Utilization of machine learning for identifying symptom severity military-related PTSD subtypes and their biological correlates

We sought to find clinical subtypes of posttraumatic stress disorder (PTSD) in veterans 6-10 years post-trauma exposure based on current symptom assessments and to examine whether blood biomarkers could differentiate them. Samples were males deployed to Iraq and Afghanistan studied by the PTSD Systems Biology Consortium: a discovery sample of 74 PTSD cases and 71 healthy controls (HC), and a validation sample of 26 PTSD cases and 36 HC. A machine learning method, random forests (RF), in conjunction with a clustering method, partitioning around medoids, were used to identify subtypes derived from 16 self-report and clinician assessment scales, including the clinician-administered PTSD scale for DSM-IV (CAPS). Two subtypes were identified, designated S1 and S2, differing on mean current CAPS total scores: S2 = 75.6 (sd 14.6) and S1 = 54.3 (sd 6.6). S2 had greater symptom severity scores than both S1 and HC on all scale items. The mean first principal component score derived from clinical summary scales was three times higher in S2 than in S1. Distinct RFs were grown to classify S1 and S2 vs. HCs and vs. each other on multi-omic blood markers feature classes of current medical comorbidities, neurocognitive functioning, demographics, pre-military trauma, and psychiatric history. Among these classes, in each RF intergroup comparison of S1, S2, and HC, multi-omic biomarkers yielded the highest AUC-ROCs (0.819-0.922); other classes added little to further discrimination of the subtypes. Among the top five biomarkers in each of these RFs were methylation, micro RNA, and lactate markers, suggesting their biological role in symptom severity.

Gabapentin Enacarbil Extended-Release Versus Placebo: A Likely Responder Reanalysis of a Randomized Clinical Trial

BACKGROUND

We reanalyzed a multisite 26-week randomized double-blind placebo-controlled clinical trial of 600 mg twice-a-day Gabapentin Enacarbil Extended-Release (GE-XR), a gabapentin prodrug, designed to evaluate safety and efficacy for treating alcohol use disorder. In the original analysis (n = 338), published in 2019, GE-XR did not differ from placebo. Our aim is to advance precision medicine by identifying likely responders to GE-XR from the trial data and to determine for likely responders if GE-XR is causally superior to placebo.

METHODS

The primary outcome measure in the reanalysis is the reduction from baseline of the number of heavy drinking days (ΔHDD). Baseline features including measures of alcohol use, anxiety, depression, mood states, sleep, and impulsivity were used in a random forest (RF) model to predict ΔHDD to treatment with GE-XR based on those assigned to GE-XR. The resulting RF model was used to obtain predicted outcomes for those randomized to GE-XR and counterfactually to those randomized to placebo. Likely responders to GE-XR were defined as those predicted to have a reduction of 14 days or more. Tests of causal superiority of GE-XR to placebo were obtained for likely responders and for the whole sample.

RESULTS

For likely responders, GE-XR was causally superior to placebo (p < 0.0033), while for the whole sample, there was no difference. Likely responders exhibited improved outcomes for the related outcomes of percent HDD and drinks per week. Compared with unlikely responders, at baseline likely responders had higher HDDs; lower levels of anxiety, depression, and general mood disturbances; and higher levels of cognitive and motor impulsivity.

CONCLUSIONS

There are substantial causal benefits of treatment with GE-XR for a subset of patients predicted to be likely responders. The likely responder statistical paradigm is a promising approach for analyzing randomized clinical trials to advance personalized treatment.

Prevalence and Diagnosis Rates of Childhood ADHD Among Racial-Ethnic Groups in a Public Mental Health System

OBJECTIVE

This study estimated the proportions of Hispanic and non-Hispanic white and black children ages three to 17 with a diagnosis of attention-deficit hyperactivity disorder (ADHD) receiving services from the New York State public mental health system (NYS PMHS) and their annual treated ADHD prevalence rates. Findings were compared with those of recent national studies of general population samples.

