Brent A. Coull

Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions

Abstract For interval estimation of a proportion, coverage probabilities tend to be too large for “exact” confidence intervals based on inverting the binomial test and too small for the interval based on inverting the Wald large-sample normal test (i.e., sample proportion ± z-score × estimated standard error). Wilsons suggestion of inverting the related score test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes. The 95% score interval has similar behavior as the adjusted Wald interval obtained after adding two “successes” and two “failures” to the sample. In elementary courses, with the score and adjusted Wald methods it is unnecessary to provide students with awkward sample size guidelines.

The Teratogenicity of Anticonvulsant Drugs

BACKGROUND The frequency of major malformations, growth retardation, and hypoplasia of the midface and fingers, known as the anticonvulsant embryopathy, is increased in infants exposed to anticonvulsant drugs in utero. However, whether the abnormalities are caused by the maternal epilepsy itself or by exposure to anticonvulsant drugs is not known. METHODS We screened 128,049 pregnant women at delivery to identify three groups of infants: those exposed to anticonvulsant drugs, those unexposed to anticonvulsant drugs but with a maternal history of seizures, and those unexposed to anticonvulsant drugs with no maternal history of seizures (control group). The infants were examined systematically for the presence of major malformations, signs of hypoplasia of the midface and fingers, microcephaly, and small body size. RESULTS The combined frequency of anticonvulsant embryopathy was higher in 223 infants exposed to one anticonvulsant drug than in 508 control infants (20.6 percent vs. 8.5 percent; odds ratio, 2.8; 95 percent confidence interval, 1.1 to 9.7). The frequency was also higher in 93 infants exposed to two or more anticonvulsant drugs than in the controls (28.0 percent vs. 8.5 percent; odds ratio, 4.2; 95 percent confidence interval, 1.1 to 5.1). The 98 infants whose mothers had a history of epilepsy but took no anticonvulsant drugs during the pregnancy did not have a higher frequency of those abnormalities than the control infants. CONCLUSIONS A distinctive pattern of physical abnormalities in infants of mothers with epilepsy is associated with the use of anticonvulsant drugs during pregnancy, rather than with epilepsy itself.

Prevalence of hyperhomocyst(e)inemia in patients with peripheral arterial occlusive disease.

A micromethod adapted for automated determinations was used to measure basal plasma levels of homocyst(e)ine [H(e)]. These levels included the sum of free and bound forms of homocysteine, its disulfide oxidation product, homocystine, and the homocysteine-cysteine-mixed disulfide. Two groups of subjects were studied: apparently healthy individuals (n = 103) and patients with peripheral arterial occlusive disease (PAOD) (n = 47). Because age in PAOD patients was higher than in control subjects, the control subjects were subdivided into younger and older groups (aged 60 years or less and more than 60 years, respectively). The H(e) levels in the younger groups were 11.18 +/- 3.58 (mean +/- SD, expressed as homocysteine) and 8.58 +/- 2.82 nmol/ml in men and women, respectively; in the older groups, the levels were 10.74 +/- 2.16 and 9.04 +/- 2.16 nmol/ml in men and women, respectively. There was a positive correlation of H(e) levels with age in the younger control women (r = 0.373; p less than 0.02); no significant correlations were present in the other three control groups. Levels of H(e) in PAOD patients (15.44 +/- 5.76 and 17.04 +/- 8.26 nmol/ml in men and women, respectively) were significantly higher than those indicated above in the older controls. Next, the PAOD patients were assigned to two subgroups: 1) those with normal levels of H(e) (within two standard deviations of the mean of the control values) and 2) those with elevated levels of H(e). Age, cholesterolemia, and the prevalence of smoking and diabetes were similar in both subgroups. These results suggest that elevated plasma H(e) is an independent risk factor for arterial occlusive disease.

