Sequential Decision Procedure Research Articles

Stratification model based on early postprostatectomy prostate-specific antigen kinetics may help to reduce the risk of overtreatment in candidates for adjuvant radiotherapy

Objective: The aim of this study was to construct a stratification model based on early postoperative kinetics of prostate-specific antigen (PSA) to select the most suitable high-risk patients for early intervention after radical prostatectomy (RP).Materials and methods: The study evaluated 205 men who had undergone RP without any adjuvant treatment. All of the patients had positive surgical margins, extracapsular extension and/or seminal vesicle invasion. The patients underwent multiple ultrasensitive PSA measurements on days 14, 30, 60 and 90 after RP, and subsequently at 3 month intervals. The ability of particular PSA measurements to predict biochemical recurrence (BCR) was assessed using the area under the curve (AUC). A sequential mathematical decision procedure was constructed to create a stratification model.Results: During the median follow-up of 45.9 months, 106 patients (51%) experienced BCR. Prediction of BCR in terms of the AUC for PSA measurements on days 14, 30, 60 and 90 after the surgery was 0.61, 0.70, 0.80 and 0.82, respectively. In the multivariate analysis, only PSA after RP remained as a predictor of progression-free survival (p < 0.001). The stratification model based on calculated cut-off values for PSA on day 30 (0.068 ng/ml) and PSA on day 60 (0.015 ng/ml) reduced the potential overtreatment rate by 37%.Conclusions: The results imply that ultrasensitive PSA values obtained very early after RP correlate with the presence of recurrent disease in high-risk patients. Incorporating these readily available variables into risk stratification models may help to individualize the administration of adjuvant radiotherapy and thus to minimize overtreatment.

Energy-aware resource allocation for cooperative cognitive radio dynamic spectrum access networks

The resource allocation problem is investigated for cooperative cognitive radio networks, considering energy efficiency of the primary users (PUs) and spectrum efficiency of the secondary users (SUs). The cooperation framework involves a PU selecting a SU as the relay and allocating the spectrum access intervals for the selected SU as a reward. The above sequential decision procedure is formulated as a Stackelberg game. Based on the knowledge of the effects of PUs decision on the behavior of a SU, the leader (PU) determines a fraction of the time slot duration to be used for the primary. The follower (SU) is allowed to transmit its own data to the corresponding receiver in the remaining duration and determines its optimal transmission power. The outcomes of the proposed cooperative resource allocation scheme, including primary user and secondary user power control, as well as dynamic access spectrum, are analyzed. Numerical results demonstrate that, with the proposed resource allocation scheme, the PU can achieve high energy saving by cooperation with the SU.

Towards a more precise neurophysiological assessment of cognitive functions in patients with disorders of consciousness

To analyze the principles that guide inference of covert cognitive functions and consciousness in patients with extremely severe brain damage on the basis of neurophysiological test results. (1) A quantitative analysis of a range of possible inferences based on neurophysiological findings in low- and non-responsive patients; (2) a logical analysis of the various possible orders of application of neurophysiological tests in such patients. Surprisingly, improvement of neurophysiological test qualities contributes to the improvement of diagnostic results less than some other factors, such as the structure of the patient population, the quality of the previous clinical diagnosis, and the variability of the methods used. A sequential decision procedure is suggested. Different test paradigms should be combined most effectively to arrive at a reliable evaluation of cognitive functions in this patient population.

A survey of Stackelberg differential game models in supply and marketing channels

Stackelberg differential game models have been used to study sequential decision making in noncooperative games in diverse fields. In this paper, we survey recent applications of Stackelberg differential game models to the supply chain management and marketing channels literatures. A common feature of these applications is the specification of the game structure: a decentralized channel composed of a manufacturer and independent retailers, and a sequential decision procedure with demand and supply dynamics and coordination issues. In supply chain management, Stackelberg differential games have been used to investigate inventory issues, wholesale and retail pricing strategies, and outsourcing in dynamic environments. The underlying demand typically has growth dynamics or seasonal variation. In marketing, Stackelberg differential games have been used to model cooperative advertising programs, store brand and national brand advertising strategies, shelf space allocation, and pricing and advertising decisions. The demand dynamics are usually extensions of the classical advertising capital models or sales-advertising response models. We begin by explaining the Stackelberg differential game solution methodology and then provide a description of the models and results reported in the literature.

The consequences of endogenizing information for the performance of a sequential decision procedure

We analyse the implications of endogenizing information collection and reputational concerns for the performance of a sequential decision structure. In this model, two agents decide in a sequence whether to implement a public project. The cost of gathering information is private. We derive two results. First, endogenizing information replaces the herding problem with a free-rider problem. Second, endogenizing information aggravates the distortionary effect of reputational concerns.

