A general binomial regression model to estimate standardized risk differences from binary response data

Estimating and presenting hazard ratios and absolute risks from a Cox model with complex nonlinear interactions

Interaction analysis is a critical component of clinical and public health research and represents a key topic in precision health and medicine. In applied settings, however, interaction assessment is usually limited to the test of a product term in a regression model and to the presentation of results stratified by levels of additional covariates. Stratification of results often relies on categorizing or making linearity assumptions for continuous covariates, with substantial loss of precision and of relevant information. In time-to-event analysis, moreover, interaction assessment is often limited to the multiplicative hazard scale by inclusion of a product term in a Cox regression model, disregarding the clinically relevant information that is captured by the absolute risk scale. In this paper we present a user-friendly procedure, based on the prediction of individual absolute risks from the Cox model, for the estimation and presentation of interactive effects on both the multiplicative and additive scales in survival analysis. We describe how to flexibly incorporate interactions with continuous covariates, which potentially operate in a nonlinear fashion, provide software for replicating our procedure, and discuss different approaches to deriving CIs. The presented approach will allow clinical and public health researchers to assess complex relationships between multiple covariates as they relate to a clinical endpoint, and to provide a more intuitive and precise depiction of the results in applied research papers focusing on interaction and effect stratification.

Virologic outcomes after early referral of stable HIV-positive adults initiating ART to community-based adherence clubs in Cape Town, South Africa: A randomised controlled trial

Background

Differentiated service delivery (DSD) models are recommended for stable people living with HIV on antiretroviral therapy (ART) but there are few rigorous evaluations of patient outcomes.

Methods

Adherence clubs (ACs) are a form of DSD run by community health workers at community venues with 2–4 monthly ART refills and annual nurse assessments). Clinic-based care involves 2-monthly ART refills and 4-monthly nurse/doctor assessments. We compared virologic outcomes in stable adults randomised to ACs at four months post-ART initiation to those randomised to primary health care (PHC) ART clinics through 12 months on ART in Cape Town, South Africa (NCT03199027). We hypothesised that adults randomised to ACs would be more likely to be virally suppressed at 12 months post-ART initiation, versus adults randomised to continued PHC care. We enrolled consecutive adults on ART for 3–5 months who met local DSD [‘adherence clubs’ (AC)] eligibility (clinically stable, VL<400 copies/mL). The primary outcome was VL<400 copies/mL at 12 months on ART.

Results

Between January 2017 and April 2018, 220 adults were randomised (mean age 35 years; 67% female; median ART duration 18 weeks); 85% and 94% of participants randomised to ACs and PHCs attended their first service visit on schedule respectively. By 12 months on ART, 91% and 93% randomised to ACs and PHCs had a VL<400 copies/mL, respectively. In a binomial model adjusted for age, gender, previous ART use and nadir CD4 cell count, there was no evidence of superiority of ACs compared to clinic-based care (RD, -2.42%; 95% CI, -11.23 to 6.38). Findings were consistent when examining the outcome at a threshold of VL <1000 copies/mL.

Conclusion

Stable adults referred to DSDs at 4 months post-ART initiation had comparable virologic outcomes at 12 months on ART versus PHC clinics, with no evidence of superiority. Further research on long-term outcomes is required.

Introducing riskCommunicator: An R package to obtain interpretable effect estimates for public health

Common statistical modeling methods do not necessarily produce the most relevant or interpretable effect estimates to communicate risk. Overreliance on the odds ratio and relative effect measures limit the potential impact of epidemiologic and public health research. We created a straightforward R package, called riskCommunicator, to facilitate the presentation of a variety of effect measures, including risk differences and ratios, number needed to treat, incidence rate differences and ratios, and mean differences. The riskCommunicator package uses g-computation with parametric regression models and bootstrapping for confidence intervals to estimate effect measures in time-fixed data. We demonstrate the utility of the package using data from the Framingham Heart Study to estimate the effect of prevalent diabetes on the 24-year risk of cardiovascular disease or death. The package promotes the communication of public-health relevant effects and is accessible to a broad range of epidemiologists and health researchers with little to no expertise in causal inference methods or advanced coding.

