Statistical cost-effectiveness analysis of two treatments based on net health benefits.

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, lambda, 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 lambda, 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 lambda 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 lambda 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.

The prevalence and correlates of untreated serious mental illness.

OBJECTIVE: To identify the number of people in the United States with untreated serious mental illness (SMI) and the reasons for their lack of treatment. DATA SOURCE/STUDY DESIGN: The National Comorbidity Survey; cross-sectional, nationally representative household survey. DATA COLLECTION: An operationalization of the SMI definition set forth in the Alcohol, Drug Abuse, and Mental Health Administration Reorganization Act identified individuals with SMI in the 12 months prior to the interview. The presence of SMI then was related to the use of mental health services in the past 12 months. PRINCIPAL FINDINGS: Of the 6.2 percent of respondents who had SMI in the year prior to interview, fewer than 40 percent received stable treatment. Young adults and those living in nonrural areas were more likely to have unmet needs for treatment. The majority of those who received no treatment felt that they did not have an emotional problem requiring treatment. Among those who did recognize this need, 52 percent reported situational barriers, 46 percent reported financial barriers, and 45 percent reported perceived lack of effectiveness as reasons for not seeking treatment. The most commonly reported reason both for failing to seek treatment (72 percent) and for treatment dropout (58 percent) was wanting to solve the problem on their own. CONCLUSIONS: Although changes in the financing of services are important, they are unlikely by themselves to eradicate unmet need for treatment of SMI. Efforts to increase both self-recognition of need for treatment and the patient centeredness of care also are needed.

Assessing the onset of relief of a treatment for migraine.

It is common for clinical trials designed to compare treatments for migraine to incorporate a component for estimating onset. Our objective is to describe a stopwatch method for collecting data on time to meaningful relief and a conceptual framework for describing and analysing the results. The survival distribution of onset is modelled in two parts: the probability that onset does not occur, and the survival distribution conditional on its occurrence. Using data from a clinical trial comparing an active treatment and placebo, we illustrate the method and find that the distributions of onset among those with onset do not differ, but the probabilities that onset occurs are substantially different. We illustrate how the model can be used to help determine how long patients without onset should wait before further intervention, how patients interpret the phrase meaningful relief, and how baseline clinical characteristics affect the onset.

Power and sample size in cost-effectiveness analysis.

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.

Ratio-based and net benefit-based approaches to health care resource allocation: proofs of optimality and equivalence.

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.

The usefulness of average cost-effective ratios.

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 dominance 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.

Classification of the effectiveness of combination treatments.

According to FDA regulations, a combination drug is not efficacious unless each component contributes to the claimed effects. For a univariate endpoint, this implies that the combination at specific doses must be superior to each of its components at the same doses. More demanding is the property of synergy, in which the effect of the combination must be superior to the effect expected based on those of its components. If it is equal to those effects, it is additive, and if it is inferior, it is antagonistic. We give regions in the combination dose plane where these concepts are well defined. If the effect of the combination is greater than the greatest effect achievable by any of its components it is therapeutically synergistic. A combination can be antagonistic, yet its components can still contribute to the claimed effects. If it is additive, synergistic or therapeutically synergistic, its components must contribute to the claimed effects. We relate these concepts and provide designs and sequential procedures for determining whether a combination is therapeutically synergistic, synergistic, additive, antagonistic and contributing or antagonistic and non-contributing.

Statistical inference for cost-effectiveness ratios.

