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1.  Estimation of the Standardized Risk Difference and Ratio in a Competing Risks Framework: Application to Injection Drug Use and Progression to AIDS After Initiation of Antiretroviral Therapy 
American Journal of Epidemiology  2014;181(4):238-245.
There are few published examples of absolute risk estimated from epidemiologic data subject to censoring and competing risks with adjustment for multiple confounders. We present an example estimating the effect of injection drug use on 6-year risk of acquired immunodeficiency syndrome (AIDS) after initiation of combination antiretroviral therapy between 1998 and 2012 in an 8-site US cohort study with death before AIDS as a competing risk. We estimate the risk standardized to the total study sample by combining inverse probability weights with the cumulative incidence function; estimates of precision are obtained by bootstrap. In 7,182 patients (83% male, 33% African American, median age of 38 years), we observed 6-year standardized AIDS risks of 16.75% among 1,143 injection drug users and 12.08% among 6,039 nonusers, yielding a standardized risk difference of 4.68 (95% confidence interval: 1.27, 8.08) and a standardized risk ratio of 1.39 (95% confidence interval: 1.12, 1.72). Results may be sensitive to the assumptions of exposure-version irrelevance, no measurement bias, and no unmeasured confounding. These limitations suggest that results be replicated with refined measurements of injection drug use. Nevertheless, estimating the standardized risk difference and ratio is straightforward, and injection drug use appears to increase the risk of AIDS.
PMCID: PMC4325676  PMID: 24966220
AIDS; cohort study; competing risks; HIV; survival function
2.  Risk 
American Journal of Epidemiology  2015;181(4):246-250.
The epidemiologist primarily studies transitions between states of health and disease. The purpose of the present article is to define a foundational parameter for such studies, namely risk. We begin simply and build to the setting in which there is more than 1 event type (i.e., competing risks or competing events), as well as more than 1 treatment or exposure level of interest. In the presence of competing events, the risks are a set of counterfactual cumulative incidence functions for each treatment. These risks can be depicted visually and summarized numerically. We use an example from the study of human immunodeficiency virus to illustrate concepts.
PMCID: PMC4325680  PMID: 25660080
causal inference; cohort study; semi-Bayes method; semiparametric inference; survival analysis
3.  Meta-analysis of randomized trials on the association of prophylactic acyclovir and HIV-1 viral load in individuals coinfected with herpes simplex virus-2 
AIDS (London, England)  2011;25(10):1265-1269.
To summarize the randomized evidence regarding the association between acyclovir use and HIV-1 replication as measured by plasma HIV-1 RNA viral load among individuals coinfected with herpes simplex virus (HSV)-2.
Meta-analysis of seven randomized trials conducted between 2000 and 2009. Inclusion criteria composed of acyclovir or valacyclovir use as prophylaxis among individuals coinfected with HIV-1 and HSV-2 who were ineligible for highly active antiretroviral therapy. HIV-1 viral load was the outcome.
Random-effects summarization was used to combine treatment effect estimates. Stratified and meta-regression analyses were used to compare estimated treatment effects by characteristics of trials and participants.
The summary treatment effect estimate was −0.33 (95% confidence interval: −0.56, −0.10, 95% population effects interval: −0.74, 0.08) log10 copies, an approximate halving of plasma viral load. However, there was marked heterogeneity (P < 0.001). Older median age, valacyclovir, higher compliance, earlier publication, and shorter study length were associated with a larger decrease in viral load as compared with their counterparts.
Current evidence suggests a range of favorable effects of acyclovir on plasma HIV-1 viral load among persons coinfected with HSV-2.
PMCID: PMC4501265  PMID: 21666542
acyclovir; herpes simplex virus; HIV; meta-analysis
4.  Illustration of a measure to combine viral suppression and viral rebound in studies of HIV therapy 
Viral load is an important tool for assessing antiretroviral treatment efficacy. However, the most common viral load endpoint, virologic failure, may be flawed. We illustrate an alternative endpoint that estimates the average time patients spent suppressed prior to rebound in the AIDS Clinical Trials Group A5095 trial. Patients averaged 644 days suppressed in the 3-drug arm and 686 days suppressed in the 4-drug arm, for a difference of 42 days in favor of the 4-drug regimen (95% CI: −11, 96). These results agree with results using virologic failure as the endpoint but better emphasize the separate suppression and rebound processes.
