A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health.

We develop a flexible two-equation copula model to address endogeneity of medical expenditures in a distribution regression for health. The expenditure margin uses the compound gamma distribution, a special case of the Tweedie family of distributions, to account for a spike at zero and a highly skewed continuous part. An efficient estimation algorithm offers flexible choices of copulae and link functions, including logit, probit and cloglog for the health margin. Our empirical application revisits data from the Rand Health Insurance Experiment. In the joint model, using random insurance plan assignment as instrument for spending, a $1000 increase is estimated to reduce the probability of a low post-program mental health index by 1.9 percentage points. The effect is not statistically significant. Ignoring endogeneity leads to a spurious positive effect estimate.

Correcting for selection bias in HIV prevalence estimates: an application of sample selection models using data from population-based HIV surveys in seven sub-Saharan African countries.

INTRODUCTION: Population-based biomarker surveys are the gold standard for estimating HIV prevalence but are susceptible to substantial non-participation (up to 30%). Analytical missing data methods, including inverse-probability weighting (IPW) and multiple imputation (MI), are biased when data are missing-not-at-random, for example when people living with HIV more frequently decline participation. Heckman-type selection models can, under certain assumptions, recover unbiased prevalence estimates in such scenarios. METHODS: We pooled data from 142,706 participants aged 15-49 years from nationally representative cross-sectional Population-based HIV Impact Assessments in seven countries in sub-Saharan Africa, conducted between 2015 and 2018 in Tanzania, Uganda, Malawi, Zambia, Zimbabwe, Lesotho and Eswatini. We compared sex-stratified HIV prevalence estimates from unadjusted, IPW, MI and selection models, controlling for household and individual-level predictors of non-participation, and assessed the sensitivity of selection models to the copula function specifying the correlation between study participation and HIV status. RESULTS: In total, 84.1% of participants provided a blood sample to determine HIV serostatus (range: 76% in Malawi to 95% in Uganda). HIV prevalence estimates from selection models diverged from IPW and MI models by up to 5% in Lesotho, without substantial precision loss. In Tanzania, the IPW model yielded lower HIV prevalence estimates among males than the best-fitting copula selection model (3.8% vs. 7.9%). CONCLUSIONS: We demonstrate how HIV prevalence estimates from selection models can differ from those obtained under missing-at-random assumptions. Further benefits include exploration of plausible relationships between participation and outcome. While selection models require additional assumptions and careful specification, they are an important tool for triangulating prevalence estimates in surveys with substantial missing data due to non-participation.

Did the ACA's "guaranteed issue" provision cause adverse selection into nongroup insurance? Analysis using a copula-based hurdle model.

Prior to the Affordable Care Act (ACA), insurance companies could charge higher premiums, or outright deny coverage, to people with preexisting health problems. But the ACA's "guaranteed issue" provision forbids such price discrimination and denials of coverage. This paper seeks to determine whether, after implementation of the ACA, nongroup private insurance plans have experienced adverse selection. Our empirical approach employs a copula-based hurdle regression model, with dependence modeled as a function of dimensions along which adverse selection might occur. Our main finding is that, after implementation of the ACA, nongroup insurance enrollees with preexisting health problems do not appear to exhibit adverse selection. This finding suggests that the ACA's mandate that everyone acquire coverage might have attracted enough healthy enrollees to offset any adverse selection.

Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection.

Penalized factor analysis is an efficient technique that produces a factor loading matrix with many zero elements thanks to the introduction of sparsity-inducing penalties within the estimation process. However, sparse solutions and stable model selection procedures are only possible if the employed penalty is non-differentiable, which poses certain theoretical and computational challenges. This article proposes a general penalized likelihood-based estimation approach for single- and multiple-group factor analysis models. The framework builds upon differentiable approximations of non-differentiable penalties, a theoretically founded definition of degrees of freedom, and an algorithm with integrated automatic multiple tuning parameter selection that exploits second-order analytical derivative information. The proposed approach is evaluated in two simulation studies and illustrated using a real data set. All the necessary routines are integrated into the R package penfa.

The Association between Supraphysiologic Arterial Oxygen Levels and Mortality in Critically Ill Patients. A Multicenter Observational Cohort Study.