Methods for statistical inference for cost-effectiveness (C/E) ratios for individual treatment and for incremental cost-effectiveness (delta C/ delta E) ratios when two treatments are compared are presented. In a lemma, we relate the relative magnitude of two C/E ratios to the delta C/ delta E ratio. We describe a statistical procedure to test for dominance, or admissibility, that can be used to eliminate an inferior treatment. The one-sided Bonferroni's confidence interval procedure is generalized to the two-sided case. The method requires only that two confidence intervals be available, one for cost and one for effectiveness. We describe Fieller-based confidence intervals and show them to be shorter than Bonferroni intervals. When distribution assumptions hold and variance and covariance estimates are available, Fieller intervals are preferable. However, Bonferroni intervals can be applied in more diverse situations and are easier to calculate. A simple Bonferroni based technique, and a likelihood ratio statistic given by Siegel, Laska and Meisner, for testing the null hypothesis that the C/E ratios of two treatments are equal is presented. The approaches are applied to the data from a phase II clinical trial of a new treatment for sepsis considered previously by others.

Estimating population size when duplicates are present.

Each of K mental health programmes reports the number of patients served in a year. The sum of these numbers, y, is an overcount because some patients are seen in more than one programme. Health care planners need to know the unduplicated number served by the mental health system. Thus, there is an unknown number, M, of distinct individuals who appear on one or more of K lists; some appear on multiple lists and the duplicates are not readily identifiable. Let X be the number of lists on which a randomly selected individual appears. When E(X) is known, y/E(X) is the natural estimator of M. We assume that we know the number of programmes, Xi, used by the ith individual in a random sample of recipients of service. Here, the intuitive estimator, Y/X has desirable statistical properties. We give confidence interval estimators for M. We apply the method to estimate the number of individuals served in 1991 by the mental health programmes in New York State.

Placebo washout in trials of antipsychotic drugs.

For antipsychotic phase 3 clinical trials, we compare the relative merits of a placebo washout period with an alternate design strategy using a low-dose antipsychotic treatment. Evaluations are made with respect to the achievement of specific clinical trial design goals including the effect on power for detecting between-treatment and within-treatment pre-post differences. The relative merits of these two designs are discussed separately for those patients who enter the initial leadin period after withdrawal from previous antipsychotic medication and for those not on medication immediately before that period.

Characterizing onset in psychopharmacological clinical trials.

In addition to describing treatment efficacy in terms of changes in rating scale scores, the distributions of time to occurrence of major clinical events such as onset and response are clinically important information. Issues in the design, conduct and analysis of clinical trials in which the time to onset of effect or time to response is to be characterized are discussed. A criterion must be defined to signal that the clinical event has occurred. Onset properties are given in terms of (1) the probability of obtaining onset and (2) for patients who obtain onset, the distribution of time to onset. A statistical model and methods to estimate parameters and compare onset times of treatments are described. A simple formula that can be used to aid in clinical decision making as to when to alter treatment if onset has not yet occurred is presented.

Simple designs and model-free tests for synergy.

Current statistical designs for studying whether two or more agents in combination act synergistically nearly always require the study of several doses of many dose ratios. The analysis is usually based on an assumed parametric model of the dose-response surface. In this paper, for both quantal and quantitative response variables, sufficient conditions are given for establishing synergy at a dose of the combination without the need to specify the model. This enables the use of simple designs with few doses even when there is sparse knowledge of the dose-response curves of the individual agents. The Min test, used for testing whether an identified treatment is best, may be used for testing synergy. Power issues are discussed.

A plant-capture method for estimating the size of a population from a single sample.

To estimate the size of a population a plant-capture method, an alternative to the classic capture-mark-recapture model, is presented. Known or marked individuals otherwise indistinguishable from the remainder of the population are planted followed by an effort to capture members from the augmented population. Maximum likelihood estimators and a confidence region together with the expected length of the confidence interval for the size of the population as a function of the number of plants are given. A methodology for comparing the cost efficiency of plant-capture to capture-recapture is developed. An application to counting the homeless is given.

Nonparametric estimation and testing in a cure model.

Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.

Importance of pharmacologic control in PET studies: effects of thiothixene and haloperidol on cerebral glucose utilization in chronic schizophrenia.