PMCID: PMC4294958  PMID: 25415292
5.  Association Between Unprotected Ultraviolet Radiation Exposure and Recurrence of Ocular Herpes Simplex Virus 
American Journal of Epidemiology  2013;179(2):208-215.
Studies have suggested that exposure to ultraviolet (UV) light may increase risk of herpes simplex virus (HSV) recurrence. Between 1993 and 1997, the Herpetic Eye Disease Study (HEDS) randomized 703 participants with ocular HSV to receipt of acyclovir or placebo for prevention of ocular HSV recurrence. Of these, 308 HEDS participants (48% female and 85% white; median age, 49 years) were included in a nested study of exposures thought to cause recurrence and were followed for up to 15 months. We matched weekly UV index values from the National Oceanic and Atmospheric Administration to each participant's study center and used marginal structural Cox models to account for time-varying psychological stress and contact lens use and selection bias from dropout. There were 44 recurrences of ocular HSV, yielding an incidence of 4.3 events per 1,000 person-weeks. Weighted hazard ratios comparing persons with ≥8 hours of time outdoors to those with less exposure were 0.84 (95% confidence interval (CI): 0.27, 2.63) and 3.10 (95% CI: 1.14, 8.48) for weeks with a UV index of <4 and ≥4, respectively (ratio of hazard ratios = 3.68, 95% CI: 0.43, 31.4). Though results were imprecise, when the UV index was higher (i.e., ≥4), spending 8 or more hours per week outdoors was associated with increased risk of ocular HSV recurrence.
PMCID: PMC3873108  PMID: 24142918
cohort studies; herpes simplex virus; recurrence; sunlight; ultraviolet light; UV index
6.  Maximum Likelihood, Profile Likelihood, and Penalized Likelihood: A Primer 
American Journal of Epidemiology  2013;179(2):252-260.
The method of maximum likelihood is widely used in epidemiology, yet many epidemiologists receive little or no education in the conceptual underpinnings of the approach. Here we provide a primer on maximum likelihood and some important extensions which have proven useful in epidemiologic research, and which reveal connections between maximum likelihood and Bayesian methods. For a given data set and probability model, maximum likelihood finds values of the model parameters that give the observed data the highest probability. As with all inferential statistical methods, maximum likelihood is based on an assumed model and cannot account for bias sources that are not controlled by the model or the study design. Maximum likelihood is nonetheless popular, because it is computationally straightforward and intuitive and because maximum likelihood estimators have desirable large-sample properties in the (largely fictitious) case in which the model has been correctly specified. Here, we work through an example to illustrate the mechanics of maximum likelihood estimation and indicate how improvements can be made easily with commercial software. We then describe recent extensions and generalizations which are better suited to observational health research and which should arguably replace standard maximum likelihood as the default method.
PMCID: PMC3873110  PMID: 24173548
epidemiologic methods; maximum likelihood; modeling; penalized estimation; regression; statistics
7.  Sociodemographic disparities in survival from colorectal cancer in South Australia: a population-wide data linkage study 
Inequalities in survival from colorectal cancer (CRC) across socioeconomic groups and by area of residence have been described in various health care settings. Few population-wide datasets which include clinical and treatment information are available in Australia to investigate disparities. This study examines socio-demographic differences in survival for CRC patients in South Australia (SA), using a population-wide database derived via linkage of administrative and surveillance datasets.
The study population comprised all cases of CRC diagnosed in 2003-2008 among SA residents aged 50-79 yrs in the SA Central Cancer Registry. Measures of socioeconomic status (area level), geographical remoteness, clinical characteristics, comorbid conditions, treatments and outcomes were derived through record linkage of central cancer registry, hospital-based clinical registries, hospital separations, and radiotherapy services data sources. Socio-demographic disparities in CRC survival were examined using competing risk regression analysis.