METHODS

Data were from a 2011 survey of users of NYS PMHS nonresidential services. Adjusted odds ratios compared the probability of an ADHD diagnosis among the groups by age, gender, and insurance type. Prevalence rates were compared among groups by age and gender.

RESULTS

An estimated 133,091 children used the NYS PMHS, of whom 31% had an ADHD diagnosis. The prevalence rate of ADHD among whites was significantly lower than that among Hispanics or blacks in all gender and age groups except Hispanic females ages 13 to 17. White children were significantly less likely than black children to receive an ADHD diagnosis.

CONCLUSIONS

National studies have reported higher ADHD rates among white children. Compared with children in the NYS PMHS, those in national studies had multiple access points to care, including private psychiatrists and clinicians and primary care practitioners. The higher reported ADHD rates in national studies may reflect higher rates of private insurance among white children, which would increase the likelihood of their using private practitioners. Cultural factors that influence whether and where care is sought and whether practitioners appropriately diagnosis ADHD may also explain the difference in findings.

Access to and use of non-inpatient services in New York State among racial-ethnic groups

OBJECTIVE Nationwide studies contrasting service use of racial-ethnic groups provide an overview of disparities, but because of variation in populations and service systems, local studies are required to identify specific targets for remedial action. The authors report on the use of non-inpatient services regulated in New York State (NYS) and report use by the state's larger cultural groups. METHODS Data from the NYS Patient Characteristics Survey were used to estimate annual treated prevalence and treatment intensity, defined as the average number of annual weeks in service for non-Hispanic blacks, Hispanics, Asians, and non-Hispanic whites. The latter rates were obtained for specific types of treatment use, by person's age and diagnosis, for the state and for population density-defined regions. Statistical methods contrasted rates of whites with other groups. RESULTS A total of 578,496 individuals in these racial-ethnic groups were served in 2,500 programs, and 51% of those served were nonwhite. Treated prevalence rates of whites were lower than those of blacks and Hispanics and were substantially higher than prevalence rates for Asians. Statewide treatment intensity rates of all racial-ethnic and age groups were comparable except for lower use among Asians &gt;65. Key findings from granular analyses were lower treatment intensity rates for black youths with disruptive disorders, Hispanic adults with anxiety disorders, and Asians &gt;65 with depression compared with white counterparts. In upstate metropolitan areas, black youths and Hispanic adults received services in fewer weeks than whites, and in the New York City metropolitan area, whites &gt;65 had higher treatment intensity rates than contrast groups. CONCLUSIONS Findings suggest a need for assistance to black families in negotiating the multiple systems used by their children, clinical training focusing on cultural symptom presentation, screening of Asians in community settings, and mandated cultural competency assessments for all programs.

Declining use of electroconvulsive therapy in United States general hospitals

BACKGROUND

Falling duration of psychiatric inpatient stays over the past 2 decades and recent recommendations to tighten federal regulation of electroconvulsive therapy (ECT) devices have focused attention on trends in ECT use, but current national data have been unavailable.

METHODS

We calculated the annual number of inpatient stays involving ECT and proportion of general hospitals conducting the procedure at least once in the calendar year with a national sample of discharges from 1993 to 2009. We estimated adjusted probabilities that inpatients with severe recurrent major depression (n = 465,646) were treated in a hospital that conducts ECT and, if so, received the procedure.

RESULTS

The annual number of stays involving ECT fell from 12.6 to 7.2/100,000 adult US residents, driven by dramatic declines among elderly persons, whereas the percentage of hospitals conducting ECT decreased from 14.8% to 10.6%. The percentage of stays for severe recurrent major depression in hospitals that conducted ECT fell from 70.5% to 44.7%, whereas receipt of ECT where conducted declined from 12.9% to 10.5%. For depressed inpatients, the adjusted probability that the treating hospital conducts ECT fell 34%, whereas probability of receiving ECT was unchanged for patients treated in facilities that conducted the procedure. Adjusted declines were greatest for elderly persons. Throughout the period inpatients from poorer neighborhoods or who were publicly insured or uninsured were less likely to receive care from hospitals conducting ECT.