Generalized linear mixed hidden semi-Markov models in longitudinal settings: A Bayesian approach

Hidden Markov and semi-Markov models (H(S)MMs) constitute useful tools for modeling observations subject to certain dependency structures. The hidden states render these models very flexible and allow them to capture many different types of latent patterns and dynamics present in the data. This has led to the increased popularity of these models, which have been applied to a variety of problems in various domains and settings, including longitudinal data. In many longitudinal studies, the response variable is categorical or count-type. Generalized linear mixed models (GLMMs) can be used to analyze a wide range of variables, including categorical and count. The present study proposes a model that combines HSMMs with GLMMs, leading to generalized linear mixed hidden semi-Markov models (GLM-HSMMs). These models can account for time-varying unobserved heterogeneity and handle different response types. Parameter estimation is achieved using a Monte Carlo Newton-Raphson (MCNR)-like algorithm. In our proposed model, the distribution of the random effects depends on hidden states. We illustrate the applicability of GLM-HSMMs with an example in the field of occupational health, where the response variable consists of count values. Furthermore, we assess the performance of our MCNR-like algorithm through a simulation study.

Statistical analysis plan for the POLAR-RCT: The Prophylactic hypOthermia trial to Lessen trAumatic bRain injury-Randomised Controlled Trial

Background

The Prophylactic hypOthermia to Lessen trAumatic bRain injury-Randomised Controlled Trial (POLAR-RCT) will evaluate whether early and sustained prophylactic hypothermia delivered to patients with severe traumatic brain injury improves patient-centred outcomes.

Methods

The POLAR-RCT is a multicentre, randomised, parallel group, phase III trial of early, prophylactic cooling in critically ill patients with severe traumatic brain injury, conducted in Australia, New Zealand, France, Switzerland, Saudi Arabia and Qatar. A total of 511 patients aged 18–60 years have been enrolled with severe acute traumatic brain injury.

The trial intervention of early and sustained prophylactic hypothermia to 33 °C for 72 h will be compared to standard normothermia maintained at a core temperature of 37 °C.

The primary outcome is the proportion of favourable neurological outcomes, comprising good recovery or moderate disability, observed at six months following randomisation utilising a midpoint dichotomisation of the Extended Glasgow Outcome Scale (GOSE). Secondary outcomes, also assessed at six months following randomisation, include the probability of an equal or greater GOSE level, mortality, the proportions of patients with haemorrhage or infection, as well as assessment of quality of life and health economic outcomes. The planned sample size will allow 80% power to detect a 30% relative risk increase from 50% to 65% (equivalent to a 15% absolute risk increase) in favourable neurological outcome at a two-sided alpha of 0.05.

Discussion

Consistent with international guidelines, a detailed and prospective analysis plan has been developed for the POLAR-RCT. This plan specifies the statistical models for evaluation of primary and secondary outcomes, as well as defining covariates for adjusted analyses and methods for exploratory analyses. Application of this statistical analysis plan to the forthcoming POLAR-RCT trial will facilitate unbiased analyses of these important clinical data.

Trial registration

ClinicalTrials.gov, NCT00987688 (first posted 1 October 2009); Australian New Zealand Clinical Trials Registry, ACTRN12609000764235. Registered on 3 September 2009.

Electronic supplementary material

The online version of this article (10.1186/s13063-018-2610-y) contains supplementary material, which is available to authorized users.

Considerations when assessing heterogeneity of treatment effect in patient-centered outcomes research

When baseline risk of an outcome varies within a population, the effect of a treatment on that outcome will vary on at least one scale (e.g., additive, multiplicative). This treatment effect heterogeneity is of interest in patient-centered outcomes research. Based on a literature review and solicited expert opinion, we assert the following: (1) Treatment effect heterogeneity on the additive scale is most interpretable to health-care providers and patients using effect estimates to guide treatment decision-making; heterogeneity reported on the multiplicative scale may be misleading as to the magnitude or direction of a substantively important interaction. (2) The additive scale may give clues about sufficient-cause interaction, although such interaction is typically not relevant to patients' treatment choices. (3) Statistical modeling need not be conducted on the same scale as results are communicated. (4) Statistical testing is one tool for investigations, provided important subgroups are identified a priori, but test results should be interpreted cautiously given nonequivalence of statistical and clinical significance. (5) Qualitative interactions should be evaluated in a prespecified manner for important subgroups. Principled analytic plans that take into account the purpose of investigation of treatment effect heterogeneity are likely to yield more useful results for guiding treatment decisions.

