Glycemia Reduction in Type 2 Diabetes - Microvascular and Cardiovascular Outcomes.

BACKGROUND: Data are lacking on the comparative effectiveness of commonly used glucose-lowering medications, when added to metformin, with respect to microvascular and cardiovascular disease outcomes in persons with type 2 diabetes. METHODS: We assessed the comparative effectiveness of four commonly used glucose-lowering medications, added to metformin, in achieving and maintaining a glycated hemoglobin level of less than 7.0% in participants with type 2 diabetes. The randomly assigned therapies were insulin glargine U-100 (hereafter, glargine), glimepiride, liraglutide, and sitagliptin. Prespecified secondary outcomes with respect to microvascular and cardiovascular disease included hypertension and dyslipidemia, confirmed moderately or severely increased albuminuria or an estimated glomerular filtration rate of less than 60 ml per minute per 1.73 m2 of body-surface area, diabetic peripheral neuropathy assessed with the Michigan Neuropathy Screening Instrument, cardiovascular events (major adverse cardiovascular events [MACE], hospitalization for heart failure, or an aggregate outcome of any cardiovascular event), and death. Hazard ratios are presented with 95% confidence limits that are not adjusted for multiple comparisons. RESULTS: During a mean 5.0 years of follow-up in 5047 participants, there were no material differences among the interventions with respect to the development of hypertension or dyslipidemia or with respect to microvascular outcomes; the mean overall rate (i.e., events per 100 participant-years) of moderately increased albuminuria levels was 2.6, of severely increased albuminuria levels 1.1, of renal impairment 2.9, and of diabetic peripheral neuropathy 16.7. The treatment groups did not differ with respect to MACE (overall rate, 1.0), hospitalization for heart failure (0.4), death from cardiovascular causes (0.3), or all deaths (0.6). There were small differences with respect to rates of any cardiovascular disease, with 1.9, 1.9, 1.4, and 2.0 in the glargine, glimepiride, liraglutide, and sitagliptin groups, respectively. When one treatment was compared with the combined results of the other three treatments, the hazard ratios for any cardiovascular disease were 1.1 (95% confidence interval [CI], 0.9 to 1.3) in the glargine group, 1.1 (95% CI, 0.9 to 1.4) in the glimepiride group, 0.7 (95% CI, 0.6 to 0.9) in the liraglutide group, and 1.2 (95% CI, 1.0 to 1.5) in the sitagliptin group. CONCLUSIONS: In participants with type 2 diabetes, the incidences of microvascular complications and death were not materially different among the four treatment groups. The findings indicated possible differences among the groups in the incidence of any cardiovascular disease. (Funded by the National Institute of Diabetes and Digestive and Kidney Diseases and others; GRADE ClinicalTrials.gov number, NCT01794143.).

Cost-effectiveness analysis under multiple effectiveness outcomes: A probabilistic approach.

Probability based criteria are proposed for the assessment of cost-effectiveness of a new treatment compared to a standard treatment when there are multiple effectiveness measures. Depending on the preferences of a policy maker, there are several options to define such criteria. Two such metrics are investigated in detail. One metric is defined as the conditional probability that a new treatment is more effective with respect to the multiple effectiveness measures for patients having lower costs under the new treatment. A second metric is defined as the conditional probability that a new treatment is less costly for patients having greater health benefits under the new treatment. The metrics offer considerable flexibility to a policy maker as thresholds for cost and effectiveness can be incorporated into the metrics. Parametric confidence limits are developed using a percentile bootstrap approach assuming multivariate normality for the joint distribution of the log(cost) and effectiveness measures. A non-parametric estimation procedure is also developed using the theory of U-statistics. Numerical results indicate that the proposed confidence limits accurately maintain coverage probabilities. The methodologies are illustrated using a study on the treatment of type two diabetes. Code implementing the proposed methods are provided in the supporting information.

Cost-Efficient Multiply Matched Case-Control Study Designs.