CONCLUSIONS

Electroconvulsive therapy use for severely depressed inpatients has fallen markedly, driven exclusively by a decline in the probability that their hospital conducts ECT.

Racial differences in the availability and use of electroconvulsive therapy for recurrent major depression

BACKGROUND

Black Americans with depression were less likely to receive electroconvulsive therapy (ECT) than whites during the 1970s and 80s. This pattern was commonly attributed to treatment of blacks in lower quality hospitals where ECT was unavailable. We investigated whether a racial difference in receiving ECT persists, and, if so, whether it arises from lesser ECT availability or from lesser ECT use within hospitals conducting the procedure.

METHODS

Black or white inpatient stays for recurrent major depression from 1993 to 2007 (N=419,686) were drawn from an annual sample of US community hospital discharges. The marginal disparity ratio estimated adjusted racial differences in the probabilities of (1) admission to a hospital capable of conducting ECT (availability), and (2) ECT utilization if treated where ECT is conducted (use).

RESULTS

Across all hospitals, the probability of receiving ECT for depressed white inpatients (7.0%) greatly exceeded that for blacks (2.0%). Probability of ECT availability was slightly greater for whites than blacks (62.0% versus 57.8%), while probability of use was markedly greater (11.8% versus 3.9%). The white versus black marginal disparity ratio for ECT availability was 1.07 (95% confidence interval 1.06-1.07) and stable over the period, while the ratio for use fell from 3.2 (3.1-3.4) to 2.5 (2.4-2.7).

LIMITATIONS

Depressed persons treated in outpatient settings or receive no care are excluded from analyses.

CONCLUSIONS

Depressed black inpatients continue to be far less likely than whites to receive ECT. The difference arises almost entirely from lesser use of ECT within hospitals where it is available.

Length of stay of pediatric mental health emergency department visits in the United States

OBJECTIVE

To compare pediatric mental health emergency department visits to other pediatric emergency department visits, focusing on length of stay.

METHOD

We analyzed data from the National Hospital Ambulatory Medical Care Survey, a nationally representative sample of US emergency department visits from 2001 to 2008, for patients aged ≤18 years (n = 73,015). Visits with a principal diagnosis of a mental disorder (n = 1,476) were compared to visits (n = 71,539) with regard to patient and hospital characteristics, treatment, and length of stay. Predictors of prolonged mental health visits were identified.

RESULTS

Mental health visits were more likely than other visits to arrive by ambulance (21.8% versus 6.3%, p < .001), to be triaged to rapid evaluation (27.9% versus 14.9%, p < .001), and to be admitted (16.4% versus 7.6%, p < .001) or transferred (15.7% versus 1.5%, p < .001). The median length of stay for mental health visits (169 minutes) significantly exceeded that of other visits (108 minutes). The odds of extended stay beyond 4 hours for mental health visits was almost twice that for other visits (adjusted odds ratio 1.9, 95% CI = 1.5-2.4) and was not explained by observed differences in evaluation, treatment, or disposition. Among mental health visits, advancing calendar year of study, intentional self-injury, age 6-13 years, Northeastern, Southern, and metropolitan hospital location, use of laboratory studies, and patient transfer all predicted extended stays.

CONCLUSIONS

Compared with other pediatric emergency visits, mental health visits are longer, are more frequently triaged to urgent evaluation, and more likely to result in patient admission or transfer, thereby placing distinctive burdens on US emergency departments.