Integration of postpartum healthcare services for HIV-infected women and their infants in South Africa: A randomised controlled trial

BACKGROUND

As the number of HIV-infected women initiating lifelong antiretroviral therapy (ART) during pregnancy increases globally, concerns have emerged regarding low levels of retention in HIV services and suboptimal adherence to ART during the postpartum period. We examined the impact of integrating postpartum ART for HIV+ mothers alongside infant follow-up within maternal and child health (MCH) services in Cape Town, South Africa.

METHODS AND FINDINGS

We conducted a randomised trial among HIV+ postpartum women aged ≥18 years who initiated ART during pregnancy in the local antenatal care clinic and were breastfeeding when screened before 6 weeks postpartum. We compared an integrated postnatal service among mothers and their infants (the MCH-ART intervention) to the local standard of care (control)-immediate postnatal referral of HIV+ women on ART to general adult ART services and their infants to separate routine infant follow-up. Evaluation data were collected through medical records and trial measurement visits scheduled and located separately from healthcare services involved in either arm. The primary trial outcome was a composite endpoint of women's retention in ART care and viral suppression (VS) (viral load < 50 copies/ml) at 12 months postpartum; secondary outcomes included duration of any and exclusive breastfeeding, mother-to-child HIV transmission, and infant mortality. Between 5 June 2013 and 10 December 2014, a total of 471 mother-infant pairs were enrolled and randomised (mean age, 28.6 years; 18% nulliparous; 57% newly diagnosed with HIV in pregnancy; median duration of ART use at randomisation, 18 weeks). Among 411 women (87%) with primary endpoint data available, 77% of women (n = 155) randomised to the MCH-ART intervention achieved the primary composite outcome of retention in ART services with VS at 12 months postpartum, compared to 56% of women (n = 117) randomised to the control arm (absolute risk difference, 0.21; 95% CI: 0.12-0.30; p < 0.001). The findings for improved retention in care and VS among women in the MCH-ART intervention arm were consistent across subgroups of participants according to demographic and clinical characteristics. The median durations of any breastfeeding and exclusive breastfeeding were longer in women randomised to the intervention versus control arm (6.9 versus 3.0 months, p = 0.006, and 3.0 versus 1.4 months, p < 0.001, respectively). For the infants, overall HIV-free survival through 12 months of age was 97%: mother-to-child HIV transmission was 1.2% overall (n = 4 and n = 1 transmissions in the intervention and control arms, respectively), and infant mortality was 1.9% (n = 6 and n = 3 deaths in the intervention and control arms, respectively), and these outcomes were similar by trial arm. Interpretation of these findings should be qualified by the location of this study in a single urban area as well as the self-reported nature of breastfeeding outcomes.

CONCLUSIONS

In this study, we found that integrating ART services into the MCH platform during the postnatal period was a simple and effective intervention, and this should be considered for improving maternal and child outcomes in the context of HIV.

TRIAL REGISTRATION

ClinicalTrials.gov NCT01933477.

Poor glycaemic control and its metabolic and demographic risk factors in a Malaysian community-based study

OBJECTIVES

The lack of population-based evidence on the risk factors for poor glycaemic control in diabetics, particularly in resource-poor settings, is a challenge for the prevention of long-term complications. This study aimed to identify the metabolic and demographic risk factors for poor glycaemic control among diabetics in a rural community in Malaysia.

METHODS

A total of 1844 (780 males and 1064 females) known diabetics aged ≥ 35 years were identified from the South East Asia Community Observatory (SEACO) health and demographic surveillance site database.