In multiply matched case-control studies, a number of cases and controls may be included in each matched set. However, when per-participant costs between cases and controls differ, investigators should be aware of how the numbers of cases and controls per matched set affect the overall total study cost. Traditional statistical approaches to designing case-control studies do not account for study costs. Given an effect size, the power to detect differences is typically a function of the numbers of cases and controls within each matched set. Therefore, the same level of statistical power will be achieved based on various combinations of the numbers of cases and controls. Typical matched case-control studies match a case to a number of controls by levels of 1 or more known factors. Several authors have shown that for study designs with 1 case per matched set, the optimal number of controls within each matched set that minimizes the total study cost is the square root of the ratio of the cost of a case to the cost of a control. Herein, we extend this result to the setting of a multiply matched case-control study design, when 1 or more cases are matched to controls within each matched set. A Shiny web application implementation of the proposed methods is presented.

Refractive Error and Retinopathy Outcomes in Type 1 Diabetes: The Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications Study.

PURPOSE: To determine the relationship between refractive error and diabetic retinopathy (DR). DESIGN: Clinical trial. PARTICIPANTS: Type I diabetes individuals with serial refractive error and DR stage measurements over 30 years in the Diabetes Control and Complications Trial (DCCT) and Epidemiology of Diabetes Interventions and Complications (EDIC) follow-up study. METHODS: Stage of DR was measured every 6 months from standard fundus photographs, and refractive error was measured annually during the 6.5 years of DCCT; then, both were staggered every fourth year during EDIC with the full cohort measured at EDIC years 4 and 10. Outcomes of DR were 2- or 3-step progression, presence of proliferative DR (PDR), clinically significant macular edema (CSME), diabetic macular edema (DME), or ocular surgery. Myopia, emmetropia, and hyperopia were defined as a spherical equivalent of ≤-0.5, >-0.5 and <0.5, and ≥0.5, respectively. MAIN OUTCOME MEASURES: For each outcome separately, Cox proportional hazard (PH) models assessed the association between the refractive error status and the subsequent risk of that outcome, both without and with adjustment for potential risk factors. RESULTS: Hyperopia was associated with a higher risk of 2-step progression (hazard ratio [HR], 1.29; 95% confidence interval [CI], 1.05-1.59), 3-step progression (HR, 1.35; 95% CI, 1.05-1.73), and PDR (HR, 1.40; 95% CI, 1.02-1.92) compared with emmetropia in unadjusted models. These associations remained significant after adjustment for DCCT treatment group, cohort, age, sex, smoking, duration of diabetes, systolic and diastolic blood pressures, pulse, low-density lipoprotein, high-density lipoprotein, triglycerides, albumin excretion rate, and DCCT/EDIC mean updated hemoglobin A1c (HbA1c) (2-step progression: HR, 1.28; 95% CI, 1.03-1.58; 3-step progression: HR, 1.30; 95% CI, 1.00-1.68; PDR: HR, 1.38; 95% CI, 1.00-1.90). Myopia was not associated with any of the 5 DR outcomes in the unadjusted models and only marginally associated with 2-step progression (HR, 1.11; 95% CI, 1.00-1.24) in the adjusted models. CONCLUSIONS: Myopia is not associated with DR progression risk. Hyperopia is an independent risk factor for 2-step and 3-step DR progression and PDR.

Cost-efficient clinical studies with continuous time survival outcomes.