Rationale: There is conflicting evidence on harm related to exposure to supraphysiologic PaO2 (hyperoxemia) in critically ill patients.Objectives: To examine the association between longitudinal exposure to hyperoxemia and mortality in patients admitted to ICUs in five United Kingdom university hospitals.Methods: A retrospective cohort of ICU admissions between January 31, 2014, and December 31, 2018, from the National Institute of Health Research Critical Care Health Informatics Collaborative was studied. Multivariable logistic regression modeled death in ICU by exposure to hyperoxemia.Measurements and Main Results: Subsets with oxygen exposure windows of 0 to 1, 0 to 3, 0 to 5, and 0 to 7 days were evaluated, capturing 19,515, 10,525, 6,360, and 4,296 patients, respectively. Hyperoxemia dose was defined as the area between the PaO2 time curve and a boundary of 13.3 kPa (100 mm Hg) divided by the hours of potential exposure (24, 72, 120, or 168 h). An association was found between exposure to hyperoxemia and ICU mortality for exposure windows of 0 to 1 days (odds ratio [OR], 1.15; 95% compatibility interval [CI], 0.95-1.38; P = 0.15), 0 to 3 days (OR 1.35; 95% CI, 1.04-1.74; P = 0.02), 0 to 5 days (OR, 1.5; 95% CI, 1.07-2.13; P = 0.02), and 0 to 7 days (OR, 1.74; 95% CI, 1.11-2.72; P = 0.02). However, a dose-response relationship was not observed. There was no evidence to support a differential effect between hyperoxemia and either a respiratory diagnosis or mechanical ventilation.Conclusions: An association between hyperoxemia and mortality was observed in our large, unselected multicenter cohort. The absence of a dose-response relationship weakens causal interpretation. Further experimental research is warranted to elucidate this important question.

Mixed binary-continuous copula regression models with application to adverse birth outcomes.

Bivariate copula regression allows for the flexible combination of two arbitrary, continuous marginal distributions with regression effects being placed on potentially all parameters of the resulting bivariate joint response distribution. Motivated by the risk factors for adverse birth outcomes, many of which are dichotomous, we consider mixed binary-continuous responses that extend the bivariate continuous framework to the situation where one response variable is discrete (more precisely, binary) whereas the other response remains continuous. Utilizing the latent continuous representation of binary regression models, we implement a penalized likelihood-based approach for the resulting class of copula regression models and employ it in the context of modeling gestational age and the presence/absence of low birth weight. The analysis demonstrates the advantage of the flexible specification of regression impacts including nonlinear effects of continuous covariates and spatial effects. Our results imply that racial and spatial inequalities in the risk factors for infant mortality are even greater than previously suggested.

Copula selection models for non-Gaussian outcomes that are missing not at random.

Missing not at random (MNAR) data pose key challenges for statistical inference because the substantive model of interest is typically not identifiable without imposing further (eg, distributional) assumptions. Selection models have been routinely used for handling MNAR by jointly modeling the outcome and selection variables and typically assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection approaches, for example, estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption compared with those assuming that nonresponse and outcome are jointly normally distributed. However, the proposed methods have been mostly restricted to a specific joint distribution (eg, bivariate t-distribution). This paper discusses a flexible copula-based selection approach (which accommodates a wide range of non-Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterizes the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data. We illustrate the methods in the REFLUX study, which evaluates the effect of laparoscopic surgery on long-term quality of life in patients with reflux disease. We provide software code for implementing the proposed copula framework using the R package GJRM.

National South African HIV prevalence estimates robust despite substantial test non-participation.

BACKGROUND: South African (SA) national HIV seroprevalence estimates are of crucial policy relevance in the country, and for the worldwide HIV response. However, the most recent nationally representative HIV test survey in 2012 had 22% test non-participation, leaving the potential for substantial bias in current seroprevalence estimates, even after controlling for selection on observed factors. OBJECTIVE: To re-estimate national HIV prevalence in SA, controlling for bias due to selection on both observed and unobserved factors in the 2012 SA National HIV Prevalence, Incidence and Behaviour Survey. METHODS: We jointly estimated regression models for consent to test and HIV status in a Heckman-type bivariate probit framework. As selection variable, we used assigned interviewer identity, a variable known to predict consent but highly unlikely to be associated with interviewees' HIV status. From these models, we estimated the HIV status of interviewed participants who did not test. RESULTS: Of 26 710 interviewed participants who were invited to test for HIV, 21.3% of females and 24.3% of males declined. Interviewer identity was strongly correlated with consent to test for HIV; declining a test was weakly associated with HIV serostatus. Our HIV prevalence estimates were not significantly different from those using standard methods to control for bias due to selection on observed factors: 15.1% (95% confidence interval (CI) 12.1 - 18.6) v. 14.5% (95% CI 12.8 - 16.3) for 15 - 49-year-old males; 23.3% (95% CI 21.7 - 25.8) v. 23.2% (95% CI 21.3 - 25.1) for 15 - 49-year-old females. CONCLUSION: The most recent SA HIV prevalence estimates are robust under the strongest available test for selection bias due to missing data. Our findings support the reliability of inferences drawn from such data.