Four thousand six hundred and forty one eligible cases were followed for an average of 4.7 yrs, during which time 1525 died from CRC and 416 died from other causes. Results of competing risk regression indicated higher risk of CRC death with higher grade (HR high v low =2.25, 95 % CI 1.32-3.84), later stage (HR C v A = 7.74, 95 % CI 5.75-10.4), severe comorbidity (HR severe v none =1.21, 95 % CI 1.02-1.44) and receiving radiotherapy (HR = 1.41, 95 % CI 1.18-1.68). Patients from the most socioeconomically advantaged areas had significantly better outcomes than those from the least advantaged areas (HR =0.75, 95 % 0.62-0.91). Patients residing in remote locations had significantly worse outcomes than metropolitan residents, though this was only evident for stages A-C (HR = 1.35, 95 % CI 1.01-1.80). These disparities were not explained by differences in stage at diagnosis between socioeconomic groups or area of residence. Nor were they explained by differences in patient factors, other tumour characteristics, comorbidity, or treatment modalities.
Socio-economic and regional disparities in survival following CRC are evident in SA, despite having a universal health care system. Of particular concern is the poorer survival for patients from remote areas with potentially curable CRC. Reasons for these disparities require further exploration to identify factors that can be addressed to improve outcomes.
PMCID: PMC4721049  PMID: 26792195
Colorectal cancer; Socio-demographic inequalities; Stage; Survival
8.  A Blood Test for Methylated BCAT1 and IKZF1 vs. a Fecal Immunochemical Test for Detection of Colorectal Neoplasia 
To compare the performance of a new blood test for colorectal cancer (CRC) to an established fecal immunochemical test (FIT) in a study population with the full range of neoplastic and non-neoplastic pathologies encountered in the colon and rectum.
Volunteers were asked to complete a FIT prior to colonoscopy. Blood was collected after bowel preparation but prior to colonoscopy, and plasma was assayed for the presence of methylated BCAT1 and IKZF1 DNA using a multiplex real-time PCR assay. Sensitivity and specificity estimates for the blood test were calculated from true- and false-positive rates for neoplasia and compared with FIT at a range of fecal hemoglobin (Hb) concentration positivity thresholds.
In total, 1,381 volunteers (median age 64 years; 49% male) completed both tests prior to colonoscopy. Estimated sensitivity of the BCAT1/IKZF1 blood test for CRC was 62% (41/66; 95% confidence interval 49–74%) with a specificity of 92% (1207/1315; 90–93%). FIT returned the same specificity at a cutoff of 60 μg Hb/g, at which its corresponding sensitivity for cancer was 64% (42/66; 51–75%). In the range of commonly used FIT cutoffs, respective cancer sensitivity and specificity estimates with FIT were: 59% (46–71%) and 93% (92–95%) at 80 μg Hb/g, and 79% (67–88%) and 81% (78–83%) at 10 μg Hb/g. Although estimated sensitivities were not significantly different between the two tests for any stage of cancer, FIT showed a significantly higher sensitivity for advanced adenoma at the lower cutoffs. Specificity of FIT, but not of the BCAT1/IKZF1 blood test, deteriorated substantially in people with overt blood in the feces. When combining FIT (cutoff 10 μg Hb/g) with the BCAT1/IKZF1 blood test, sensitivity for cancer was 89% (79–96%) at 74% (72–77%) specificity.
A test based on detection of methylated BCAT1/IKZF1 DNA in blood has comparable sensitivity but better specificity for CRC than FIT at the commonly used positivity threshold of 10 μg Hb/g. Further evaluation of the new test relative to FIT in the population screening context is now required to fully understand the potential advantages and disadvantages of these biomarkers in screening.
PMCID: PMC4737873  PMID: 26765125
9.  A prospective study of alcohol consumption and HIV acquisition among injection drug users 
AIDS (London, England)  2011;25(2):221-228.
Estimate the effect of alcohol consumption on HIV acquisition while appropriately accounting for confounding by time-varying risk factors.
African American injection drug users in the AIDS Link to Intravenous Experience cohort study. Participants were recruited and followed with semiannual visits in Baltimore, Maryland between 1988 and 2008.
Marginal structural models were used to estimate the effect of alcohol consumption on HIV acquisition.