Time-to-event outcomes are common in clinical studies. For example, the time to a first major adverse cardiovascular event (MACE, defined as CVD death, nonfatal myocardial infarction, or stroke) is a commonly used outcome in cardiovascular outcome trials. Owing to the lengthy time frame and other factors, the high costs of conducting such studies has been identified as one of the major obstacles in conducting clinical trials in the United States. However, typical approaches for designing clinical trials with time-to-event outcomes do not consider study costs. For a given effect size (eg, hazard ratio), the power to detect differences between two groups is typically a function of the total number of events observed in the study. Therefore, the same level of power will be achieved based on various combinations of the total number of participants, length of enrollment and total follow-up times, and group allocation probability. Herein, we provide a general framework for designing cost-efficient studies comparing treatments with respect to continuous time-to-event outcomes. Among the various designs that achieve the desired level of power to detect a given effect size for a fixed type-I error level, the optimal cost-efficient design is the design that minimizes the expected total study cost. The method is general and can be used for Cox proportional hazards models or Aalen additive models, and under various recruitment and censoring assumptions. The proposed approach for designing cost-efficient studies is illustrated for a Weibull time-to-event outcome with uniform recruitment and exponentially distributed censoring time. The case of an additive hazards model is also described. A Shiny web application implementation of the proposed methods is presented.

Models to Assess the Association of a Semiquantitative Exposure With Outcomes.

A semiquantitative risk factor has 2 components: any exposure (yes/no) and the quantitative amount of exposure (if exposed). We describe the statistical properties of alternative analyses with such a risk factor using linear, logistic, or Cox proportional hazards models. Often analyses employ the amount exposed as a single quantitative covariate, including the nonexposed with value zero. However, this analysis provides a biased estimate of the exposure coefficient (slope) and we describe the magnitude of the bias. This bias can be eliminated by adding a binary covariate for exposed versus not to the model. This 2-factor analysis captures the full risk-factor effect on the outcome. However, the coefficient for any exposure versus not does not have a meaningful interpretation. Alternatively, when exposure values among those exposed are centered (by subtracting the mean), the estimate of this coefficient represents the difference in the outcome between those exposed versus not in aggregate. We also show that the biased model provides biased estimates of the coefficients for other covariates added to the model. Proper analysis of a semiquantitative risk factor should start with a 2-factor model, with centering, to assess the joint contributions of the 2 components of the risk-factor exposure. Properties of models were illustrated using data from a multisite study in North America (1983-2019).

Frequency of Evidence-Based Screening for Retinopathy in Type 1 Diabetes.

BACKGROUND: In patients who have had type 1 diabetes for 5 years, current recommendations regarding screening for diabetic retinopathy include annual dilated retinal examinations to detect proliferative retinopathy or clinically significant macular edema, both of which require timely intervention to preserve vision. During 30 years of the Diabetes Control and Complications Trial (DCCT) and its longitudinal follow-up Epidemiology of Diabetes Interventions and Complications (EDIC) study, retinal photography was performed at intervals of 6 months to 4 years. METHODS: We used retinal photographs from the DCCT/EDIC study to develop a rational screening frequency for retinopathy. Markov modeling was used to determine the likelihood of progression to proliferative diabetic retinopathy or clinically significant macular edema in patients with various initial retinopathy levels (no retinopathy or mild, moderate, or severe nonproliferative diabetic retinopathy). The models included recognized risk factors for progression of retinopathy. RESULTS: Overall, the probability of progression to proliferative diabetic retinopathy or clinically significant macular edema was limited to approximately 5% between retinal screening examinations at 4 years among patients who had no retinopathy, 3 years among those with mild retinopathy, 6 months among those with moderate retinopathy, and 3 months among those with severe nonproliferative diabetic retinopathy. The risk of progression was also closely related to mean glycated hemoglobin levels. The risk of progression from no retinopathy to proliferative diabetic retinopathy or clinically significant macular edema was 1.0% over 5 years among patients with a glycated hemoglobin level of 6%, as compared with 4.3% over 3 years among patients with a glycated hemoglobin level of 10%. Over a 20-year period, the frequency of eye examinations was 58% lower with our practical, evidence-based schedule than with routine annual examinations, which resulted in substantial cost savings. CONCLUSIONS: Our model for establishing an individualized schedule for retinopathy screening on the basis of the patient's current state of retinopathy and glycated hemoglobin level reduced the frequency of eye examinations without delaying the diagnosis of clinically significant disease. (Funded by the National Institute of Diabetes and Digestive and Kidney Diseases and others; DCCT/EDIC ClinicalTrials.gov numbers, NCT00360893 and NCT00360815 .).