Diabetes, Obesity, and Hypertension May Enhance Associations between AirPollution and Markers of Systemic Inflammation

Airborne particulate matter (PM) may lead to increased cardiac risk through an inflammatory pathway. Therefore, we investigated associations between ambient PM and markers of systemic inflammation among repeated measures from 44 senior citizens (≥ 60 years of age) and examined susceptibility by conditions linked to chronic inflammation. Mixed models were used to identify associations between concentrations of fine PM [aerodynamic diameter ≤ 2.5 μm (PM2.5)] averaged over 1–7 days and measures of C-reactive protein (CRP), interleukin-6 (IL-6), and white blood cells (WBCs). Effect modification was investigated for diabetes, obesity, hypertension, and elevated mean inflammatory markers. We found positive associations between longer moving averages of PM2.5 and WBCs across all participants, with a 5.5% [95% confidence interval (CI), 0.10 to 11%] increase per interquartile increase (5.4 μg/m3) of PM2.5 averaged over the previous week. PM2.5 and CRP also exhibited positive associations among all individuals for averages longer than 1 day, with the largest associations for persons with diabetes, obesity, and hypertension. For example, an interquartile increase in the 5-day mean PM2.5 (6.1 μg/m3) was associated with a 14% increase in CRP (95% CI, −5.4 to 37%) for all individuals and an 81% (95% CI, 21 to 172%) increase for persons with diabetes, obesity, and hypertension. Persons with diabetes, obesity, and hypertension also exhibited positive associations between PM2.5 and IL-6. Individuals with elevated mean inflammatory markers exhibited enhanced associations with CRP, IL-6, and WBCs. We found modest positive associations between PM2.5 and indicators of systemic inflammation, with larger associations suggested for individuals with diabetes, obesity, hypertension, and elevated mean inflammatory markers.

A Case–Control Analysis of Exposure to Traffic and Acute Myocardial Infarction

Background Long-term exposure to particulate air pollution has been associated with an increased risk of dying from cardiopulmonary and ischemic heart disease, yet few studies have evaluated cardiovascular end points other than mortality. We investigated the relationship between long-term exposure to traffic and occurrence of acute myocardial infarction (AMI) in a case–control study. Methods A total of 5,049 confirmed cases of AMI were identified between 1995 and 2003 as part of the Worcester Heart Attack Study, a community-wide study examining changes over time in the incidence of AMI among greater Worcester, Massachusetts, residents. Population controls were selected from Massachusetts resident lists. We used cumulative traffic within 100 m of subjects’ residence and distance from major roadway as proxies for exposure to traffic-related air pollution. We estimated the relationship between exposure to traffic and occurrence of AMI using logistic regression, and we adjusted for the following potential confounders: age, sex, section of the study area, point sources emissions of particulate matter with aerodynamic diameter < 2.5 μm, area socioeconomic characteristics, and percentage of open space. Results An increase in cumulative traffic near the home was associated with a 4% increase in the odds of AMI per interquartile range [95% confidence interval (CI), 2–7%], whereas living near a major roadway was associated with a 5% increase in the odds of AMI per kilometer (95% CI, 3–6%). Conclusions hese results provide support for an association between long-term exposure to traffic and the risk of AMI.

Ambient gas concentrations and personal particulate matter exposures: implications for studying the health effects of particles.

Background: Data from a previous study conducted in Baltimore, MD, showed that ambient fine particulate matter less than 2.5 &mgr;m in diameter (PM2.5) concentrations were strongly correlated with corresponding personal PM2.5 exposures, whereas ambient O3, NO2, and SO2 concentrations were weakly correlated with their personal exposures to these gases. In contrast, many of the ambient gas concentrations were reasonable surrogates of personal PM2.5 exposures. Methods: Personal multipollutant exposures and corresponding ambient air pollution concentrations were measured for 43 subjects living in Boston, MA. The cohort consisted of 20 healthy senior citizens and 23 schoolchildren. Simultaneous 24-hour integrated PM2.5, O3, NO2, and SO2 personal exposures and ambient concentrations were measured. All PM2.5 samples were also analyzed for SO42− (sulfate). We analyzed personal exposure and ambient concentration data using correlation and mixed model regression analyses to examine relationships among (1) ambient PM2.5 concentrations and corresponding ambient gas concentrations; (2) ambient PM2.5 and gas concentrations and their respective personal exposures; (3) ambient gas concentrations and corresponding personal PM2.5 exposures; and (4) personal PM2.5 exposures and corresponding personal gas exposures. Results: We found substantial correlations between ambient PM2.5 concentrations and corresponding personal exposures over the course of time. Additionally, our results support the earlier finding that summertime gaseous pollutant concentrations may be better surrogates of personal PM2.5 exposures (especially personal exposures to PM2.5 of ambient origin) than they are surrogates of personal exposures to the gases themselves. Conclusions: Particle health effects studies that include both ambient PM2.5 and gaseous concentrations as independent variables must be analyzed carefully and interpreted cautiously, since both parameters may be serving as surrogates for PM2.5 exposures.