At entry, 28% of 1,525 participants were female with a median (quartiles) age of 37 (32; 42) years and 10 (10; 12) years of formal education. During follow up, 155 participants acquired HIV and alcohol consumption was 24%, 24%, 26%, 17%, and 9% for 0, 1–5, 6–20, 21–50 and 51–140 drinks/week over the prior two years, respectively. In analyses accounting for socio-demographic factors, drug use, and sexual activity, hazard ratios for participants reporting 1–5, 6–20, 21–50, and 51–140 drinks/week in the prior two years compared to participants who reported 0 drinks/week were 1.09 (0.60, 1.98), 1.18 (0.66, 2.09), 1.66 (0.94, 2.93) and 2.12 (1.15, 3.90), respectively. A trend test indicated a dose-response relationship between alcohol consumption and HIV acquisition (P value for trend = 9.7×10−4).
A dose-response relationship between alcohol consumption and subsequent HIV acquisition is indicated, independent of measured known risk factors.
PMCID: PMC3006640  PMID: 21099668
Alcohol consumption; HIV infection; Bias; Cohort studies; Injection drug users
10.  Worth the Weight: Using Inverse Probability Weighted Cox Models in AIDS Research 
AIDS Research and Human Retroviruses  2014;30(12):1170-1177.
In an observational study with a time-to-event outcome, the standard analytical approach is the Cox proportional hazards regression model. As an alternative to the standard Cox model, in this article we present a method that uses inverse probability (IP) weights to estimate the effect of a baseline exposure on a time-to-event outcome. IP weighting can be used to adjust for multiple measured confounders of a baseline exposure in order to estimate marginal effects, which compare the distribution of outcomes when the entire population is exposed versus when the entire population is unexposed. For example, IP-weighted Cox models allow for estimation of the marginal hazard ratio and marginal survival curves. IP weights can also be employed to adjust for selection bias due to loss to follow-up. This approach is illustrated using an example that estimates the effect of injection drug use on time until AIDS or death among HIV-infected women.
PMCID: PMC4250953  PMID: 25183195
11.  A Hybrid Bayesian Hierarchical Model Combining Cohort and Case-control Studies for Meta-analysis of Diagnostic Tests: Accounting for Partial Verification Bias 
To account for between-study heterogeneity in meta-analysis of diagnostic accuracy studies, bivariate random effects models have been recommended to jointly model the sensitivities and specificities. As study design and population vary, the definition of disease status or severity could differ across studies. Consequently, sensitivity and specificity may be correlated with disease prevalence. To account for this dependence, a trivariate random effects model had been proposed. However, the proposed approach can only include cohort studies with information estimating study-specific disease prevalence. In addition, some diagnostic accuracy studies only select a subset of samples to be verified by the reference test. It is known that ignoring unverified subjects may lead to partial verification bias in the estimation of prevalence, sensitivities and specificities in a single study. However, the impact of this bias on a meta-analysis has not been investigated. In this paper, we propose a novel hybrid Bayesian hierarchical model combining cohort and case-control studies and correcting partial verification bias at the same time. We investigate the performance of the proposed methods through a set of simulation studies. Two case studies on assessing the diagnostic accuracy of gadolinium-enhanced magnetic resonance imaging in detecting lymph node metastases and of adrenal fluorine-18 fluorodeoxyglucose positron emission tomography in characterizing adrenal masses are presented.
PMCID: PMC4245380  PMID: 24862512
Bayesian method; cohort and case-control studies; diagnostic test; partial verification bias; meta-analysis
12.  Joint Modeling of Longitudinal and Survival Data with Missing and Left-Censored Time-Varying Covariates 
Statistics in medicine  2014;33(26):4560-4576.
We propose a joint model for longitudinal and survival data with time-varying covariates subject to detection limits and intermittent missingness at random (MAR). The model is motivated by data from the Multicenter AIDS Cohort Study (MACS), in which HIV+ subjects have viral load and CD4 cell count measured at repeated visits along with survival data. We model the longitudinal component using a normal linear mixed model, modeling the trajectory of CD4 cell count by regressing on viral load and other covariates. The viral load data are subject to both left-censoring due to detection limits (17%) and intermittent missingness (27%). The survival component of the joint model is a Cox model with time-dependent covariates for death due to AIDS. The longitudinal and survival models are linked using the trajectory function of the linear mixed model. A Bayesian analysis is conducted on the MACS data using the proposed joint model. The proposed method is shown to improve the precision of estimates when compared to alternative methods.