Penalized likelihood estimation of a trivariate additive probit model.

This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina.

Ultrasound-detected subclinical inflammation was better reflected by the disease activity score (DAS-28) in patients with suspicion of inflammatory arthritis compared to established rheumatoid arthritis.

Limited data are available about the ultrasound (US)-detected inflammatory features in patients with suspicion of inflammatory arthritis (S-IA) vs. established rheumatoid arthritis (RA). Our study aimed to assess if the presence of power Doppler (PD) can be predicted by a combination of clinical, laboratory and US parameters. We conducted a real-life, retrospective cohort study comparing clinical, laboratory and US parameters of 108 patients with established RA and 93 patients with S-IA. We propose a PD signal prediction model based on a beta-binomial distribution for PD variable using a mix of outcome measures. Patients with RA in clinical remission had significantly more active inflammation and erosions on US when compared with patients with S-IA with similar disease scores (p = 0.03 and p = 0.01, respectively); however, RA patients with different disease activity score (DAS-28) scores had similar PD scores (p = 0.058). The PD scores did not correlate with erosions (p = 0.38) or DAS-28 scores (p = 0.28) in RA patients, but they correlated with high disease activity in S-IA patients (p = 0.048). Subclinical inflammation is more common in patients with RA in clinical remission or with low disease activity than in patients with S-IA; therefore, US was more useful in assessing for true remission in RA rather than diagnosing IA in patients with low disease activity scores. This is the first study to propose a PD prediction model integrating several outcome measures in the two different groups of patients. Further research into validating this model can minimise the risk of underdiagnosing subclinical inflammation.

Adjusting HIV prevalence estimates for non-participation: an application to demographic surveillance.

INTRODUCTION: HIV testing is a cornerstone of efforts to combat the HIV epidemic, and testing conducted as part of surveillance provides invaluable data on the spread of infection and the effectiveness of campaigns to reduce the transmission of HIV. However, participation in HIV testing can be low, and if respondents systematically select not to be tested because they know or suspect they are HIV positive (and fear disclosure), standard approaches to deal with missing data will fail to remove selection bias. We implemented Heckman-type selection models, which can be used to adjust for missing data that are not missing at random, and established the extent of selection bias in a population-based HIV survey in an HIV hyperendemic community in rural South Africa. METHODS: We used data from a population-based HIV survey carried out in 2009 in rural KwaZulu-Natal, South Africa. In this survey, 5565 women (35%) and 2567 men (27%) provided blood for an HIV test. We accounted for missing data using interviewer identity as a selection variable which predicted consent to HIV testing but was unlikely to be independently associated with HIV status. Our approach involved using this selection variable to examine the HIV status of residents who would ordinarily refuse to test, except that they were allocated a persuasive interviewer. Our copula model allows for flexibility when modelling the dependence structure between HIV survey participation and HIV status. RESULTS: For women, our selection model generated an HIV prevalence estimate of 33% (95% CI 27-40) for all people eligible to consent to HIV testing in the survey. This estimate is higher than the estimate of 24% generated when only information from respondents who participated in testing is used in the analysis, and the estimate of 27% when imputation analysis is used to predict missing data on HIV status. For men, we found an HIV prevalence of 25% (95% CI 15-35) using the selection model, compared to 16% among those who participated in testing, and 18% estimated with imputation. We provide new confidence intervals that correct for the fact that the relationship between testing and HIV status is unknown and requires estimation. CONCLUSIONS: We confirm the feasibility and value of adopting selection models to account for missing data in population-based HIV surveys and surveillance systems. Elements of survey design, such as interviewer identity, present the opportunity to adopt this approach in routine applications. Where non-participation is high, true confidence intervals are much wider than those generated by standard approaches to dealing with missing data suggest.

On the assumption of bivariate normality in selection models: a Copula approach applied to estimating HIV prevalence.