The minimum intensity of a mixed exposure that increases the risk of an outcome.

Semi-quantitative exposures, such as smoking and alcohol consumption, are common in clinical studies. Their association with outcomes is captured using either a single quantitative variable that includes nonexposed with a value of zero, or using two variables by adding an additional binary variable exposed versus not exposed. Herein, we propose two approaches to determine a lower bound on the amount of such an exposure (eg, number of cigarettes smoked per day) that significantly increases the risk of outcomes. Using smoking as illustration, the first approach consists of sequentially testing the effect of 1, 2, and so on, cigarettes per day, which requires an adjustment for multiplicity to protect the overall type-I error. An alternative gatekeeping approach is also described. The proposed methods are illustrated for the association of smoking with clinically confirmed neuropathy in a logistic regression model, and for the association of smoking with the risk of CVD in a Cox PH regression model.

Closed testing of each group versus the others combined in a multiple group analysis.

BACKGROUND: Many studies, such as a study of comparative effectiveness, entail a comparison of the beneficial and adverse effects of multiple K> 2 competing therapies. Often, the analysis consists of a comparison of the K groups using an omnibus (T2-like) test for any difference among the groups followed by pairwise comparisons with adjustments for multiple tests. METHODS: We evaluate the properties of an analysis strategy in which each group is compared to the average of the others in hopes of establishing the overall superiority (or harm) of at least one of the therapies. Testing of one-versus-others can be accomplished for virtually any model using simple tests, and the type I error probability α can be controlled by conducting such tests under the closed testing principle. Testing using linear models, the family of generalized linear models, and Cox proportional hazards models is described with examples. RESULTS: Since each tested hypothesis compares one treatment to the average of the others, the K-level null hypothesis in the tree of closed testing is equivalent to any of the (K-1)-level tests, thus reducing the number of tests required. This applies to linear, generalized linear, and Cox proportional hazards models. While the Bonferroni, Holm, and Hommel procedures preserve the desired level α, all are conservative relative to closed one-versus-others testing and closed testing in general provides greater power. CONCLUSION: Testing each of the multiple treatments versus the average of the others is readily and efficiently conducted under the closed testing principle and may be especially useful in the assessment of studies of comparative effectiveness.

Serum apolipoproteins and apolipoprotein-defined lipoprotein subclasses: a hypothesis-generating prospective study of cardiovascular events in T1D.

APOB, APOC3, and APOE and apolipoprotein-defined lipoprotein subclasses (ADLSs; based on qualitative apolipoprotein complement) have been associated with dyslipidemia and CVD. Our main objective was to define associations of serum apolipoproteins and ADLSs with "any CVD" and "major atherosclerotic cardiovascular events" (MACEs) in a prospective study of T1D. Serum apolipoproteins and ADLSs (14 biomarkers in total) were measured in sera (obtained between 1997 and 2000) from a subset (n = 465) of the Epidemiology of Diabetes Interventions and Complications cohort. Prospective associations of "any CVD" (myocardial infarction, stroke, confirmed angina, silent myocardial infarction, revascularization, or congestive heart failure) and MACEs (fatal or nonfatal myocardial infarction or stroke), over 5,943 and 6,180 patient-years follow-up, respectively, were investigated using Cox proportional hazards models that were unadjusted and adjusted for risk factors. During 15 years of follow-up, 50 "any CVD" events and 24 MACEs occurred. Nominally significant positive univariate associations with "any CVD" were APOB, APOC3 and its subfractions [heparin precipitate, heparin-soluble (HS)], and ADLS-defined Lp-B. In adjusted analyses, APOC3-HS remained nominally significant. Nominally significant positive univariate associations with MACEs were APOC3 and its subfractions and Lp-B:C; those with total APOC3 and APOC3-HS persisted in adjusted analyses. However, these associations did not reach significance after adjusting for multiple testing. There were no significant associations of APOA1, APOA2, APOE, or other ADLSs with either "any CVD" or MACEs. These hypothesis-generating data suggest that total serum APOC3 and APOC3 in HDL are potentially important predictive biomarkers for any CVD and MACEs in adults with T1D.