PMCID: PMC4189992  PMID: 24947785
Detection Limit; Joint Modeling; Missing Data; Multicenter AIDS Cohort Study
13.  Beyond Core Indicators of Retention in HIV Care: Missed Clinic Visits Are Independently Associated With All-Cause Mortality 
Missed HIV care visits have independent prognostic value for clinical events beyond core indicators of retention in care. As this information is readily available and immediately actionable, missed HIV care visits should be incorporated into clinical, programmatic, and policy initiatives.
Background. The continuum of care is at the forefront of the domestic human immunodeficiency virus (HIV) agenda, with the Institute of Medicine (IOM) and Department of Health and Human Services (DHHS) recently releasing clinical core indicators. Core indicators for retention in care are calculated based on attended HIV care clinic visits. Beyond these retention core indicators, we evaluated the additional prognostic value of missed clinic visits for all-cause mortality.
Methods. We conducted a multisite cohort study of 3672 antiretroviral-naive patients initiating antiretroviral therapy (ART) during 2000–2010. Retention in care was measured by the IOM and DHHS core indicators (2 attended visits at defined intervals per 12-month period), and also as a count of missed primary HIV care visits (no show) during a 24-month measurement period following ART initiation. All-cause mortality was ascertained by query of the Social Security Death Index and/or National Death Index, with adjusted survival analyses starting at 24 months after ART initiation.
Results. Among participants, 64% and 59% met the IOM and DHHS retention core indicators, respectively, at 24 months. Subsequently, 332 patients died during 16 102 person-years of follow-up. Failure to achieve the IOM and DHHS indicators through 24 months following ART initiation increased mortality (hazard ratio [HR] = 2.23; 95% confidence interval [CI], 1.79–2.80 and HR = 2.36; 95% CI, 1.89–2.96, respectively). Among patients classified as retained by the IOM or DHHS clinical core indicators, >2 missed visits further increased mortality risk (HR = 3.61; 95% CI, 2.35–5.55 and HR = 3.62; 95% CI, 2.30–5.68, respectively).
Conclusions. Beyond HIV retention core indicators, missed clinic visits were independently associated with all-cause mortality. Caution is warranted in relying solely upon retention in care core indicators for policy, clinical, and programmatic purposes.
PMCID: PMC4215067  PMID: 25091306
HIV; AIDS; antiretroviral therapy; engagement in care; continuum of care
14.  Assessment and Indirect Adjustment for Confounding by Smoking in Cohort Studies Using Relative Hazards Models 
American Journal of Epidemiology  2014;180(9):933-940.
Workers' smoking histories are not measured in many occupational cohort studies. Here we discuss the use of negative control outcomes to detect and adjust for confounding in analyses that lack information on smoking. We clarify the assumptions necessary to detect confounding by smoking and the additional assumptions necessary to indirectly adjust for such bias. We illustrate these methods using data from 2 studies of radiation and lung cancer: the Colorado Plateau cohort study (1950–2005) of underground uranium miners (in which smoking was measured) and a French cohort study (1950–2004) of nuclear industry workers (in which smoking was unmeasured). A cause-specific relative hazards model is proposed for estimation of indirectly adjusted associations. Among the miners, the proposed method suggests no confounding by smoking of the association between radon and lung cancer—a conclusion supported by adjustment for measured smoking. Among the nuclear workers, the proposed method suggests substantial confounding by smoking of the association between radiation and lung cancer. Indirect adjustment for confounding by smoking resulted in an 18% decrease in the adjusted estimated hazard ratio, yet this cannot be verified because smoking was unmeasured. Assumptions underlying this method are described, and a cause-specific proportional hazards model that allows easy implementation using standard software is presented.
PMCID: PMC4375397  PMID: 25245043
cohort studies; lung cancer; smoking
15.  Occupational radon exposure and lung cancer mortality: estimating intervention effects using the parametric G formula 
Epidemiology (Cambridge, Mass.)  2014;25(6):829-834.
Traditional regression analysis techniques used to estimate associations between occupational radon exposure and lung cancer focus on estimating the effect of cumulative radon exposure on lung cancer, while public health interventions are typically based on regulating radon concentration rather than workers’ cumulative exposure. Moreover, estimating the direct effect of cumulative occupational exposure on lung cancer may be difficult in situations vulnerable to the healthy worker survivor bias.
