On Multi-Treatment Adaptive Allocation Design for Dichotomous Response

The use of ridit, as a probability score, is a very common practice to compare discrete random variables in discrete data analysis. In the present work we formulate ridit reliability functionals for some comparison of K independent binary random variables. We use such functionals to provide a generalized response-adaptive design (GRAD) on K(≥ +2) treatment-arms for dichotomous response variables. We exhibit some properties of the proposed design and compare it with some of the existing competitors by computing its various performance measures. We also provide a discussion towards a possible modification of the GRAD in the presence of covariates.     

On approaches to OR modelling

The paper examines the various relationships between theory and practice of OR Models in developed and developing economies. Relationships between theory and practice are classified into three sets: (i) during model construction stage, (ii) during the decision-making stage and (iii) in the implementation stage. Various case studies from U.K. and India are analysed to get an insight into these relationships. Various factors responsible for divergence of practice from theory are critically examined and drawing from the lessons of the case studies, ways and means of making models which are implementable in practice are suggested. Environments, the nature of the problems and objectives vary between developed and developing economies. However, in spite of these variations the basic nature of the relationships and the scientific method of problem solving are the same in both.     

Sequential-type nonparametric test using Mann-Whitney statistics

The paper provides a nonparametric test for the identity of two continuous univariate distribution functions when observations are drawn in pairs from the populations, by adopting a sampling scheme which, using Mann-Whitney scores, generalizes the existing inverse binomial sampling technique. Some exact performance characteristics of the proposed test are formulated and compared numerically with existing competitors of the proposed test. The applicability of the proposed test is illustrated using real-life data.     

On a two-treatment adaptive allocation rule for continuous response

In recent years adaptive designs have been becoming popular in the context of clinical trials. The purpose of the present work is to provide a sequential two-treatment allocation rule for when the response variables are continuous. The rule is ethical as well as sometimes optimal depending upon the nature of the distribution of the study variables. We examine the various properties of the rule.     

Controlling Type-I Error Rate in Monitoring Structural Changes Using Partially Sequential Procedures

In the present article, we develop some asymptotically power on partially sequential nonparametric tests for monitoring structural changes. Our test procedures are based on Wilcoxon score. We use the idea of curved stopping boundaries. We derive some exact results and perform simulation studies to provide various properties of the tests. We see that one of the proposed procedures significantly controls the Type I error rate. This procedure may be very effective for fluctuation monitoring. We illustrate the procedures by using real life data from the stock market.     

Reverse Auctions with Multiple Reinforcement Learning Agents*

Reverse auctions in business‐to‐business (B2B) exchanges provide numerous benefits to participants. Arguably the most notable benefit is that of lowered prices driven by increased competition in such auctions. The competition between sellers in reverse auctions has been analyzed using a game‐theoretic framework and equilibria have been established for several scenarios. One finding of note is that, in a setting in which sellers can meet total demand with the highest‐bidding seller being able to sell only a fraction of the total capacity, the sellers resort to a mixed‐strategy equilibrium. Although price randomization in industrial bidding is an accepted norm, one might argue that in reality managers do not utilize advanced game theory calculations in placing bids. More likely, managers adopt simple learning strategies. In this situation, it remains an open question as to whether the bid prices converge to the theoretical equilibrium over time. To address this question, we model reverse‐auction bidding behavior by artificial agents as both two‐player and n‐player games in a simulation environment. The agents begin the game with a minimal understanding of the environment but over time analyze wins and losses for use in determining future bids. To test for convergence, the agents explore the price space and exploit prices where profits are higher, given varying cost and capacity scenarios. In the two‐player case, the agents do indeed converge toward the theoretical equilibrium. The n‐player case provides results that reinforce our understanding of the theoretical equilibria. These results are promising enough to further consider the use of artificial learning mechanisms in reverse auctions and other electronic market transactions, especially as more sophisticated mechanisms are developed to tackle real‐life complexities. We also develop the analytical results when one agent does not behave strategically while the other agent does and show that our simulations for this environment also result in convergence toward the theoretical equilibrium. Because the nature of the best response in the new setting is very different (pure strategy as opposed to mixed), it indicates the robustness of the devised algorithm. The use of artificial agents can also overcome the limitations in rationality demonstrated by human managers. The results thus have interesting implications for designing artificial agents in automating bid responses for large numbers of bids where human intervention might not always be possible.     

On an ethical cum optimal adaptive allocation design

In the present work, we formulate a two-treatment single period two-stage adaptive allocation design for achieving larger allocation proportion to the better treatment arm in the course of the trial with increased precision of the parameter estimator. We examine some properties of the proposed rule and compare it with some of the existing allocation rules and report substantial gain in efficiency with a considerably larger number of allocations to the better treatment even for moderate sample sizes.     

A response-adaptive design in crossover trial

In the present work, whenever the response variables are binary, we frame an adaptive allocation rule for a two-treatment two-period crossover design in the presence of possible carry-over effects. The proposed rule is a combination of the play-the-winner and randomized play-the-winner rules. We study various properties of the proposed rule through asymptotics and simulations. Some related inferential problems are also considered. The proposed procedure is compared with some possible competitor.