BACKGROUND: Heckman-type selection models have been used to control HIV prevalence estimates for selection bias when participation in HIV testing and HIV status are associated after controlling for observed variables. These models typically rely on the strong assumption that the error terms in the participation and the outcome equations that comprise the model are distributed as bivariate normal. METHODS: We introduce a novel approach for relaxing the bivariate normality assumption in selection models using copula functions. We apply this method to estimating HIV prevalence and new confidence intervals (CI) in the 2007 Zambia Demographic and Health Survey (DHS) by using interviewer identity as the selection variable that predicts participation (consent to test) but not the outcome (HIV status). RESULTS: We show in a simulation study that selection models can generate biased results when the bivariate normality assumption is violated. In the 2007 Zambia DHS, HIV prevalence estimates are similar irrespective of the structure of the association assumed between participation and outcome. For men, we estimate a population HIV prevalence of 21% (95% CI = 16%-25%) compared with 12% (11%-13%) among those who consented to be tested; for women, the corresponding figures are 19% (13%-24%) and 16% (15%-17%). CONCLUSIONS: Copula approaches to Heckman-type selection models are a useful addition to the methodological toolkit of HIV epidemiology and of epidemiology in general. We develop the use of this approach to systematically evaluate the robustness of HIV prevalence estimates based on selection models, both empirically and in a simulation study.

A semiparametric bivariate probit model for joint modeling of outcomes in STEMI patients.

In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation myocardial infarction. The main idea is to carry out a joint modeling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for several reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient's condition at admission time. Moreover, they can also directly influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent or biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit nonlinear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response.

Benchmarking network for clinical and humanistic outcomes in diabetes (BENCH-D) study: protocol, tools, and population.

BACKGROUND: In the context of the DAWN-2 initiatives, the BENCH-D Study aims to test a model of regional benchmarking to improve not only the quality of diabetes care, but also patient-centred outcomes. METHODS/DESIGN: As part of the AMD-Annals quality improvement program, 32 diabetes clinics in 4 Italian regions extracted clinical data from electronic databases for measuring process and outcome quality indicators. A random sample of patients with type 2 diabetes filled in a questionnaire including validated instruments to assess patient-centred indicators: SF-12 Health Survey, WHO-5 Well-Being Index, Diabetes Empowerment Scale, Problem Areas in Diabetes, Health Care Climate Questionnaire, Patients Assessment of Chronic Illness Care, Barriers to Medications, Patient Support, Diabetes Self-care Activities, and Global Satisfaction for Diabetes Treatment. Data were discussed with participants in regional meetings. Main problems, obstacles and solutions were identified through a standardized process, and a regional mandate was produced to drive the priority actions. Overall, clinical indicators on 78,854 patients have been measured; additionally, 2,390 patients filled-in the questionnaire. The regional mandates were officially launched in March 2012. Clinical and patient-centred indicators will be evaluated again after 18 months. A final assessment of clinical indicators will take place after 30 months. DISCUSSION: In the context of the BENCH-D study, a set of instruments has been validated to measure patient well-being and satisfaction with the care. In the four regional meetings, different priorities were identified, reflecting different organizational resources of the different areas. In all the regions, a major challenge was represented by the need of skills and instruments to address psychosocial issues of people with diabetes. The BENCH-D study allows a field testing of benchmarking activities focused on clinical and patient-centred indicators.

Penalised regression splines: theory and application to medical research.

Generalised additive models (GAMs) allow for flexible functional dependence of a response variable on covariates. The aim of this article is to provide an accessible overview of GAMs based on the penalised likelihood approach with regression splines. In contrast to the classical backfitting, the penalised likelihood framework taken here provides researchers with an efficient computational method for automatic multiple smoothing parameter selection, which can determine the functional form of any relationship from the data. We illustrate through an example how the use of this methodology can help to gain insights into medical research.

The DIAB.&TE.S Project: how patients perceive diabetes and diabetes therapy.

Assessment of quality of life (QoL) in diabetic patients is increasingly retained as a crucial parameter to take into account before concluding on the efficacy of new therapies. Indeed, the trend is to adopt treatments providing a genuine clinical benefit associated with a positive impact on QoL. In this context, DIAB.&TE.S Project aimed at analyzing patient's perception of psychological well-being, quality of treatment and their correlation with glyco-metabolic values control. A total of 1918 diabetic patients, mostly from southern Italy, were enrolled in this observational study. DIAB.&TE.S included a wide range of patients taking insulin monotherapy, OHA (oral hypoglycemic agents) monotherapy or combined therapy (insulin + OHA). Internationally recognized instruments such as the Well-Being Questionnaire (WBQ) and Diabetes Treatment Satisfaction Questionnaire (DTSQ) were used to assess general well-being and diabetes treatment satisfaction. Combined therapy was not highly efficient in achieving both glycemic and quality of life goals when compared to insulin or OHA monotherapies. Oral monotherapy produced better results if compared to insulin treatment, as demonstrated by DTSQand WBQ scores. However, among the insulin treated subjects, higher scores were reached in patients using advanced devices to administrate insulin, Finally, a correlation between questionnaires outcomes and metabolic control in patients could be established. Our findings support the idea that in diabetes therapy, integration of clinical and psychosocial cares could be helpful in both identifying subjects that need a treatment re-examination and improving patient's quality of life. In addition, this survey by its magnitude provides an overview of diabetes management in Italy and contributes to set up an accurate profile of diabetic people in this part of Europe.