Workers in the Colorado Plateau Uranium Miners cohort (N=4,134) entered the study between 1950 and 1964 and were followed for lung cancer mortality through 2005. We use the parametric g-formula to compare the observed lung cancer mortality to the potential lung cancer mortality had each of 3 policies to limit monthly radon exposure been in place throughout follow-up.
There were 617 lung cancer deaths over 135,275 person-years of follow-up. With no intervention on radon exposure, estimated lung cancer mortality by age 90 was 16%. Lung cancer mortality was reduced for all interventions considered, and larger reductions in lung cancer mortality were seen for interventions with lower monthly radon exposure limits. The most stringent guideline, the Mine Safety and Health Administration standard of 0.33 working level months, reduced lung cancer mortality from 16% to 10% (risk ratio 0.67; 95% confidence interval 0.61, 0.73).
This work illustrates the utility of the parametric g-formula for estimating the effects of policies regarding occupational exposures, particularly in situations vulnerable to the healthy worker survivor bias.
PMCID: PMC4524349  PMID: 25192403
radon; lung neoplasms; occupational health; healthy worker effect; epidemiologic methods
16.  Temporal changes in the outcomes of HIV-exposed infants in Kinshasa, Democratic Republic of Congo during a period of rapidly evolving guidelines for care (2007–2013) 
AIDS (London, England)  2014;28(0 3):S301-S311.
Guidelines for prevention of mother-to-child transmission of HIV have developed rapidly, yet little is known about how outcomes of HIV-exposed infants have changed over time. We describe HIV-exposed infant outcomes in Kinshasa, Democratic Republic of Congo, between 2007 and 2013.
Cohort study of mother–infant pairs enrolled in family-centered comprehensive HIV care.
Accounting for competing risks, we estimated the cumulative incidences of early infant diagnosis, HIV transmission, death, loss to follow-up, and combination antiretroviral therapy (cART) initiation for infants enrolled in three periods (2007–2008, 2009–2010, and 2011–2012).
1707 HIV-exposed infants enrolled at a median age of 2.6 weeks. Among infants whose mothers had recently enrolled into HIV care (N = 1411), access to EID by age two months increased from 28% (95% confidence limits [CL]: 24,34%) among infants enrolled in 2007-2008 to 63% (95% CL: 59,68%) among infants enrolled in 2011–2012 (Gray's p-value <0.01). The 18-month cumulative incidence of HIV declined from 16% (95% CL: 11,22%) for infants enrolled in 2007–2008 to 11% (95% CL: 8,16%) for infants enrolled in 2011–2012 (Gray's p-value = 0.19). The 18-month cumulative incidence of death also declined, from 8% (95% CL: 5,12%) to 3% (95% CL: 2,5%) (Gray's p-value = 0.02). LTFU did not improve, with 18-month cumulative incidences of 19% (95% CL: 15,23%) for infants enrolled in 2007-2008 and 22% (95% CL: 18,26%) for infants enrolled in 2011–2012 (Gray's p-value = 0.06). Among HIV-infected infants, the 24-month cumulative incidence of cART increased from 61% (95% CL: 43,75%) to 97% (95% CL: 82,100%) (Gray's p-value < 0.01); the median age at cART decreased from 17.9 to 9.3 months. Outcomes were better for infants whose mothers enrolled before pregnancy.
We observed encouraging improvements, but continued efforts are needed.
PMCID: PMC4600322  PMID: 24991903
Democratic Republic of Congo; HIV-exposed infant; mother-infant pair; pediatric HIV; prevention of mother-to-child HIV transmission/vertical transmission
17.  Sodium Intake and Incident Hypertension among Chinese Adults: Estimated Effects Across Three Different Exposure Periods 
Epidemiology (Cambridge, Mass.)  2013;24(3):410-418.
Although it is clear that there are short-term effects of sodium intake on blood pressure, little is known about the most relevant timing of sodium exposure for the onset of hypertension. This question can only be addressed in cohorts with repeated measures of sodium intake.
Using up to 7 measures of dietary sodium intake and blood pressure between 1991 and 2009, we compared baseline, the mean of all measures, and the most recent sodium intake in association with incident hypertension, in 6578 adults enrolled in the China Health and Nutrition Survey aged 18 to 65 free of hypertension at baseline. We used survival methods that account for the interval-censored nature of this study, and inverse probability weights to generate adjusted survival curves and time-specific cumulative risk differences; hazard ratios were also estimated.