RESULTS

41.3% of the sample had poor glycaemic control. Poor glycaemic control was associated with age and ethnicity, with older participants (65+) better controlled than younger adults (45-54), and Malaysian Indians most poorly controlled, followed by Malay and then Chinese participants. Metabolic risk factors were also highly associated with poor glycaemic control.

CONCLUSIONS

There is a critical need for evidence for a better understanding of the mechanisms of the associations between risk factors and glycaemic control.

Interaction between childhood maltreatment on immunogenetic risk in depression: Discovery and replication in clinical case-control samples

Major depressive disorder (MDD) is a prevalent disorder with moderate heritability. Both MDD and interpersonal adversity, including childhood maltreatment, have been consistently associated with elevated inflammatory markers. We investigated interaction between exposure to childhood maltreatment and extensive genetic variation within the inflammation pathway (CRP, IL1b, IL-6, IL11, TNF, TNFR1, and TNFR2) in relation to depression diagnosis. The discovery RADIANT sample included 262 cases with recurrent DSM-IV/ICD-10 MDD, and 288 unaffected controls. The replication Münster cohort included 277 cases with DSM-IV MDD, and 316 unaffected controls. We identified twenty-five single nucleotide polymorphisms (SNPs) following multiple testing correction that interacted with childhood maltreatment to predict depression in the discovery cohort. Seven SNPs representing independent signals (rs1818879, rs1041981, rs4149576, rs616645, rs17882988, rs1061622, and rs3093077) were taken forward for replication. Meta-analyses of the two samples presented evidence for interaction with rs1818879 (IL6) (RD=0.059, SE=0.016, p<0.001), with the replication Münster sample approaching statistical significance in analyses restricted to recurrent MDD and controls following correction for multiple testing (q=0.066). The CRP locus (rs3093077) showed a similar level of evidence for interaction in the meta-analysis (RD=0.092, SE=0.029, p=0.002), but less compelling evidence in the replication sample alone (recurrent MDD q=0.198; all MDD q=0.126). Here we present evidence suggestive of interaction with childhood maltreatment for novel loci in IL-6 (rs1818879) and CRP (rs3093077), increasing risk of depression. Replication is needed by independent groups, targeting these specific variants and interaction with childhood maltreatment on depression risk.

A general framework for constraint approaches to adjusted risk differences

The risk difference is an intelligible measure for comparing disease incidence in two exposure or treatment groups. Despite its convenience in interpretation, it is less prevalent in epidemiological and clinical areas where regression models are required in order to adjust for confounding. One major barrier to its popularity is that standard linear binomial or Poisson regression models can provide estimated probabilities out of the range of (0,1), resulting in possible convergence issues. For estimating adjusted risk differences, we propose a general framework covering various constraint approaches based on binomial and Poisson regression models. The proposed methods span the areas of ordinary least squares, maximum likelihood estimation, and Bayesian inference. Compared to existing approaches, our methods prevent estimates and confidence intervals of predicted probabilities from falling out of the valid range. Through extensive simulation studies, we demonstrate that the proposed methods solve the issue of having estimates or confidence limits of predicted probabilities out of (0,1), while offering performance comparable to its alternative in terms of the bias, variability, and coverage rates in point and interval estimation of the risk difference. An application study is performed using data from the Prospective Registry Evaluating Myocardial Infarction: Event and Recovery (PREMIER) study.

Do sex hormones or hormone therapy modify the relation of n-3 fatty acids with incident depressive symptoms in postmenopausal women? The MESA Study

INTRODUCTION

Considering that estradiol (E2) and n-3 polyunsaturated fatty acids (PUFAs) have roles in neurogenesis and in neurotransmission, we examined whether the association of PUFAs with incident depressive symptoms in postmenopausal women is modified by hormone therapy (HT) use or estrogen status.