The Nathan Kline Institute cultural competency assessment scale: psychometrics and implications for disparity reduction

The NKI Cultural Competency Assessment Scale measures organizational CC in mental health outpatient settings. We describe its development and results of tests of its psychometric properties. When tested in 27 public mental health settings, factor analysis discerned three factors explaining 65% of the variance; each factor related to a stage of implementation of CC. Construct validity and inter-rater reliability were satisfactory. In tests of predictive validity, higher scores on items related to linguistic and service accommodations predicted a reduction in service disparities for engagement and retention outcomes for Hispanics. Disparities for Blacks essentially persisted independent of CC scores.

Randomized, double-blind, placebo-controlled trial of vigabatrin for the treatment of cocaine dependence in Mexican parolees

OBJECTIVE

Cocaine dependence is associated with severe medical, psychiatric, and social morbidity, but no pharmacotherapy is approved for its treatment in the United States. The atypical antiepileptic vigabatrin (gamma-vinyl gamma-aminobutyric acid [GABA]) has shown promise in animal studies and open-label trials. The purpose of the present study was to assess the efficacy of vigabatrin for short-term cocaine abstinence in cocaine-dependent individuals.

METHOD

Participants were treatment seeking parolees who were actively using cocaine and had a history of cocaine dependence. Subjects were randomly assigned to a fixed titration of vigabatrin (N=50) or placebo (N=53) in a 9-week double-blind trial and 4-week follow-up assessment. Cocaine use was determined by directly observed urine toxicology testing twice weekly. The primary endpoint was full abstinence for the last 3 weeks of the trial.

RESULTS

Full end-of-trial abstinence was achieved in 14 vigabatrin-treated subjects (28.0%) versus four subjects in the placebo arm (7.5%). Twelve subjects in the vigabatrin group and two subjects in the placebo group maintained abstinence through the follow-up period. The retention rate was 62.0% in the vigabatrin arm versus 41.5% in the placebo arm. Among subjects who reported prestudy alcohol use, vigabatrin, relative to placebo, was associated with superior self-reported full end-of-trial abstinence from alcohol (43.5% versus 6.3%). There were no differences between the two groups in drug craving, depressed mood, anxiety, or Clinical Global Impression scores, and no group differences in adverse effects emerged.

CONCLUSIONS

This first randomized, double-blind, placebo-controlled trial supports the safety and efficacy of short-term vigabatrin treatment of cocaine dependence.

Assessing onset of treatment benefit in depression and anxiety: conceptual considerations

OBJECTIVE

Methods for characterizing the onset of treatment benefit in major depressive disorder and generalized anxiety disorder have been studied for some time, yet there is no universal agreement as to the best approaches. Our purpose is to summarize the conceptual framework underlying modern methods for characterizing onset and detailed approaches for which there is consensus from the perspective of a clinician, clinical researcher, and statistician. Possible alternatives to unresolved issues are discussed.

PARTICIPANTS

There were 17 experts from academia, the pharmaceutical industry, and the US Food and Drug Administration who met on April 19, 2007, to consider the issues. Many others from sponsoring firms observed the proceedings.

EVIDENCE

A series of papers was presented at a consensus meeting and, after discussions, a sense of the participants was obtained. A small group subsequently reviewed the material and articles from the literature and prepared this article, which was reviewed by all of the participants.

CONCLUSIONS

The elements that form the basis for describing onset of treatment benefit include defining a clinical event or measurable threshold that validly signals that a treatment has begun to provide clinically meaningful and sustained improvement and utilizing methods for estimating the probability of crossing the onset threshold, the distribution of time to onset for those who do cross, and when to alter or change interventions if the treatment is unsuccessful.

Model-based multiplicity estimation of population size

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.

Estimating population size and duplication rates when records cannot be linked

The capture-recapture approach to estimating the size of a population is a well-studied area of statistics. The number of distinct individuals, N(A) and N(B), on each of two lists, A and B, and the number common to both lists, N(AB), 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 N(AB). 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 beta of birth dates of those on list B, N(A) and N(B), 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 beta. 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.