For mean and most recent measures, the probability of hypertension-free survival was the lowest among those in the highest intake sodium group compared to all other intake groups across the entire follow-up. In addition, the most recent sodium intake measure had a positive dose-response association with incident hypertension [Risk Difference at 11 years of follow-up = 0.04 (95%CI −0.01, 0.09), 0.06 (0.00, 0.13), 0.18 (0.12, 0.24) and 0.20 (0.12, 0.27) for the second to fifth sodium intake groups compared to the lowest group respectively]. Baseline sodium intake was not associated with incident hypertension.
These results suggest caution when using baseline sodium intake measures with long-term follow up.
PMCID: PMC3909658  PMID: 23466527
China; sodium intake; incident hypertension; interval-censored; adjusted survival curves
19.  Joint effects of alcohol consumption and high-risk sexual behavior on HIV seroconversion among men who have sex with men 
AIDS (London, England)  2013;27(5):815-823.
PMCID: PMC3746520  PMID: 23719351
Alcohol Drinking; HIV Seropositivity; Men who Have Sex with Men; Prospective Studies; Sexual Behavior
20.  Lymphoma Immune Reconstitution Inflammatory Syndrome in the Center for AIDS Research Network of Integrated Clinical Systems Cohort 
In a multicenter cohort, unmasking immune reconstitution inflammatory syndrome (IRIS) was observed in 12% of HIV-associated lymphomas. Presentation and survival for lymphoma IRIS were similar to non-IRIS, with possibly increased early mortality among IRIS cases.
Background. Lymphoma incidence is increased among human immunodeficiency virus (HIV)–infected individuals soon after antiretroviral therapy (ART), perhaps due to unmasking immune reconstitution inflammatory syndrome (IRIS). Clinical characteristics and survival for unmasking lymphoma IRIS have not been described.
Methods. We studied lymphoma patients in the Centers for AIDS Research Network of Integrated Clinical Systems (CNICS) from 1996 until 2011. Unmasking lymphoma IRIS was defined as lymphoma within 6 months after ART accompanied by a ≥0.5 log10 copies/mL HIV RNA reduction. Differences in presentation and survival were examined between IRIS and non-IRIS cases.
Results. Of 482 lymphoma patients, 56 (12%) met criteria for unmasking lymphoma IRIS. Of these, 12 (21%) had Hodgkin lymphoma, 22 (39%) diffuse large B-cell lymphoma, 5 (9%) Burkitt lymphoma, 10 (18%) primary central nervous system lymphoma, and 7 (13%) other non-Hodgkin lymphoma. Median CD4 cell count at lymphoma diagnosis among IRIS cases was 173 cells/µL (interquartile range, 73–302), and 48% had suppressed HIV RNA <400 copies/mL. IRIS cases were similar overall to non-IRIS cases in histologic distribution and clinical characteristics, excepting more frequent hepatitis B and C (30% vs 19%, P = .05), and lower HIV RNA at lymphoma diagnosis resulting from the IRIS case definition. Overall survival at 5 years was similar between IRIS (49%; 95% confidence interval [CI], 37%–64%) and non-IRIS (44%; 95% CI, 39%–50%), although increased early mortality was suggested among IRIS cases.
Conclusions. In a large HIV-associated lymphoma cohort, 12% of patients met a uniformly applied unmasking lymphoma IRIS case definition. Detailed studies of lymphoma IRIS might identify immunologic mechanisms of lymphoma control.
PMCID: PMC4102912  PMID: 24755860
HIV/AIDS; lymphoma; Hodgkin lymphoma; non-Hodgkin lymphoma; immune reconstitution inflammatory syndrome
21.  Hospital-Acquired Clostridium difficile Infections Estimating All-Cause Mortality and Length of Stay 
Epidemiology (Cambridge, Mass.)  2014;25(4):570-575.
Clostridium difficile is a health care–associated infection of increasing importance. The purpose of this study was to estimate the time until death from any cause and time until release among patients with C. difficile, comparing the burden of those in the intensive care unit (ICU) with those in the general hospital population.
A parametric mixture model was used to estimate event times, as well as the case-fatality ratio in ICU and non-ICU patients within a cohort of 609 adult incident cases of C. difficile in the Southeastern United States between 1 July 2009 and 31 December 2010.