Testing independent sparse heterogeneous mixtures

We study the sequential discernibility between the independent fair coin tossing μ 0 and the sparse heterogeneous mixtures HM ( α , γ ) ≡ ( 1 - ε n ) · Bernoulli ( 1 / 2 ) + ε n · Bernoulli ( ( 1 + θ n ) / 2 ) with ε n ∼ n - γ and θ n ∼ n - α . Extending the result in Lim (2003), we show that HM ( α , γ ) and μ 0 are sequentially discernible when 0 < α + γ ⩽ 0.5 , but are not so when 0.5 < γ + α < 1 . It will be shown that each of the three different discernibility in [Lim, 2003. Testing stochastic processes: stationarity, independence, and ergodicity. Technical Report], (1) discernibility with an entire sample path, (2) uniformly discernibility with an entire sample path, and (3) sequentially discernibility, is equivalent to each other under this setting, and furthermore, it follows that sequential decision procedures are equivalent to the decisions based on an entire sequence. Finally, we show that the coin tossing with finitely many trials of biased coins is not sequentially discernible from that with infinitely many trials.

A top-down, step up approach to pharmacogenetic discovery using CEPH family cell lines

Background/Aims Previously Watters et al. (PNAS, 2004) found strong cell viability dose-response for 5-FU (0.21–0.70), and identified QTLs (chromosome 9: LOD=3.4) using public microsatellite data. We try to localize these toxicity genes using the HapMap published SNPs. Methods 30 CEPH HapMap trio cell lines, treated with 9 different doses of 5-FU, were analyzed at 4928 SNPs in the chromosome 9 QTL region. We used various statistical methods (179 SNPs were significant at p<0.05, uncorrected), including the False Discovery Rate, Storey's Q, and Sequential Multiple Decision Procedures (SMDP). Results Five SNPs were chosen as significant signals by SMDP at a power of 95% (but requiring only 78% of the sample), with sequential R2 of 0.16, 0.16, 0.17, 0.17, 0.11 respectively. Subselecting LD tag SNPs (Lazarus et al., 2004) reduces the number by nearly half, thus improving power. We employ a step up strategy from single SNPs to LD blocks to haplotypes, and finally to gene-based associations. Conclusions CEPH family cell lines are a powerful, unique resource for in vitro phamacogenetic toxicity gene discovery. Clinical Pharmacology & Therapeutics (2005) 77, P8–P8; doi: 10.1016/j.clpt.2004.11.031

A single, sequential, genome-wide test to identify simultaneously all promising areas in a linkage scan.

Inflation of type I error occurs when conducting a large number of statistical tests in genome-wide linkage scans. Stringent alpha-levels protect against the high numbers of expected false positives but at the cost of more false negatives. A more balanced tradeoff is provided by the theory of sequential analysis, which can be used in a genome scan even when the data are collected using a fixed-sample design. Sequential tests allow complete, simultaneous control of both the type I and II errors of each individual test while using the smallest possible sample size for analysis. For fixed samples, the excess N "saved" can be used in a confirmatory, replication phase of the original findings. Using the theory of sequential multiple decision procedures [Bechhoffer et al., 1968], we can replace the series of individual marker tests with a new single, simultaneous genome-wide test that has multiple possible outcomes and partitions all markers into two subsets: the "signal" versus the "noise," with an a priori specifiable genome-wide error rate. These tests are demonstrated for the Haseman-Elston approach, are applied to real data, and are contrasted with traditional fixed-sampling tests in Monte Carlo simulations of repeated genome-wide scans. The method allows efficient identification of the true signals in a genome scan, uses the smallest possible sample sizes, saves the excess to confirm those findings, controls both types of error, and provides one elegant solution to the debate over the best way to balance between false positives and negatives in genome scans.

Bayesian Sequential Two-Phase Sampling

Abstract We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a population of fish using data on covariates (e.g., length, weight) obtained from all members of the first-phase sample and data on age obtained from the fish in the second-phase subsample.

The VPRT: A Sequential Testing Procedure Dominating the SPRT

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

A sequential test for the failure rate of an exponential distribution with censored data

This paper provides an optimal sequential decision procedure for deciding between two composite hypotheses about the unknown failure rate of an exponential distribution, using censored data. The procedure has two components, a stopping time and a decision function. The optimal stopping time minimizes the expected total loss due to a wrong decision plus cost of observing the process. The optimal decision function is easily characterized once a stopping time has been specified. The main result determines the continuation region for the optimal decision procedure

On the empirical Bayes approach to multiple decision problems with sequential components

The empirical Bayes approach to multiple decision problems with a sequential decision problem as the component is studied. An empirical Bayesm-truncated sequential decision procedure is exhibited for general multiple decision problems. With a sequential component, an empirical Bayes sequential decision procedure selects both a stopping rule function and a terminal decision rule function for use in the component. Asymptotic results are presented for the convergence of the Bayes risk of the empirical Bayes sequential decision procedure.

On empirical bayes sequential estimation

We study the empirical Bayes approach to the sequential estimation problem. An empirical Bayes sequential decision procedure, which consists of a stopping rule and a terminal decision rule, is constructed for use in the component. Asymptotic behaviors of the empirical Bayes risk and the empirical Bayes stopping times are investigated as the number of components increase.

