Approaches for optimal sequential decision analysis in clinical trials.

Unlike traditional approaches, Bayesian methods enable formal combination of expert opinion and objective information into interim and final analyses of clinical trial data. However, most previous Bayesian approaches have based the stopping decision on the posterior probability content of one or more regions of the parameter space, thus implicitly determining a loss and decision structure. In this paper, we offer a fully Bayesian approach to this problem, specifying not only the likelihood and prior distributions but appropriate loss functions as well. At each data monitoring point, we enumerate the available decisions and investigate the use of backward induction, implemented via Monte Carlo methods, to choose the optimal course of action. We then present a forward sampling algorithm that substantially eases the analytic and computational burdens associated with backward induction, offering the possibility of fully Bayesian optimal sequential monitoring for previously untenable numbers of interim looks. We show that forward sampling can always identify the optimal sequential strategy in the case of a one-parameter exponential family with a conjugate prior and monotone loss functions as well as the best member of a certain class of strategies when backward induction is infeasible. Finally, we illustrate and compare the forward and backward approaches using data from a recent AIDS clinical trial.

Bayesian demography: projecting the Iraqi Kurdish population, 1977-1990.

"Projecting populations that have sparse or unreliable data, such as those of many developing countries, presents a challenge to demographers. The assumptions that they make to project data-poor populations frequently fall into the realm of ¿educated guesses', and the resulting projections, often regarded as forecasts, are valid only to the extent that the assumptions on which they are based reasonably represent the past or future, as the case may be. These traditional projection techniques do not incorporate a demographer's assessment of uncertainty in the assumptions. Addressing the challenges of forecasting a data-poor population, we project the Iraqi Kurdish population using a Bayesian approach. This approach incorporates a demographer's uncertainty about past and future characteristics of the population in the form of elicited prior distributions."

Prime time for Bayes.

This paper reviews what Bayesian statistics is and gives pointers to the literature. The need for a subjectively determined prior distribution, likelihood, and loss function is often taken to be the principal disadvantage of Bayesian statistics. This paper argues that the requirement that these be explicitly stated is a distinct Bayesian advantage. Advances in Bayesian technology make it ready now to be the main inferential tool for clinical trials.

Bayesian statistical methods in public health and medicine.

This article reviews the Bayesian statistical approach to the design and analysis of research studies in the health sciences. The central idea of the Bayesian method is the use of study data to update the state of knowledge about a quantity of interest. In study design, the Bayesian approach explicitly incorporates expressions for the loss resulting from an incorrect decision at the end of the study. The Bayesian method also provides a flexible framework for the monitoring of sequential clinical trials. We present several examples of Bayesian methods in practice including a study of disease progression in AIDS, a comparison of two therapies in a clinical trial, and a case-control study investigating the link between dietary factors and breast cancer.

Adjusting the 1980 census of population and housing.

"In 1980, several cities and states sued the U.S. Census Bureau to correct census results. This correction would adjust for the differential undercounting of Blacks and Hispanics, especially in cities. In this article, the authors, each of whom testified for New York City and State in their joint lawsuit against the Census Bureau, describe the likely pattern of the undercount and present a method to adjust for it." The authors describe available methods for data adjustment and introduce a regression-based composite method of adjustment, which is used to estimate the undercounts for 66 areas. "As expected, we find that the highest undercount rates are in large cities, and the lowest are in states and state remainders with small percentages of Blacks and Hispanics. Next, we analyze how sensitive our estimates are to changes in data and modeling assumptions. We find that these changes do not affect the estimates very much. Our conclusion is that regardless of whether we use one of the simple methods or the composite method and regardless of how we vary the assumptions of the composite method, an adjustment reliably reduces population shares in states with few minorities and increases the shares of large cities."

Progress toward a more ethical method for clinical trials.