Role of hyperglycemia in nitrotyrosine postprandial generation.

OBJECTIVE: Recently, much attention has been paid to the possibility that postprandial hyperglycemia may be a cardiovascular risk factor in diabetes. Oxidative stress has been involved in the pathogenesis of diabetic complications, and increased plasma levels of nitrotyrosine, a product of peroxynitrite action, have been found in the plasma of diabetic subjects. The aim of the present study was to evaluate whether postprandial hyperglycemia is accompanied by nitrotyrosine generation and, if so, to explore a possible direct role of hyperglycemia in such a phenomenon. RESEARCH DESIGN AND METHODS: A total of 23 type 2 diabetic patients and 15 matched normal healthy subjects were recruited for this study. Two different tests were performed in diabetic patients: a standard meal preceded by regular insulin (0.15 units/kg body wt) or insulin aspart (0.15 units/kg body wt) to achieve different levels of postprandial hyperglycemia. The meal test was also performed in healthy control subjects. At 0 min and 1, 2, 4, and 6 h after each meal, blood glucose, triglyceride, and nitrotyrosine levels were measured. RESULTS: Fasting nitrotyrosine was significantly increased in diabetic patients and was further increased during both meal tests in diabetic subjects but not normal subjects. As compared with regular insulin, aspart administration significantly reduced the area under the curve of both glycemia (P < 0.04) and nitrotyrosine (P < 0.03), whereas that of triglycerides was not significantly affected by the treatment. CONCLUSIONS: This study shows a direct correlation between postprandial hyperglycemia and the production of nitrotyrosine, a marker of oxidative stress, in patients with type 2 diabetes.

Early increase of oxidative stress and reduced antioxidant defenses in patients with uncomplicated type 1 diabetes: a case for gender difference.

OBJECTIVE: Diabetes increases the risk of coronary heart disease (CHD) to a greater extent in women than in men. We investigated whether type 1 diabetic patients with short duration of disease and without complications have an altered oxidative status and whether there are differences between men and women. RESEARCH DESIGN AND METHODS: We investigated oxidative status in 29 control subjects and 37 patients with uncomplicated type 1 diabetes with duration of 6 +/- 3 years. RESULTS: Compared with control subjects, type 1 diabetic patients had lower total plasma antioxidant capacity (TRAP) (720.3 +/- 111.2 vs. 972.5 +/- 97.7 micromol/l in men, P < 0.001; 579.8 +/- 95.4 vs. 930.1 +/- 84.2 in women, P < 0.001), higher lipid hydroperoxide (ROOH) levels (6.4 +/- 2.2 vs. 2.0 +/- 0.7 micromol/l in men, P < 0.001; 8.1 +/- 1.9 vs. 2.2 +/- 0.6 in women, P < 0.001), higher total conjugated diene (CD) levels (0.037 +/- 0.003 vs. 0.033 +/- 0.002 A.U. in men, P < 0.001), lower 246-nm CD levels (0.0032. +/- 0.0010 vs. 0.0070 +/- 0.0012 A.U. in men, P < 0.001; 0.0022 +/- 0.0011 vs. 0.0072 +/- 0.0014 A.U. in women, P < 0.001), and higher 232-nm CD levels (0.0348 +/- 0.0041 vs. 0.0257 +/- 0.0022 A.U. in men, P < 0.001; 0.0346 +/- 0.0031 vs. 0.0246 +/- 0.0074 A.U. in women, P < 0.001). Compared with diabetic men, diabetic women had lower TRAP (P < 0.01), higher ROOH levels (P < 0.01), and lower 246-nm CD levels (P < 0.05). Plasma concentration of uric acid was significantly lower in patients with type 1 diabetes than in control subjects (3.3 +/- 0.3 vs. 4.3 +/- 0.2 mg/dl; P = 0.009) with a significant difference between women and men with type 1 diabetes (2.6 +/- 0.3 vs. 3.9 +/- 0.3, respectively; P = 0.009). CONCLUSIONS: Our findings suggest that reduced antioxidant activity and increased oxidative stress occur early after the diagnosis of type 1 diabetes, especially in women, and this might explain, at least in part, the increased susceptibility of diabetic women to cardiovascular complications.