METHODS

Women (N=1616) free of depressive symptoms at baseline (2000-2002) in the Multi-Ethnic Study of Atherosclerosis were classified by HT usage and quartiles of dietary eicosapentaenoic acid (EPA), docosahexaenoic acid (DHA), and the sum EPA+DHA. Women with serum E2 ≤0.073 nmol/L (sample median), were classified low on E2. Poisson regression was used to model incident depressive symptoms at examination 3 (2004-05), defined by the Center for Epidemiological Studies Depression Scale ≥16 or taking an antidepressant, first as a function of HT use and n-3 PUFA quartiles, and second, as a function of low E2 status and n-3 PUFA quartiles.

RESULTS

Among HT non- users, positive, graded relationships (p-trends≤0.003) were found between PUFAs and incident depressive symptoms. Compared to the lowest quartile, the adjusted risk ratios (RRs) for the highest were 2.10, 2.39, and 2.04 for EPA, DHA, and EPA+DHA, respectively. For HT users, no associations were seen. When analyses were run for E2 status, the RRs over quartiles of the PUFAs were positive and graded for low E2 women, but were null for High E2 women.

CONCLUSIONS

Higher intakes of DHA and EPA were associated with higher risk of depressive symptoms in nonusers of HT, contrary to hypothesis.

Flexible regression models for rate differences, risk differences and relative risks

Generalized additive models (GAMs) based on the binomial and Poisson distributions can be used to provide flexible semi-parametric modelling of binary and count outcomes. When used with the canonical link function, these GAMs provide semi-parametrically adjusted odds ratios and rate ratios. For adjustment of other effect measures, including rate differences, risk differences and relative risks, non-canonical link functions must be used together with a constrained parameter space. However, the algorithms used to fit these models typically rely on a form of the iteratively reweighted least squares algorithm, which can be numerically unstable when a constrained non-canonical model is used. We describe an application of a combinatorial EM algorithm to fit identity link Poisson, identity link binomial and log link binomial GAMs in order to estimate semi-parametrically adjusted rate differences, risk differences and relative risks. Using smooth regression functions based on B-splines, the method provides stable convergence to the maximum likelihood estimates, and it ensures that the estimates always remain within the parameter space. It is also straightforward to apply a monotonicity constraint to the smooth regression functions. We illustrate the method using data from a clinical trial in heart attack patients.

Invited commentary: How big is that interaction (in my community)--and in which direction?

In an accompanying article, Turner et al. (Am J Epidemiol. 2014;180(12):1145-1149) compare the joint effects of smoking and air pollution to make inferences about the reduction in lung cancer mortality achieved when reducing each exposure separately and when reducing both together. In this commentary, we use first principles to quantify the difference between the risk or mortality reduction obtained from reducing each of 2 exposures together and the sum of the risk differences obtained from reducing the 2 exposures separately. Metrics of the impact of joint effects or comparisons of joint effects presented in units of absolute risk, such as Rothman's I, can provide more meaningful quantitative measures of public health impact than unitless metrics (e.g., ratios) and standardized metrics (e.g., the population attributable fraction) of potential interventions for reducing smoking and air pollution exposure. In particular, the venerable attributable community risk metric can provide an estimate of the community impact of such interventions in units of absolute risk. A spreadsheet we provide demonstrates the calculation of the various metrics for hypothetical data similar to those reported by Turner et al. Using algebra, graphics, and examples, we show that positive interaction, or synergy, on the additive scale implies that the impact on risk reduction from a program that applies both interventions will be lesser than the sum of the impacts of the separate interventions.

Time to smoke first morning cigarette and lung cancer in a case-control study

BACKGROUND

Targeting smokers at higher lung cancer risk can improve efficiency and reduce false-positive detection in lung cancer screening. We evaluated whether time to first cigarette after waking (TTFC), a single-item measure of nicotine dependency, could improve stratification of lung cancer risk beyond standard smoking metrics (intensity, duration, and pack-years).

METHODS

In 3249 ever-smokers (n = 1812 case subjects; n = 1437 control subjects) from a population-based case-control study in Italy, we examined the association between TTFC and lung cancer using logistic regression and estimated lung cancer incidence by levels of TTFC, and intensity, duration, and pack-years using absolute risk regression. Significance tests were two-sided.