Methodology for conducting clinical trials of new drugs and treatments on people need not be regarded as fixed. After reviewing the currently most popular method (randomization) and its ethical problems, this paper explores the possibilities of a new method for conducting such trials. It relies on new Bayesian technology for eliciting the opinions of medical experts. These opinions are conditioned on specific predictor variables, and are held in a computer. At any stage in a trial, these opinions can be updated in the computer using the information collected in the trial up to that point. Consider as an admissible treatment for a patient having specific values of predictor variables only those treatments that at least one expert regards as best (in the computer model) for this patient. It is proposed that only admissible treatments, so defined, be allowed to be assigned to the patient. The ethical and statistical consequences of this principle are explored. Experience to date with a trial at Johns Hopkins designed on this principle is reported.

KIE: Kadane explores the possibilities of using new methods of conducting clinical trials which assign patients to a treatment that at least one expert judges best for that patient. Bayesian methods are used for eliciting the opinions of medical experts which can be changed as information on treatments is collected. The author believes that, while most patients in clinical trials receive reasonable care, they may not receive the best possible care, and that alternatives to standard randomization techniques must be devised. He describes experience with a trial at Johns Hopkins using the optimal treatment method.

Using administrative lists to estimate census omissions.

"We present a method for estimating omission rates from censuses. Our method is based on the merger of administrative lists, sampling from these lists, and matching against census rolls. We describe the method, present the results of a test in New York City...in 1980, and evalute the results. We compare our proposed method to other procedures for estimating omission rates."

Discrimination between schizophrenic and control subjects by means of plasma dehydroepiandrosterone measurements.

In this study we were able to distinguish 10 schizophrenic subjects from 10 control subjects with 100% accuracy by measuring plasma dehydroepiandrosterone (DHEA) diurnal rhythms and analyzing the data using a linear function equation. Discrimination with this high level of accuracy is in contrast to most studies of altered biological functioning in schizophrenia which have yielded inconsistent results. These findings are regarded as preliminary; further study is necessary to elicit any consistent DHEA disturbance in schizophrenics and to discover the significance for the pathophysiology of the illness. Measurements of plasma cortisol, aldosterone, DHEA-SO4, and testosterone did not provide such a basis for discrimination.

Scaling data on inter-nation action.

We conclude (i) that the marker-card method is as reliable a measure as the ordinary Q-sort method; (ii) that Q and the marker-card score are measuring very nearly the same thing-in this case, presumably conflict; and (iii) that the use of marker cards permits comparison of judgments about a given quantity in the context of different situations and may even permit comparison of results obtained by different research teams if the different teams use the same marker decks. A fundamental issue involved in scoring the entries on the cards in this study by either Q-sort or marker cards is the "judgability" of the items as indicators of conflict. We noted above that items with the highest variances in scoring, from judge to judge, were concentrated at the low-conflict end of the scale. A possible explanation is that judges are able to make finer distinctions concerning an attribute when it is present than when it is absent. Differences in scoring could also arise from a lack of unidimensionality in the attribute being scaled. If juidges find that conflict has several distinct aspects, the task of placing items in a single order becomes more difficult. Difficulties in making judgments also arose from the fact that the actions were being judged out of context, or in contexts that varied from judge to judge, since no standard context was supplied. But these difficulties lie outside our problem, which was to find an alternative to Q-sorting which would permit intersituational comparisons. Our sLIccess in finding an alternative is apparent in our results, but problems of judgability remain with both techniques. Beyond providing a standard for intersitLiational comparisons, the markercard technique has other advantages. It is possible that the use of marker decks will be of help in training judges to score such a variable as conflict. In our study it permitted identification of a judge inadequately trained to do so. Possibly the marker cards will be useful in assigning scale values to hatches of data too small for Q-sort, or even to individual items. It further appears that the marker cards should be useful in discriminating among highconflict items which heretofore would all have tended to appear in the top Q-sort category. The marker-card technique has given us a reliable alternative to Q-sort for scaling conflict. The method should be capable of extension to dimensions other than conflict.