Safety and efficacy of ?-vinyl GABA (GVG) for the treatment of methamphetamine and/or cocaine addiction

This study examined the safety and efficacy of gamma vinyl-GABA (GVG, vigabatrin) for the treatment of methamphetamine and/or cocaine addiction. A total of 30 subjects, who met DSM-IV criteria for methamphetamine and/or cocaine dependence, were enrolled in an open label 9-week safety study. The protocol was specifically designed to include extensive visual field monitoring as well as outcome measures of therapeutic efficacy. Patients were screened twice weekly for the presence of urinary cocaine, methamphetamine, heroin, alcohol, and marijuana. In total, 18/30 subjects completed the study and 16/18 tested negative for methamphetamine and cocaine during the last 6 weeks of the trial. GVG did not produce any visual field defects or alterations in visual acuity. Furthermore, it did not produce changes in vital signs even with continued use of methamphetamine and cocaine. Thus, under conditions that appear to be appropriate for the successful treatment of methamphetamine and/or cocaine addiction, GVG is safe.

Statistical determination of cost-effectiveness frontier based on net health benefits

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.

The familywise error rate of a simultaneous confidence band for the incremental net health benefit

Interest in the use of net health benefit in cost-effectiveness analysis derives from its optimality property for decision-making. A description of the results of an economic evaluation of health care interventions is incomplete if it does not include point and interval estimates of this outcome measure. A simultaneous confidence band for the incremental net health benefit, INHB(lambda), for all lambda may be obtained by forming a confidence interval based on student's t statistic, and letting the willingness-to-pay value, lambda, run over all values. The familywise error rate (FWER) of the simultaneous confidence band is the probability that the confidence interval does not cover the true INHB(lambda) for some value of lambda. We show that the FWER equals P(T(2)>t(2)), where T(2) follows Hotelling's central distribution and that the simultaneous confidence band does not cover the true INHB(lambda) if and only if a T(2) based confidence ellipsoid does not cover the true mean c-e vector.

National Depressive and Manic-Depressive Association consensus statement on the use of placebo in clinical trials of mood disorders

A consensus conference on the use of placebo in mood disorder studies consisted of expert presentations on bioethics, biostatistics, unipolar depression, and bipolar disorder. Work groups considered evidence and presented statements to the group. Although it was not possible to write a document for which there was complete agreement on all issues, the final document incorporated input from all authors. There was consensus that placebo has a definite role in mood disorder studies. Findings of equivalence between a new drug and standard treatment in active control studies is not evidence of efficacy unless the new drug is also significantly more effective than placebo. Add-on studies in which patients are randomized to standard therapy plus the investigational drug or standard therapy plus placebo are especially indicated for high-risk patients. Mood disorders in elderly and pediatric patients are understudied, and properly designed trials are urgently needed. Research is needed on the ethical conduct of studies to limit risks of medication-free intervals and facilitate poststudy treatment. Patients must fully understand the risks and lack of individualized treatment involved in research.

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.

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.

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.

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.

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.

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.

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.

The correlation between blood levels of ibuprofen and clinical analgesic response

A clinical trial comparing ibuprofen, 400, 600, and 800 mg, with aluminum ibuprofen, 400 mg, and placebo was conducted in patients with moderate or severe pain subsequent to third molar extraction. Pain intensity ratings and ibuprofen serum levels were obtained at baseline, 30 minutes, 1 hour, and hourly thereafter for 3 hours. Pain intensity ratings were also obtained at hours 4, 5, and 6. Serum levels at 1, 2, and 3 hours correlated significantly with the log dose of ibuprofen (r = 0.35, 0.49, and 0.48, respectively) and with global analgesic response as measured by the percentage of the sum of the pain intensity scores (r = 0.28, 0.34, and 0.26, respectively). However, possibly because of differences in drug formulation, the percentage of the sum of the pain intensity scores did not correlate significantly with log dose. The highest correlations were found between contemporaneous serum levels and pain intensity difference values, particularly at hour 1 (r = 0.54). Our results support the proposition that increased ibuprofen serum levels lead to increased analgesia.