This study compares the effects of two neuroleptic drugs with different pharmacologic characteristics (thiothixene and haloperidol) on cerebral glucose utilization in chronic schizophrenic inpatients. Positron emission tomographic (PET) scans were obtained from all subjects in a neuroleptic-free condition and again after 4-6 weeks of neuroleptic treatment. Eight subjects were treated with thiothixene and 12 with haloperidol. Thiothixene and haloperidol had different metabolic effects. For example, all thiothixene-treated subjects showed increased whole brain glucose utilization; all but one haloperidol-treated subject showed decreased utilization. Different patterns of relative prefrontal and striatal metabolism were also observed. These results highlight the importance of controlling for the effects of neuroleptic treatment and indicate the difficulty of interpreting data from studies with complex or poorly defined drug regimens.

Testing whether an identified treatment is best.

We consider the problem of testing whether an identified treatment is better than each of K treatments. Suppose there are univariate test statistics Si that contrast the identified treatment with treatment i for i = 1, 2,...., K. The min test is defined to be the alpha-level procedure that rejects the null hypothesis that the identified treatment is not best when, for all i, Si rejects the one-sided hypothesis, at the alpha-level, that the identified treatment is not better than the ith treatment. In the normal case where Si are t statistics the min test is the likelihood ratio test. For distributions satisfying mild regularity conditions, if attention is restricted to test statistics that are monotone nondecreasing functions of Si, then regardless of their covariance structure the min test is an optimal alpha-level test. Tables of the sample size needed to achieve power .5, .8, .90, and .95 are given for the min test when the Si are Student's t and Wilcoxon.

Analgesic efficacy of two ibuprofen-codeine combinations for the treatment of postepisiotomy and postoperative pain.

Our purpose was to compare the analgesic efficacy and safety of single oral doses of the combination of ibuprofen 400 mg plus codeine 60 mg and the combination of ibuprofen 200 mg plus codeine 30 mg with ibuprofen 400 mg alone, codeine sulfate 60 mg alone, and placebo. One hundred ninety-five patients with severe pain resulting from episiotomy, cesarean section, or gynecologic surgery completed a randomized, double-blind, stratified, parallel-group study. Patients were observed during a 4-hour period after medication. Based on the sum of the pain intensity differences (SPID), total pain relief (TOTPAR), and most of the hourly direct measures of pain and relief, both doses of the combination and ibuprofen 400 mg alone were statistically superior to placebo. Codeine 60 mg was statistically superior to placebo based on TOTPAR, the global ratings, and a few hourly measures. The mean effect of the combination of ibuprofen 400 mg plus codeine 60 mg was significantly superior to the mean effect of ibuprofen 400 mg alone 1/2, 1, and 2 hours after medication and to the mean effect of ibuprofen 400 mg alone and codeine 60 mg alone for SPID, TOTPAR, and other measures as well. The low-dose combination was significantly more effective than codeine 60 mg for a few hourly measures but was not significantly superior to ibuprofen 400 mg. Based on these findings it appears that the combination of ibuprofen 400 mg plus codeine 60 mg, particularly in the first few hours after medication, is more efficacious than its constituents.

An analytic approach to quantifying pain scores.

Statistical problems in clinical trials frequently involve fitting regression lines when the underlying data are categorical or ordinal response variables. Usually an ad hoc a priori quantification is used to assign values to these ordinal responses. For pain intensity data collected in analgesic trials, the usual approach is to set none equal to 0, mild equal to 1, moderate equal to 2, and severe equal to 3. While this scheme has been generally accepted, on the basis that for similar clinical trials reasonably similar results are obtained by different investigators, concern exists that the distances between pain scores are probably not equal. A method is presented for quantifying categorical responses so that the resulting scores maximize the simultaneous fit of the dose-response regression lines. The optimal scores derived by this technique may then be used in a bioassay analysis to estimate the relative potency of 2 compounds. As illustrative examples, this method was applied to data from 2 clinical trials and the results were compared to the usual method.