On Empirical Bayes Testing with Sequential Components

We study the empirical Bayes decision theory with an $m$-truncated sequential statistical decision problem as the component. An empirical Bayes sequential decision procedure is constructed for the linear loss two-action problem. Asymptotic results are presented regarding the convergence of the Bayes risk of the empirical Bayes sequential decision procedure. With sequential components, an empirical Bayes sequential decision procedure selects both a stopping rule function and a terminal decision rule function for use in the component with parameter $\theta$.

Sequential decision procedures for batching and balancing in FMSs

Batching and balancing constitute two of the several scheduling and resource allocation problems important over different time scales in FMS operations. The time scale for batching and balancing is of the order of days to weeks — which puts it between long-term planning and part selection, of the order of months to years, and real-time part entry and dispatching, of the order of minutes. All these scheduling and resource allocation problems have been addressed at the Charles Stark Draper Laboratoty by a common methodology. We have used a sequential decision algorithm, each decision based on optimization of a probabilistic performance criterion designed to trade off whatever and however many competing attributes may be important in the particular problem. This paper discusses the common methodology, and its application to FMS batching and balancing in particular. Our computer program BATCH/BAL which implements the algorithms given here has been the starting point for all the other sequential decision programs subsequently developed at our laboratory.

Sequential bayesian and minimax decisions based on stochastic processes

For a large class of sequential decision problems in continuous time the problem of finding an optimal sequential decision procedure is reduced to an optimal stopping problem for a certain strochastic process (Xt). Conditions with respect to the basic data are given such that the process has continuity properties which yield the existence of an optimal stopping time. In case, in which the terminal decision is based on the observation of a stochastic process (e.g. Gaussian process, semimartingale with Gaussian martingale part, Gaussian Markovian process), a representation of (Xt) can be derived if conjugate priors and appropriate but rather general loss functions are used. In special cases explicit solutions of the optimal stopping problems can be found, too.

Flexibility, learning, and irreversibility in environmental decisions: A bayesian approach

The Bayes decision is characterized and studied for a two-period decision problem involving a proposed resource development project. It is assumed that development is irreversible and that expectations about benefits and costs during the second period vary with experiences resulting from the first-period action. The amount and types of learning achieved depend upon the particular action taken during the first period. Flexible sequential decision procedures are compared with fixed once-and-for-all decisions. It is shown that under this specification, optimal development decisions are not necessarily more conservative when a sequential procedure is used. The possibility of reneging on a fixed decision is formally specified and studied.

The control of a prosthetic arm by EMG pattern recognition

An electromyographic (EMG) signal pattern recognition system is constructed for real-time control of a prosthetic arm through precise identification of motion and speed command. A probabilistic model of the EMG patterns is first formulated in the feature space of integral absolute value (IAV) to describe the relation between a command, represented by motion and speed variables, and location and shape of the corresponding pattern. The model provides the sample probability density function of pattern classes in the decision space of variance and zero crossings based on the relations between IAV, variance, and zero crossings established in this paper. Pattern classification is carried out through a multiclass sequential decision procedure designed with an emphasis on computational simplicity. The upper bound of probability of error and the average number of sample observations are investigated. Speed and motion predictions are used in conjunction with the decision procedure to enhance decision speed and reliability. A decomposition rule is formulated for the direct assignment of speed to each primitive motion involved in a combined motion. A learning procedure is also designed for the decision processor to adapt long-term pattern variation. Experimental results are discussed in the Appendix.

Studies on the mutagenic potential of the pesticide chlordimeforme and its principal metabolites in the mouse heritable translocation assay

Chlordimeforme and its 2 principla metabolites, N-formyl-4-chloro- o-toluidine and 4-chloro- o-toluidine, were studied for induction of heritable translocations. Maximal tolerated doses of the compounds were given daily by gavage for 7 consecutive weeks. After mating with untreated females, about 1000 F 1 male offspring per group — including vehicle control and positive control (Tretamine, TEM) — were tested for their reproductive performance by use of a sequential decision procedure on litter sizes to select males with translocation heterozygosity. Partially sterile, sterile and non-classifiable F 1 males were examined cytogenetically by scoring meiotic chromosomes for translocation multivalents or analysing mitotic divisions for marker chromosomes. The 3 compounds tested at dose levels showing toxic effects did not induce translocation heterozygosity. Tretamine, the positive control, gave the expected mutagenic response.

Sequential estimation of percent correct

A sequential estimation and decision procedure is presented as an easily implemented alternative to adaptive methods. Unlike adaptive methods, the procedure does not alter stimulus values during the course of a run in order to converge at a desired level of performance. Instead, the procedure inspects a subject's cumulative performance at the end of each trial and, based on a set of well defined criteria, decides whether to continue or terminate the run. If the subject is performing well above or below the level of performance specified by the experimenter, the procedure stops the run. If the subject is operating near the specified level, the procedure continues the run (unless the specified maximum number of trials has been reached, in which case it stops the run). Regardless of why the procedure stops, a percent correct is estimated at the end of each run. In our experience, this procedure provides approximately a 50% saving in time over the fixed‐number‐of‐trials procedure. [Work supported by NIH.]