RESULTS

Compared with smokers with TTFC greater than 60 minutes, the lung cancer odds ratios for TTFC of 31 to 60 minutes, 6 to 30 minutes, and 5 or fewer minutes (by increasing dependency) were 2.57 (95% confidence interval [CI] = 2.03 to 3.26), 2.27 (95% CI = 1.79 to 2.88), and 3.50 (95% CI = 2.64 to 4.64), respectively (P trend < .0001). The average lung cancer incidence rates for smokers of 1 to 10, 11 to 20, 21 to 30 and more than 30 cigarettes per day were consistently higher among smokers with TTFC of 60 or fewer minutes vs more than 60 minutes (64.1 vs 11.7; 125.6 vs 28.6; 130.1 vs 40.7; and 260.8 vs 108.9 per 100000 person-years, respectively). The slopes of increase in lung cancer rates with smoking duration and pack-years were statistically significantly greater among smokers with higher dependency (P interaction < .001).

CONCLUSIONS

Lung cancer risk increases with shorter TTFC; this simple nicotine dependency measure increases lung cancer risk stratification beyond standard smoking measures. Assessing TTFC may improve lung cancer risk prediction and could be useful in lung cancer screening and smoking cessation programs.

Almost efficient estimation of relative risk regression

Relative risks (RRs) are often considered the preferred measures of association in prospective studies, especially when the binary outcome of interest is common. In particular, many researchers regard RRs to be more intuitively interpretable than odds ratios. Although RR regression is a special case of generalized linear models, specifically with a log link function for the binomial (or Bernoulli) outcome, the resulting log-binomial regression does not respect the natural parameter constraints. Because log-binomial regression does not ensure that predicted probabilities are mapped to the [0,1] range, maximum likelihood (ML) estimation is often subject to numerical instability that leads to convergence problems. To circumvent these problems, a number of alternative approaches for estimating RR regression parameters have been proposed. One approach that has been widely studied is the use of Poisson regression estimating equations. The estimating equations for Poisson regression yield consistent, albeit inefficient, estimators of the RR regression parameters. We consider the relative efficiency of the Poisson regression estimator and develop an alternative, almost efficient estimator for the RR regression parameters. The proposed method uses near-optimal weights based on a Maclaurin series (Taylor series expanded around zero) approximation to the true Bernoulli or binomial weight function. This yields an almost efficient estimator while avoiding convergence problems. We examine the asymptotic relative efficiency of the proposed estimator for an increase in the number of terms in the series. Using simulations, we demonstrate the potential for convergence problems with standard ML estimation of the log-binomial regression model and illustrate how this is overcome using the proposed estimator. We apply the proposed estimator to a study of predictors of pre-operative use of beta blockers among patients undergoing colorectal surgery after diagnosis of colon cancer.

A regression model for risk difference estimation in population-based case-control studies clarifies gender differences in lung cancer risk of smokers and never smokers

BACKGROUND

Additive risk models are necessary for understanding the joint effects of exposures on individual and population disease risk. Yet technical challenges have limited the consideration of additive risk models in case-control studies.

METHODS

Using a flexible risk regression model that allows additive and multiplicative components to estimate absolute risks and risk differences, we report a new analysis of data from the population-based case-control Environment And Genetics in Lung cancer Etiology study, conducted in Northern Italy between 2002-2005. The analysis provides estimates of the gender-specific absolute risk (cumulative risk) for non-smoking- and smoking-associated lung cancer, adjusted for demographic, occupational, and smoking history variables.

RESULTS

In the multiple-variable lexpit regression, the adjusted 3-year absolute risk of lung cancer in never smokers was 4.6 per 100,000 persons higher in women than men. However, the absolute increase in 3-year risk of lung cancer for every 10 additional pack-years smoked was less for women than men, 13.6 versus 52.9 per 100,000 persons.

CONCLUSIONS

In a Northern Italian population, the absolute risk of lung cancer among never smokers is higher in women than men but among smokers is lower in women than men. Lexpit regression is a novel approach to additive-multiplicative risk modeling that can contribute to clearer interpretation of population-based case-control studies.