AbstractThe Min test is a statistical tool used to test a null hypothesis such asHoi: νi≤ 0 for at least oneiversus the alternative H1: νi > 0 fori = 1, 2,…,K. This is sometimes called the sign‐testing problem. If every α‐level test of Hoi: νi≤ 0 individually rejects thei‐th null hypothesis at the α level, then the global null hypothesis is rejected according to the Min test. No adjustment for multiplicity is required. Such hypotheses arise in many clinical trials when it is desired to establish that a set of inequalities on the parameters simultaneously holds. Examples include testing whether an identified treatment is best on single or multiple endpoints; whether one treatment is equivalent to or noninferior to a control; and whether a dose of a combination is synergistic.

Recently, a maximally selected normalized Wilcoxon, whose asymptotic distribution is a Brownian Bridge, was proposed for testing symmetry of a distribution about zero. The test sequentially discards observations whose absolute value is below increasing thresholds. The Wilcoxon is obtained at each threshold, and the maximum is the test statistic. We develop a recursive function for the exact distribution of a modification of the Max Wilcoxon test (MW) and provide critical values and a program for computing the p-value for a sample. A new hybrid test that combines the sign and MW tests is introduced. The power of MW and the new hybrid test are compared with Modarres and Gastwirth's hybrid test (MGH) and the Max McNemar (MM), under the generalized lambda distributions (GLD) family and two normal mixture models. The MW and the new hybrid test outperform the MGH, which is superior to the MM test in the GLD family. In one mixture model, MM is the least powerful test and the remaining three are essentially equivalent. In the second mixture model, when the zero median assumption is nearly valid, the MW test does well; its performance degrades when this assumption is violated. In the latter case, the MM performs better than MW for the same degree of skewness because the MM simultaneously tests both symmetry and zero median. Data from a genetic study of monozygotic twins discordant for major depressive disorder is used to illustrate the new tests.

The problem of testing symmetry about zero has a long and rich history in the statistical literature. We introduce a new test that sequentially discards observations whose absolute value is below increasing thresholds defined by the data. McNemar's statistic is obtained at each threshold and the largest is used as the test statistic. We obtain the exact distribution of this maximally selected McNemar and provide tables of critical values and a program for computing p ‐values. Power is compared with the t ‐test, the Wilcoxon Signed Rank Test and the Sign Test. The new test, MM, is slightly less powerful than the t ‐test and Wilcoxon Signed Rank Test for symmetric normal distributions with nonzero medians and substantially more powerful than all three tests for asymmetric mixtures of normal random variables with or without zero medians. The motivation for this test derives from the need to appraise the safety profile of new medications. If pre and post safety measures are obtained, then under the null hypothesis, the variables are exchangeable and the distribution of their difference is symmetric about a zero median. Large pre–post differences are the major concern of a safety assessment. The discarded small observations are not particularly relevant to safety and can reduce power to detect important asymmetry. The new test was utilized on data from an on‐road driving study performed to determine if a hypnotic, a drug used to promote sleep, has next day residual effects. Copyright © 2012 John Wiley & Sons, Ltd.

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There is considerable public concern about health disparities among different cultural/racial/ethnic groups. Important process measures that might reflect inequities are treated prevalence and the service utilization rate in a defined period of time. We have previously described a method for estimating N, the distinct number who received service in a year, from a survey of service users at a single point in time. The estimator is based on the random variable 'time since last service', which enables the estimation of treated prevalence. We show that this same data can be used to estimate the service utilization rate, E(J), the mean number of services in the year. If the sample is typical with respect to the time since last visit, the MLE of E(J) is asymptotically unbiased. Confidence intervals and a global test of equality of treated prevalence and service utilization rates among several groups are given. A data set of outpatient mental health services from a county in New York State for which the true values of the parameters are known is analyzed as an illustration of the methods and an appraisal of their accuracy.

A survey is conducted at w of K selection units or lists, e.g. health care institutions or weeks in a year, to estimate N, the total number of individuals with particular characteristics. Our estimator utilizes two items determined for each survey participant: the number, u, among the w lists in S and the number, j, among all K lists on which each survey participant appears. In its traditional form, selection units are chosen using probability sampling and the statistical properties of the estimator derive from the sampling mechanism. Here, selection units are purposively chosen to maximize the chance that they are 'typical' and a model-based analysis is used for inference. If the sample is typical, the ML estimators of N and E(J) are unbiased. If a condition on the second moment of U/J is satisfied, the model-based variance of the estimator of N based on a purposively chosen typical sample is smaller than one based on a randomly chosen sample. Methods to test whether the typical assumption is valid using data from the survey are not yet available. The importance of proper selection of the sample to maximize the chance that it is typical and model breakdown does not occur must be emphasized.