ICU patients had twice the median time to death (relative time = 1.97 [95% confidence interval (CI) = 0.96–4.01]) and nearly twice the median time to release (1.88 [1.40–2.51]) compared with non-ICU patients. ICU patients also experienced 3.4 times the odds of mortality (95% CI = 1.8–6.2). Cause-specific competing risks analysis underestimated the relative survival time until death (0.65 [0.36–1.17]) compared with the mixture model.
Patients with C. difficile in the ICU experienced higher mortality and longer lengths of stay within the hospital. ICU patients with C. difficile infection represent a population in need of particular attention, both to prevent adverse patient outcomes and to minimize transmission of C. difficile to other hospitalized patients.
PMCID: PMC4224274  PMID: 24815305
22.  African American Race and HIV Virological Suppression: Beyond Disparities in Clinic Attendance 
American Journal of Epidemiology  2014;179(12):1484-1492.
Racial disparities in clinic attendance may contribute to racial disparities in plasma human immunodeficiency virus type 1 (HIV-1) RNA levels among HIV-positive patients in care. Data from 946 African American and 535 Caucasian patients receiving HIV care at the University of North Carolina Center for AIDS Research HIV clinic between January 1, 1999, and August 1, 2012, were used to estimate the association between African American race and HIV virological suppression (i.e., undetectable HIV-1 RNA) when racial disparities in clinic attendance were lessened. Clinic attendance was measured as the proportion of scheduled clinic appointments attended (i.e., visit adherence) or the proportion of six 4-month intervals with at least 1 attended scheduled clinic appointment (i.e., visit constancy). In analyses accounting for patient characteristics, the risk ratio for achieving suppression when comparing African Americans with Caucasians was 0.91 (95% confidence interval: 0.85, 0.98). Lessening disparities in adherence or constancy lowered disparities in virological suppression by up to 44.4% and 11.1%, respectively. Interventions that lessen disparities in adherence may be more effective in eliminating disparities in suppression than interventions that lessen disparities in constancy. Given that gaps in care were limited to be no more than 2 years for both attendance measures, the impact of lessening disparities in adherence may be overstated.
PMCID: PMC4051874  PMID: 24812158
clinic visits; cohort studies; health status disparities; human immunodeficiency virus; viral load
24.  Marginal Structural Models for Case-Cohort Study Designs to Estimate the Association of Antiretroviral Therapy Initiation With Incident AIDS or Death 
American Journal of Epidemiology  2012;175(5):381-390.
To estimate the association of antiretroviral therapy initiation with incident acquired immunodeficiency syndrome (AIDS) or death while accounting for time-varying confounding in a cost-efficient manner, the authors combined a case-cohort study design with inverse probability-weighted estimation of a marginal structural Cox proportional hazards model. A total of 950 adults who were positive for human immunodeficiency virus type 1 were followed in 2 US cohort studies between 1995 and 2007. In the full cohort, 211 AIDS cases or deaths occurred during 4,456 person-years. In an illustrative 20% random subcohort of 190 participants, 41 AIDS cases or deaths occurred during 861 person-years. Accounting for measured confounders and determinants of dropout by inverse probability weighting, the full cohort hazard ratio was 0.41 (95% confidence interval: 0.26, 0.65) and the case-cohort hazard ratio was 0.47 (95% confidence interval: 0.26, 0.83). Standard multivariable-adjusted hazard ratios were closer to the null, regardless of study design. The precision lost with the case-cohort design was modest given the cost savings. Results from Monte Carlo simulations demonstrated that the proposed approach yields approximately unbiased estimates of the hazard ratio with appropriate confidence interval coverage. Marginal structural model analysis of case-cohort study designs provides a cost-efficient design coupled with an accurate analytic method for research settings in which there is time-varying confounding.
PMCID: PMC3282878  PMID: 22302074
acquired immunodeficiency syndrome; case-cohort studies; cohort studies; confounding bias; HIV; pharmacoepidemiology; selection bias
25.  Bayesian Posterior Distributions Without Markov Chains 
American Journal of Epidemiology  2012;175(5):368-375.
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976–1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984–1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.
PMCID: PMC3282880  PMID: 22306565
Bayes theorem; epidemiologic methods; inference; Monte Carlo method; posterior distribution; simulation

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