Physical functioning in the elderly is measured using an extensive self-report questionnaire and/or multiple performance-based tests. The result of such measurements is the representation of cognitive ability, quality of life, or physical functioning by a numerous set of scores for each individual. When measurements of this type are also collected over time, the result is multidimensional longitudinal data. A common problem is to evaluate a treatment effect from such data. For example, clinical trials have been performed to determine if therapies can slow the rate of cognitive loss among Alzheimer's disease patients. This paper is concerned with the estimation of a treatment effect from multidimensional longitudinal data. Several statistical issues arise in evaluating a treatment effect from this type of data. A main issue is the multidimensionality. There are several response variables, each one measuring a slightly different aspect than the others. Since no single response variable sufficiently acts as a main outcome variable, methods that collectively consider all of the response variables are desired. The main question is how one can use the multiple response variables to obtain a summary measure of the treatment effect that is readily interpretable. The problem is challenging because the multiple response variables may be defined on different numerical scales. Methods that combine information from the different response variables are required. These methods must also account for the autocorrelation that exists across time within each response variable and the cross-correlation that exists between different response variables both across time and at the same time. One frequently used approach is to analyze the treatment effect on each response variable separately. While this approach is simple and easy to implement, it has limitations. Evaluating individual response variables is informative but often fails to provide an overall statement of the treatment

SUMMARY This paper proposes a method for assessing risk in developmental toxicity studies with exposure prior to implantation. The method proposed in this paper was developed to account for a dosedependent trend in the number of implantation sites per dam, which is a common problem in studies with exposure prior to implantation. Toxins may have the effect of interfering with the early reproductive process, which can prevent implantation in the uterine wall. An imputation procedure is presented for estimating the number of potential fetuses by sampling from the empirical distribution of the number of implants per litter in the control group. The marginal death outcomes and the joint malformation and survival outcomes for each potential fetus can be estimated using multiple imputation or the chained data augmentation algorithm. Logit models can then be fit and used to estimate the effect of dose on reducing the probability of a normal birth. These models accommodate multiple covariate effects and can be applied to low-dose extrapolation. A simulation study is done to evaluate the properties of model-based estimators of the mean response and the virtually safe dose level (VSD). It was found that both estimates were good approximations of the underlying dose effect. A dominant lethal assay data set (Luning et al., 1966, Mutation Research 3, 444-451) is analyzed, and the results are compared with those of Rai and Van Ryzin (1985, Biometrics 41, 1-9).

A nonparametric estimator for the joint distribution of a survival time and surrogate response time, which may occur earlier during follow-up, is presented. In the absence of the surrogate response variable, the estimator reduces to the Kaplan Meier nonparametric estimator for the survival time alone. The estimator derived in this paper is done so in a particular novel way using an exchangeable process (reinforced random walks) to model individual observations. The methodology introduced in the paper is readily extended to modelling multiple state processes.

This paper discusses interval estimation of the risk ratio (RR) between a secondary infection, given a primary infection, and the primary infection. Three asymptotic closed-form interval estimators are developed using Wald's test statistic, the logarithmic transformation, and Fieller's theorem. The performance of these interval estimators is compared with respect to the coverage probability and the expected length of the resulting confidence intervals. When the underlying probability of a primary infection is high (say, 0.80), all three estimators perform reasonably well. In fact, in this case, they are all essentially equivalent when the number of subjects n > or = 100. When the probability of a primary infection is small (say, 0.20) or moderate (say, 0.30 to 0.50), the interval estimator using the logarithmic transformation outperforms the other two estimators when n < or = 100. In fact, the coverage probability of the former estimator is consistently greater than or equal to the desired confidence level in all the situations considered in this paper and hence is recommended for general use.

The accuracy of a medical diagnostic test is typically summarized by the sensitivity and specificity when the test result is dichotomous. Receiver operating characteristic (ROC) curves are measures of test accuracy that are used when test results are continuous and are considered the analogs of sensitivity and specificity for continuous tests. ROC regression analysis allows one to evaluate effects of factors that may influence test accuracy. Such factors might include characteristics of study subjects or operating conditions for the test. Unfortunately, regression analysis methods for ROC curves are not well developed and methods that do exist have received little use to date. In this paper, we propose and compare three very different regression analysis methods. Two are modifications of methods previously proposed for radiology settings. The third is a special case of a general method recently proposed by us. The three approaches are compared with regard to settings in which they can be applied and distributional assumptions they require. In the setting where test results are normally distributed, we elucidate the correspondence between regression parameters in the different models. The methods are applied to simulated data and to data from a study of a new diagnostic test for hearing impairment. It is hoped that the presentation in this paper will both encourage the use of regression analysis for evaluating diagnostic tests and help guide the choice of the most appropriate regression analysis approach in applications.

This paper considers the estimation of the size of a closed population in a stratified capturerecapture experiment using the stratified Petersen-Lincoln model introduced by Darroch (1961, Biometrika 48, 241-260). A generalization of Darroch's model where the tagging or the recovery probabilities depend on explanatory variables possibly related to the capture mechanism is proposed. A simple scoring algorithm for the estimation of the nuisance parameters (i.e., the vectors of tagging and of recovery probabilities and the matrix for the distribution of the units in the capturerecapture area) is derived. This algorithm is based on a new closed-form expression for the inverse of the Fisher information matrix of the conditional likelihood for the estimation of the nuisance parameters. Large sample tests for the tagging and the recovery probabilities are obtained. Pooling of adjacent recovery strata with equal capture probabilities is proposed as a method for getting accurate estimators of the size of the population. Conditional and unconditional estimators of the size of the population are proposed. Analyses of data on smolt migration illustrate the methodology presented in this paper.