OBJECTIVES:We sought to increase the accuracy of New York City's estimates of its unsheltered homeless population.METHODS:We employed 2 approaches to increasing count accuracy: a plant-capture strategy in which embedded decoys (or "plants") were used to estimate the proportion of visible homeless people missed by enumerators and a postcount survey of service users designed to estimate the proportion of unsheltered homeless people who were not visible.RESULTS:Plants at 17 sites (29%) reported being missed in the count, because counters either did not visit those sites or did not interview the plants. Of 293 homeless service users who were not in shelters, 31% to 41% were in locations deemed not visible to counters.CONCLUSIONS:Both plant-capture estimation and postcount surveys are feasible approaches that can increase the accuracy of estimates of unsheltered homeless populations.

Isos is a follow-up study on the course of illness and outcomes of a subset of subjects who had been in previous WHO-coordinated research studies of schizophrenia— the International Pilot Study of Schizophrenia (IPSS), the study on the Determinants of Outcome of Severe Mental Disorders (DOSMeD), and the study on Reduction and Assessment of Psychiatric Disability (RAPyD or Disability)—and additionally, subjects who had been in studies conducted locally at three other centers (Retrospective Analysis or Invited). Throughout this volume, these four distinct long-term follow-up cohorts (IPSS, DOSMeD, RAPyD, and Retrospective Analysis) are referred to as the “subsamples” of ISoS.

Objectives. We sought to estimate the extended mental health service capacity requirements of persons affected by the September 11, 2001, terrorist attacks.Methods. We developed a formula to estimate the extended mental health service capacity requirements following disaster situations and assessed availability of the information required by the formula.Results. Sparse data exist on current services and supports used by people with mental health problems outside of the formal mental health specialty sector. There also are few systematically collected data on mental health sequelae of disasters.Conclusions. We recommend research-based surveys to understand service usage in non-mental health settings and suggest that federal guidelines be established to promote uniform data collection of a core set of items in studies carried out after disasters.

The capture‐recapture approach to estimating the size of a population is a well‐studied area of statistics. The number of distinct individuals, NA and NB, on each of two lists, A and B, and the number common to both lists, NAB, are used to form an estimate of the binomial probability of being on one of the lists, which then allows an estimate to be made of the size of the population. Critical to the method is an accurate count of NAB. We consider situations in which this count is not available. Such problems arise in a variety of behavioural health contexts in which the need for protection of privacy may prevent sharing identifying information, so it is not possible to specifically match an individual who appears on one list with an individual on the other. Suppose that the birth dates and/or other demographics of individuals on each list are known. We introduce two methods for estimating the duplication rates and the size of the population. Conditioning on the set β of birth dates of those on list B, NA and NB, the maximum likelihood estimators (MLEs) and their variance are derived. The MLEs are based on the proportion of individuals on list A whose birth dates fall in β. This approach is particularly useful if list B itself contains duplicates. The second model utilizes the full sample distribution of the birth dates. We generalize this approach to accommodate multiple demographic characteristics. The approaches are applied to the problem of estimating duplication rates and the population size of veterans who have mental illness in Kings County, NY. The data are lists of those receiving service from the Veterans Administration system and from providers funded or certified by the New York State Office of Mental Health. Copyright © 2003 John Wiley & Sons, Ltd.

Statistical methods are given for producing a cost-effectiveness frontier for an arbitrary number of programs. In the deterministic case, the net health benefit (NHB) decision rule is optimal; the rule funds the program with the largest positive NHB at each lambda, the amount a decision-maker is willing to pay for an additional unit of effectiveness. For bivariate normally distributed cost and effectiveness variables and a specified lambda, a statistical procedure is presented, based on the method of constrained multiple comparisons with the best (CMCB), for determining the program with the largest NHB. A one-tailed t test is used to determine if the NHB is positive. To obtain a statistical frontier in the lambda-NHB plane, we develop a method to produce the region in which each program has the largest NHB, by pivoting a CMCB confidence interval. A one-sided version of Fieller's theorem is used to determine the region where the NHB of each program is positive. At each lambda, the pointwise error rate is bounded by a prespecified alpha. Upper bounds on the familywise error rate, the probability of an error at any value of lambda, are given. The methods are applied to a hypothetical clinical trial of antipsychotic agents.