Traffic-related air pollution and cognitive function in a cohort of older men.

Background Traffic-related particles induce oxidative stress and may exert adverse effects on central nervous system function, which could manifest as cognitive impairment. Objective We assessed the association between black carbon (BC), a marker of traffic-related air pollution, and cognition in older men. Methods A total of 680 men (mean ± SD, 71 ± 7 years of age) from the U.S. Department of Veterans Affairs Normative Aging Study completed a battery of seven cognitive tests at least once between 1996 and 2007. We assessed long-term exposure to traffic-related air pollution using a validated spatiotemporal land-use regression model for BC. Results The association between BC and cognition was nonlinear, and we log-transformed BC estimates for all analyses [ln(BC)]. In a multivariable-adjusted model, for each doubling in BC on the natural scale, the odds of having a Mini-Mental State Examination (MMSE) score ≤ 25 was 1.3 times higher [95% confidence interval (CI), 1.1 to 1.6]. In a multivariable-adjusted model for global cognitive function, which combined scores from the remaining six tests, a doubling of BC was associated with a 0.054 SD lower test score (95% CI, −0.103 to −0.006), an effect size similar to that observed with a difference in age of 1.9 years in our data. We found no evidence of heterogeneity by cognitive test. In sensitivity analyses adjusting for past lead exposure, the association with MMSE scores was similar (odds ratio = 1.3; 95% CI, 1.1 to 1.7), but the association with global cognition was somewhat attenuated (−0.038 per doubling in BC; 95% CI, −0.089 to 0.012). Conclusions Ambient traffic-related air pollution was associated with decreased cognitive function in older men.

The effect of dose and timing of dose on the association between airborne particles and survival.

Background Understanding the shape of the concentration–response curve for particles is important for public health, and lack of such understanding was recently cited by U.S. Environmental Protection Agency (EPA) as a reason for not tightening the standards. Similarly, the delay between changes in exposure and changes in health is also important in public health decision making. We addressed these issues using an extended follow-up of the Harvard Six Cities Study. Methods Cox proportional hazards models were fit controlling for smoking, body mass index, and other covariates. Two approaches were used. First, we used penalized splines, which fit a flexible functional form to the concentration response to examine its shape, and chose the degrees of freedom for the curve based on Akaike’s information criterion. Because the uncertainties around the resultant curve do not reflect the uncertainty in model choice, we also used model averaging as an alternative approach, where multiple models are fit explicitly and averaged, weighted by their probability of being correct given the data. We examined the lag relationship by model averaging across a range of unconstrained distributed lag models. Results We found that the concentration–response curve is linear, clearly continuing below the current U.S. standard of 15 μg/m3, and that the effects of changes in exposure on mortality are seen within two years. Conclusions Reduction in particle concentrations below U.S. EPA standards would increase life expectancy.

Mortality Risk Associated with Short-Term Exposure to Traffic Particles and Sulfates

Background Many studies have shown that airborne particles are associated with increased risk of death, but attention has more recently focused on the differential toxicity of particles from different sources. Geographic information system (GIS) approaches have recently been used to improve exposure assessment, particularly for traffic particles, but only for long-term exposure. Objectives We analyzed approximately 100,000 deaths from all, cardiovascular, and respiratory causes for the years 1995–2002 using a case–crossover analysis. Methods Estimates of exposure to traffic particles were geocoded to the address of each decedent on the day before death and control days, with these estimates derived from a GIS-based exposure model incorporating deterministic covariates, such as traffic density and meteorologic factors, and a smooth function of latitude and longitude. Results We estimate that an IQR increase in traffic particle exposure on the day before death is associated with a 2.3% increase [95% confidence interval (CI), 1.2 to 3.4%] in all-cause mortality risk. Stroke deaths were particularly elevated (4.4%; 95% CI, −0.2 to 9.3%), as were diabetes deaths (5.7%; 95% CI, −1.7 to 13.7%). Sulfate particles are spatially homogeneous, and using a central monitor, we found that an IQR increase in sulfate levels on the day before death is associated with a 1.1% (95% CI, 0.1 to 2.0%) increase in all-cause mortality risk. Conclusions Both traffic and powerplant particles are associated with increased deaths in Boston, with larger effects for traffic particles.

Measurement error caused by spatial misalignment in environmental epidemiology.

In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.