Optimal screening schedules for disease progression with application to diabetic retinopathy.

Clinical management of chronic diseases requires periodic evaluations. Subjects transition between various levels of severity of a disease over time, one of which may trigger an intervention that requires treatment. For example, in diabetic retinopathy, patients with type 1 diabetes are evaluated yearly for either the onset of proliferative diabetic retinopathy (PDR) or clinically significant macular edema (CSME) that would require immediate treatment to preserve vision. Herein, we investigate methods for the selection of personalized cost-effective screening schedules and compare them with a fixed visit schedule (e.g., annually) in terms of both cost and performance. The approach is illustrated using the progression of retinopathy in the DCCT/EDIC study.

Screening eye exams in youth with type 1 diabetes under 18 years of age: Once may be enough?

Case series and registry data suggest that diabetic retinopathy requiring treatment is rare in youth with type 1 diabetes (T1D) prior to 18 years of age. We evaluated this question in the standardized clinical trial setting by retrospectively reviewing diabetic retinopathy examinations from participants in the Diabetes Control and Complications Trial (DCCT) who were 13 to <18 years of age at randomization. Standardized stereoscopic 7-field fundus photographs were obtained every 6 months during DCCT (1983-1993). Photographs were graded centrally using the Early Treatment Diabetic Retinopathy Study (ETDRS) scale. Transitions in diabetic retinopathy status over time were described. A total of 195 participants with median baseline glycated hemoglobin (HbA1c) of 9.3% (103 in the conventional and 92 in the intensive treatment groups) had an average of 5.3 diabetic retinopathy assessments during 2.3 years of follow-up (range 1-11) while under 18 years of age during the DCCT. No participant developed severe non-proliferative diabetic retinopathy or proliferative diabetic retinopathy and only one participant (in the intensive group) reached clinically significant macular edema (CSME) while less than 18 years of age. In this incident case, baseline characteristics included diabetes duration 9.3 years, HbA1c 10.3%, LDL 131 mg/dL, and mild non-proliferative diabetic retinopathy (35/35 ETDRS scale); CSME resolved without treatment. Similar analyses using age cut-offs of <19, 20, or 21 years showed a slight rise in diabetic retinopathy requiring treatment over late adolescence. Clinical trial evidence suggests that frequent eye exams may not be universally necessary in youth <18 years of age with T1D.

Properties of composite time to first event versus joint marginal analyses of multiple outcomes.

Many clinical studies (eg, cardiovascular outcome trials) investigate the effect of an intervention on multiple event time outcomes. The most common method of analysis is a so-called "composite" analysis of a composite outcome defined as the time to the first component event. Other approaches have been proposed, including the win ratio (or win difference) for ordered outcomes and the application of the Wei-Lachin test. Herein, we assess the influence of the marginal and joint distributions of the component events, and their correlation structures, on the operating characteristics of these methods for the analysis of multiple events. The operating characteristics are investigated using a bivariate exponential model with a shared frailty, under which these properties are obtained in closed form. While the composite time-to-first-event analysis provides an unbiased test of the hypothesis of equality of the distribution of the time to first event, we show that it can provide a biased test of the joint null hypothesis of equal marginal hazards when the correlation of event times differs between groups. The same applies to the win ratio. However, the operating characteristics of the Wei-Lachin or other tests of the joint equality of the marginal hazards are unaffected. Furthermore, when the correlations are equal, the Wei-Lachin test is more powerful to detect a difference in marginal hazards than the composite analysis test. Careful consideration of the properties of the various methods for analysis of composite outcome measures are in order before adopting one as primary analysis in a clinical study.

The relationship of blood glucose with cardiovascular disease is mediated over time by traditional risk factors in type 1 diabetes: the DCCT/EDIC study.