Statistical methods for cost‐effectiveness analysis (CEA) for two treatments that mimic the deterministic optimal rules of CEA are presented. In these rules the objective is to determine the treatment with the maximal effectiveness whose unit cost is less than an amount, λ, that a decision‐maker is willing to pay (WTP). This is accomplished by identifying the treatment with the largest positive net health benefit (NHB), which is a function of λ, while controlling the familywise error rate both when the WTP value is given and when it is unspecified. Fieller's theorem is used to determine a region of WTP values where the NHBs of the treatments are not distinguishable. For each λ outside of the confidence region, the larger treatment is identified. A newly developed one‐tailed analogue of Fieller's theorem is used to determine the WTP values where a treatment's NHB is positive. The situation in which both treatments are experimental is distinguished from the case where one of the treatments is usual care. The one‐tailed confidence region is used in the latter case to obtain the λ values where the NHBs are not different, and determining the region of positivity of the NHBs may be unnecessary. An example is presented in which the cost‐effectiveness of two antipsychotic treatments is evaluated. Copyright © 2001 John Wiley & Sons, Ltd.

A problem in optimal resource allocation is considered for n jobs with identically distributed service times admitting a monotone hazard function. If the hazard function is increasing, it is shown that the procedure of allocating the full resource individually to each job until its completion minimizes the expected completion time of the jth job. The procedure which at any instant of time equally allocated the resource among all of the remaining jobs is shown to minimize the expected total cumulative waiting time if the hazard is decreasing.

For resource allocation under a constrained budget, optimal decision rules for mutually exclusive programs require that the treatment with the highest incremental cost-effectiveness ratio (ICER) below a willingness-to-pay (WTP) criterion be funded. This is equivalent to determining the treatment with the smallest net health cost. The designer of a cost-effectiveness study needs to select a sample size so that the power to reject the null hypothesis, the equality of the net health costs of two treatments, is high. A recently published formula derived under normal distribution theory overstates sample-size requirements. Using net health costs, the authors present simple methods for power analysis based on conventional normal and on nonparametric statistical theory.

Both incremental cost-effectiveness ratios and net benefits have been proposed as summary measures for use in cost-effectiveness analyses. We present a unifying proof of the optimality and equivalence of ICER- and net benefit-based approaches to the health resource allocation problem, including both 'fixed budget' and 'fixed price' decision rules. If internally consistent willingness-to-pay values are used, ratio- and net benefit-based decision rules identify the same optimal allocation. Because they have identical resource allocation implications, use of one or other of the two approaches must be based on other criteria, such as their behaviour under conditions of uncertainty.

In 1990, the Census Bureau conducted two operations designed to include homeless persons in the census: an enumeration of the occupants of emergency shelters, and a late night enumeration of street sites identified by cities and census offices as places where homeless people congregate. To assess the street enumeration, the Census Bureau sponsored independent studies in which unobtrusive observers were stationed in a sample of street sites. The observers reported their observations and experience of the enumeration process in debriefing questionnaires filled out immediately after the 3 The observers reported their observations and experience of the enumeration process in debriefing questionnaires filled out immediately after the conclusion of the street enumeration. Data reported by the observers are applied here to fit a plant-capture model, which is an alternative to the classic capturerecapture method of estimating the size of a population. This method assumes that the plants (in this application, the street observers) have the same capture probability as other members of the target population. The plant-capture method has potential application as a method to evaluate coverage of the homeless population and other populations for which the assumption of closure is questionable. The paper analyzes the data to develop various estimates of the capture probabilities, and assesses the strengths and weaknesses of the method as a potential source of coverage estimates in future enumerations of the homeless population. The paper also discusses weaknesses and uncertainties in the street observer data, and evaluates how the quality of the data may affect future attempts to base coverage estimates on similar data from observers or plants.

We demonstrate that average cost-effectiveness ratios (CERs) play an important role in the evaluation of the cost-effectiveness of treatments. Criticisms of the usefulness of CERs derive mostly from the context of resource allocation under a constrained budget in which some decisions are based on incremental CERs. However, we show that in many cases, these decision rules are equivalent to decision rules on CERs. This follows for mutually exclusive treatments first, because a treatment is eliminated by extended dominance if and only if there is a mixed treatment with a smaller CER, where the mixing parameter lies in a certain interval. Second, after elimination of treatments by domainance and by extended dominance, resources can be allocated in order of increasing CERs. Moreover, the CER is a parameter that characterizes clinical and economical properties of a treatment independent of its comparators. © 1997 John Wiley & Sons, Ltd.