Chronic diseases are ubiquitous and costly in American populations. Interventions targeting health behavior change to manage chronic diseases are needed, but previous efforts have fallen short of producing meaningful change on average. Adaptive stepped-care interventions, that tailor treatment based on the needs of the individual over time, are a promising new area in health behavior change. We therefore conducted a systematic review of tests of adaptive stepped-care interventions targeting health behavior changes for adults with chronic diseases. We identified 9 completed studies and 13 research protocols testing adaptive stepped-care interventions for health behavior change. The most common health behaviors targeted were substance use, weight management, and smoking cessation. All identified studies test intermediary tailoring for treatment non-responders via sequential multiple assignment randomized trials (SMARTs) or singly randomized trials (SRTs); none test baseline tailoring. From completed studies, there were few differences between embedded adaptive interventions and minimal differences between those classified as treatment responders and non-responders. In conclusion, updates to this work will be needed as protocols identified here publish results. Future research could explore baseline tailoring variables, apply methods to additional health behaviors and target populations, test tapering interventions for treatment responders, and consider adults’ context when adapting interventions.

Qualitative models can be used for decision making under uncertainty. This provides a useful framework for evaluating the models. If the costs for every action/state of nature combination are known, decisions made using a well-calibrated model would result in actual costs being close to expected costs. In addition, the actual cost can be compared to the cost of perfect foresight actions, giving a bound on the value of a better model. Application of these procedures is made using a logit model developed to predict Missouri country grain elevator bankruptcies.

A decision-making body may utilize a wide variety of different strategies when required to make a collective decision. In principle, we would like to use the most effective decision rule, that is, the rule yielding the highest probability of making the correct decision. However, in reality we often have to choose a decision rule out of some restricted family of rules. Therefore, it is important to be able to rank various families of rules. In this paper we consider three classes of decision rules: (i) balanced expert rules, (ii) the so-called single expert rules, and (iii) restricted majority rules. For the first two classes, we show that, as we deviate from the best rule in the family, the effectiveness of the decision rule decreases. For the last class, we obtain a very different phenomenon: any inner ranking is possible.

We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making a correct choice. In this paper, we assume the correctness probabilities of the experts to be independent random variables selected from some given distribution. Moreover, the ranking of the members in the group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.

Sapir (1998) calculated the probabilities of the expert rule and of the simple majority rule being optimal under the assumption of exponentially distributed logarithmic expertise levels. Here we find the analogous probabilities for the family of restricted majority rules, including the above two extreme rules as special cases, and the family of balanced expert rules. We compare the two families, the rules within each family, and all rules of the two families with the extreme rules.

We model a selection process arising in certain storage problems. A sequence (X1, · ··, Xn) of non-negative, independent and identically distributed random variables is given. F(x) denotes the common distribution of the Xi′s. With F(x) given we seek a decision rule for selecting a maximum number of the Xi′s subject to the following constraints: (1) the sum of the elements selected must not exceed a given constant c > 0, and (2) the Xi′s must be inspected in strict sequence with the decision to accept or reject an element being final at the time it is inspected.

We prove first that there exists such a rule of threshold type, i.e. the ith element inspected is accepted if and only if it is no larger than a threshold which depends only on i and the sum of the elements already accepted. Next, we prove that if F(x) ~ Axα as x → 0 for some A, α> 0, then for fixed c the expected number, En(c), selected by an optimal threshold is characterized by Asymptotics as c → ∞and n → ∞with c/n held fixed are derived, and connections with several closely related, well-known problems are brought out and discussed.