AIMS/HYPOTHESIS: Chronic hyperglycaemia, as measured by HbA1c levels, is a major risk factor for atherosclerosis and cardiovascular disease (CVD) in type 1 diabetes. Our aim was to describe the degree to which the effect of HbA1c on the risk of CVD is mediated by its effect on traditional risk factors over time, and how these mediation pathways change over time. METHODS: The DCCT and its observational follow-up study, the Epidemiology of Diabetes Interventions and Complications (EDIC), followed 1441 participants for a mean of 27 years, with periodic measurement of HbA1c and risk factors over time. We assessed the proportion of the HbA1c effect on risk of CVD that was mediated through its effects on systolic BP (SBP), pulse rate, triacylglycerols and LDL-cholesterol (LDLc) levels, and how the proportion mediated changed over time. RESULTS: The association of HbA1c with CVD outcomes was stable over time, while that of traditional risk factors (SBP, pulse rate, triacylglycerols and LDLc) increased. At 10 years of follow-up, the effect of HbA1c on 10 year CVD risk was minimally mediated by SBP (2.7%), increasing to 26% at 20 years. Likewise, from 10 year follow-up to 20 year follow-up, the proportion of HbA1c effect mediated through pulse rate increased from 6.3% to 29.3%, through triacylglycerols from 2.2% to 22.4%, and through LDLc from 9.2% to 30.7%. CONCLUSIONS/INTERPRETATION: As participants age, the predictive association of mean HbA1c on subsequent CVD events is increasingly mediated by its effect on standard risk factors. Thus, management of traditional non-glycaemic CVD risk factors may have increasing benefits in an ageing type 1 diabetes population with longstanding hyperglycaemia. TRIAL REGISTRATION: ClinicalTrials.gov NCT00360893 and NCT00360815.

Large sample inference for a win ratio analysis of a composite outcome based on prioritized components.

Composite outcomes are common in clinical trials, especially for multiple time-to-event outcomes (endpoints). The standard approach that uses the time to the first outcome event has important limitations. Several alternative approaches have been proposed to compare treatment versus control, including the proportion in favor of treatment and the win ratio. Herein, we construct tests of significance and confidence intervals in the context of composite outcomes based on prioritized components using the large sample distribution of certain multivariate multi-sample U-statistics. This non-parametric approach provides a general inference for both the proportion in favor of treatment and the win ratio, and can be extended to stratified analyses and the comparison of more than two groups. The proposed methods are illustrated with time-to-event outcomes data from a clinical trial.

Tolerance limits and tolerance intervals for ratios of normal random variables using a bootstrap calibration.

This paper addresses the problem of deriving one-sided tolerance limits and two-sided tolerance intervals for a ratio of two random variables that follow a bivariate normal distribution, or a lognormal/normal distribution. The methodology that is developed uses nonparametric tolerance limits based on a parametric bootstrap sample, coupled with a bootstrap calibration in order to improve accuracy. The methodology is also adopted for computing confidence limits for the median of the ratio random variable. Numerical results are reported to demonstrate the accuracy of the proposed approach. The methodology is illustrated using examples where ratio random variables are of interest: an example on the radioactivity count in reverse transcriptase assays and an example from the area of cost-effectiveness analysis in health economics.

Testosterone and cardiac mass and function in men with type 1 diabetes in the Epidemiology of Diabetes Interventions and Complications Study (EDIC).

