A representative sampling plan for auditing health insurance claims

A stratified sampling plan to audit health insurance claims is offered. The stratification is by dollar amount of the claim. The plan is representative in the sense that with high probability for each stratum, the difference in the average dollar amount of the claim in the sample and the average dollar amount in the population, is ``small.'' Several notions of ``small'' are presented. The plan then yields a relatively small total sample size with the property that the overall average dollar amount in the sample is close to the average dollar amount in the population. Three different estimators and corresponding lower confidence bounds for over (under) payments are studied.Comment: Published at http://dx.doi.org/10.1214/074921707000000094 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The Interval Property in Multiple Testing of Pairwise Differences

The usual step-down and step-up multiple testing procedures most often lack an important intuitive, practical, and theoretical property called the interval property. In short, the interval property is simply that for an individual hypothesis, among the several to be tested, the acceptance sections of relevant statistics are intervals. Lack of the interval property is a serious shortcoming. This shortcoming is demonstrated for testing various pairwise comparisons in multinomial models, multivariate normal models and in nonparametric models. Residual based stepwise multiple testing procedures that do have the interval property are offered in all these cases.Comment: Published in at http://dx.doi.org/10.1214/11-STS372 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure

The problem of multiple endpoint testing for k endpoints is treated as a 2^k finite action problem. The loss function chosen is a vector loss function consisting of two components. The two components lead to a vector risk. One component of the vector risk is the false rejection rate (FRR), that is, the expected number of false rejections. The other component is the false acceptance rate (FAR), that is, the expected number of acceptances for which the corresponding null hypothesis is false. This loss function is more stringent than the positive linear combination loss function of Lehmann [Ann. Math. Statist. 28 (1957) 1-25] and Cohen and Sackrowitz [Ann. Statist. (2005) 33 126-144] in the sense that the class of admissible rules is larger for this vector risk formulation than for the linear combination risk function. In other words, fewer procedures are inadmissible for the vector risk formulation. The statistical model assumed is that the vector of variables Z is multivariate normal with mean vector \mu and known intraclass covariance matrix \Sigma. The endpoint hypotheses are H_i:\mu_i=0 vs K_i:\mu_i>0, i=1,...,k. A characterization of all symmetric Bayes procedures and their limits is obtained. The characterization leads to a complete class theorem. The complete class theorem is used to provide a useful necessary condition for admissibility of a procedure. The main result is that the step-up multiple endpoint procedure is shown to be inadmissible.Comment: Published at http://dx.doi.org/10.1214/009053604000000986 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Decision theory results for one-sided multiple comparison procedures

A resurgence of interest in multiple hypothesis testing has occurred in the last decade. Motivated by studies in genomics, microarrays, DNA sequencing, drug screening, clinical trials, bioassays, education and psychology, statisticians have been devoting considerable research energy in an effort to properly analyze multiple endpoint data. In response to new applications, new criteria and new methodology, many ad hoc procedures have emerged. The classical requirement has been to use procedures which control the strong familywise error rate (FWE) at some predetermined level \alpha. That is, the probability of any false rejection of a true null hypothesis should be less than or equal to \alpha. Finding desirable and powerful multiple test procedures is difficult under this requirement. One of the more recent ideas is concerned with controlling the false discovery rate (FDR), that is, the expected proportion of rejected hypotheses which are, in fact, true. Many multiple test procedures do control the FDR. A much earlier approach to multiple testing was formulated by Lehmann [Ann. Math. Statist. 23 (1952) 541-552 and 28 (1957) 1-25]. Lehmann's approach is decision theoretic and he treats the multiple endpoints problem as a 2^k finite action problem when there are k endpoints. This approach is appealing since unlike the FWE and FDR criteria, the finite action approach pays attention to false acceptances as well as false rejections.Comment: Published at http://dx.doi.org/10.1214/009053604000000968 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effects of changes in patterns of communication on the behaviors of problem-solving groups.

Thesis (Ph.D.)--Boston UniversityThe study of organizations in their natural state and problem-solving groups in the laboratory has received increased attention in recent years. Communication in particular has been the research concern of many investigators. Problems of changes in communication processes have been virtually ignored in experimental studies as well as in field investigations. The existence of disparate notions unsupported by empirical evidence about the effects of such changes provides somewhat confusing and conflicting references for making predictions. There is, however, a growing body of evidence coming from laboratory experimentation about the relationship between communication networks and the performances of problem-solving groups in them. As well as providing such evidence, certain of these studies also make possible the establishment of operationally distinguishable communication structures and the introduction of rigorously controlled changes in them. [TRUNCATED

Cottonfield Dance

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Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information

Consider the problem of estimating a common mean of two independent normal distributions, each with unknown variances. Note that the problem of recovery of interblock information in balanced incomplete blocks designs is such a problem. Suppose a random sample of size m is drawn from the first population and a random sample of size n is drawn from the second population. We first show that the sample mean of the first population can be improved on (with an unbiased estimator having smaller variance), provided m ≧ 2 and n ≧ 3. The method of proof is applicable to the recovery of information problem. For that problem, it is shown that interblock information could be used provided b ≧ 4. Furthermore for the case b = t = 3, or in the common mean problem, where n = 2, it is shown that the prescribed estimator does not offer improvement. Some of the results for the common mean problem are extended to the case of K means. Results similar to some of those obtained for point estimation, are also obtained for confidence estimation

Inadmissibility of Large Classes of Sequential Tests

Assume observations are from a subclass of a one parameter exponential family whose dominating measure is nonatomic. Consider a one-sided sequential testing problem where null and alternative parameter sets have one common boundary point. Let the risk function be a linear combination of probability of error and expected sample size. Our main result is that a sequential test is inadmissible if its continuation region has unbounded width in terms of the natural sufficient statistic. We apply this result to prove that weight function tests, with weight functions that contain the common boundary point in their support, are inadmissible. Furthermore any obstructive test is inadmissible, where obstructive means that the stopping time for the test does not have a finite moment generating function for some parameter point. Specific tests of the above type are cited

A new multiple testing method in the dependent case

The most popular multiple testing procedures are stepwise procedures based on $P$-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini--Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300] and their offsprings. Even for models that entail dependent data, $P$-values based on marginal distributions are used. Unlike such methods, the new method takes dependency into account at all stages. Furthermore, the $P$-value procedures often lack an intuitive convexity property, which is needed for admissibility. Still further, the new methodology is computationally feasible. If the number of tests is large and the proportion of true alternatives is less than say 25 percent, simulations demonstrate a clear preference for the new methodology. Applications are detailed for models such as testing treatments against control (or any intraclass correlation model), testing for change points and testing means when correlation is successive.Comment: Published in at http://dx.doi.org/10.1214/08-AOS616 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org