OBJECTIVE: Low testosterone concentrations have been reported to be associated with increased risk of congestive heart failure, but the mechanisms are unclear. Our objective was to examine the relationship between endogenous testosterone and measures of cardiac mass and function among men with type 1 diabetes. DESIGN: Secondary analysis of a prospective observational study. PARTICIPANTS: Men (n = 508) in the Epidemiology of Diabetes Interventions and Complications (EDIC) study, the observational follow-up of the Diabetes Control and Complications Trial (DCCT). MEASUREMENTS: Testosterone assessed by liquid chromatography mass spectrometry at EDIC year 10 and cardiac magnetic resonance imaging (CMR) measures at EDIC years 14/15. Linear regression models were used to assess the relationship between testosterone, sex hormone binding globulin (SHBG) and left ventricular (LV) mass, volume, ejection fraction and cardiac index before and after adjustment for age, randomization arm, alcohol and cigarette use, macroalbuminuria, haemoglobin A1c, insulin dose, body mass index, lipids, blood pressure, use of antihypertensive medications and microvascular complications. RESULTS: In fully adjusted models, total testosterone concentrations were significantly associated with LV mass (P = 0·014), end-diastolic volume (P = 0·002), end-systolic volume (P = 0·012) and stroke volume (P = 0·022), but not measures of LV function after adjustment for cardiac risk factors. Bioavailable testosterone was associated with LV mass, but not volume or function, while SHBG was associated with volume, but not mass or function. CONCLUSIONS: Among men with type 1 diabetes, higher total testosterone was associated with higher LV mass and volume, but not with function. The clinical significance of this association remains to be established.

Characterizing the Association Between Alcohol and HIV Virologic Failure in a Military Cohort on Antiretroviral Therapy.

BACKGROUND: The effects of at-risk drinking on HIV infection remain controversial. We investigated the impact of self-reported alcohol consumption on surrogate markers of HIV progression among individuals initiated on highly active antiretroviral therapy (HAART). METHODS: We analyzed individuals who were surveyed on alcohol use within a year of HAART initiation between 2006 and 2014. At-risk drinking was defined as consumption of at least 3 or 4 drinks/d, or 7 and 14 drinks/wk among women and men, respectively. We performed time-updated generalized estimating equation logistic regression to determine the effect of at-risk drinking on virologic failure (VF) and mixed-effects linear regression on CD4 count reconstitution, controlling for potential confounders. RESULTS: Of 801 individuals initiated on HAART, 752 individuals with alcohol survey data were included in the analysis. Of these, 45% (n = 336) met criteria for at-risk drinking at HAART initiation on at least 1 survey. The rates of VF were 4.30 per 100 person-years (95% CI [2.86, 6.21]) for at-risk drinkers and 2.45 per 100 person-years (95% CI [1.57, 3.65]) for individuals without at-risk drinking. At-risk drinking was not significantly associated with VF (OR 1.73, 95% CI [0.92, 3.25]) (p = 0.087) or CD4 reconstitution (CD4 increase 11.4; 95% CI [-19.8, 42.7]) in univariate analyses; however, in our multivariate model, a statistically significant relationship between VF and at-risk drinking was observed (OR 2.28, 95% CI [ 1.01, 5.15]). CONCLUSIONS: We found a high proportion of at-risk drinking in our military cohort, which was predictive of VF in multivariate analysis. Given alcohol's effect on myriad HIV and non-HIV outcomes, interventions to decrease the prevalence of at-risk drinking among HIV-infected individuals are warranted.

Probabilistic measures of cost-effectiveness.

Several probability-based measures are introduced in order to assess the cost-effectiveness of a treatment. The basic measure consists of the probability that one treatment is less costly and more effective compared with another. Several variants of this measure are suggested as flexible options for cost-effectiveness analysis. The proposed measures are invariant under monotone transformations of the cost and effectiveness measures. Interval estimation of the proposed measures are investigated under a parametric model, assuming bivariate normality, and also non-parametrically. The delta method and a generalized pivotal quantity approach are both investigated under the bivariate normal model. A non-parametric U-statistics-based approach is also investigated for computing confidence intervals. Numerical results show that under bivariate normality, the solution based on generalized pivotal quantities exhibits accurate performance in terms of maintaining the coverage probability of the confidence interval. The non-parametric U-statistics-based solution is accurate for sample sizes that are at least moderately large. The results are illustrated using data from a clinical trial for prostate cancer therapy. Copyright © 2016 John Wiley & Sons, Ltd.