Discussion on “A formal causal interpretation of the case-crossover design” by Zach Shahn,Miguel A. Hernán,and James M. Robins

It has always been clear that the case-crossover design works, for some definition of “works,” but some of the details have been surprisingly elusive, and it is good to see more of them nailed down by Shahn et al. My interest in case-crossover analyses has mostly been in the context of air pollution epidemiology mentioned at the end of the paper. The air pollution setting is distinctive for several reasons: as the exposure variable is plausibly exogenous, it is possible to use control times after the case time, the effects of interest are quite small, and the same measured exposure series is shared over many—perhaps all—of the cohort.     

Corrections for measurement error due to delayed onset of illness for case-crossover designs

Epidemiologic studies of the short-term effects of ambient particulate matter (PM) on the risk of acute cardiovascular or cerebrovascular events often use data from administrative databases in which only the date of hospitalization is known. A common study design for analyzing such data is the case-crossover design, in which exposure at a time when a patient experiences an event is compared to exposure at times when the patient did not experience an event within a case-control paradigm. However, the time of true event onset may precede hospitalization by hours or days, which can yield attenuated effect estimates. In this article, we consider a marginal likelihood estimator, a regression calibration estimator, and a conditional score estimator, as well as parametric bootstrap versions of each, to correct for this bias. All considered approaches require validation data on the distribution of the delay times. We compare the performance of the approaches in realistic scenarios via simulation, and apply the methods to analyze data from a Boston-area study of the association between ambient air pollution and acute stroke onset. Based on both simulation and the case study, we conclude that a two-stage regression calibration estimator with a parametric bootstrap bias correction is an effective method for correcting bias in health effect estimates arising from delayed onset in a case-crossover study.     

Under the Weather: Legionellosis and Meteorological Factors

The incidence of legionellosis, caused by the bacteria Legionella which are commonly found in the environment, has been increasing in New Jersey (NJ) over the last decade. The majority of cases are sporadic with no known source of exposure. Meteorological factors may be associated with increases in legionellosis. Time series and case-crossover study designs were used to evaluate associations of legionellosis and meteorological factors (temperature (daily minimum, maximum, and mean), precipitation, dew point, relative humidity, sea level pressure, wind speed (daily maximum and mean), gust, and visibility). Time series analyses of multi-factor models indicated increases in monthly relative humidity and precipitation were positively associated with monthly legionellosis rate, while maximum temperature and visibility were inversely associated. Case-crossover analyses of multi-factor models indicated increases in relative humidity occurring likely before incubation period was positively associated, while sea level pressure and visibility, also likely preceding incubation period, were inversely associated. It is possible that meteorological factors, such as wet, humid weather with low barometric pressure, allow proliferation of Legionella in natural environments, increasing the rate of legionellosis.     

The lag-effect pattern in the relationship of particulate air pollution to daily mortality in Seoul,Korea

To assess differences in the lag-effect pattern in the relationship between particulate matter less than 10 microm in aerodynamic diameter (PM(10)) and cause-specific mortality in Seoul, Korea, from January 1995 to December 1999, we performed a time-series analysis. We used a generalized additive Poisson regression model to control for time trends, temperature, humidity, air pressure, and the day of the week. The PM(10) effect was estimated on the basis of the time-series models using the 24-h means and the quadratic distributed-lag models using a cumulative 6-day effect. One interquartile range increase in the 6-day cumulative mean of PM(10) (43.12 microg/m(3)) was associated with an increase in non-accidental deaths [3.7%, 95% confidence interval (CI): 2.1, 5.4], respiratory disease (13.9%, 95% CI: 6.8, 21.5), cardiovascular disease (4.4%, 95% CI: -1.0, 9.0), and cerebrovascular disease (6.3%, 95% CI: 2.3, 10.5). We found the following patterns in the disease-specific lag-effect window: respiratory mortality was more affected by air pollution level on the day of death, whereas cardiovascular deaths were more affected by the previous day's air pollution level. Cerebrovascular deaths were simultaneously associated with the air pollution levels of the same day and the previous day. The patterns in the lag effect from the distributed-lag models were similar to those of a series of time-series models with 24-h means. These results contribute to our understanding of how exposure to air pollution causes adverse health effects.     

Marginal mark regression analysis of recurrent marked point process data

Summary .  Longitudinal studies typically collect information on the timing of key clinical events and on specific characteristics that describe those events. Random variables that measure qualitative or quantitative aspects associated with the occurrence of an event are known as marks. Recurrent marked point process data consist of possibly recurrent events, with the mark (and possibly exposure) measured if and only if an event occurs. Analysis choices depend on which aspect of the data is of primary scientific interest. First, factors that influence the occurrence or timing of the event may be characterized using recurrent event analysis methods. Second, if there is more than one event per subject, then the association between exposure and the mark may be quantified using repeated measures regression methods. We detail assumptions required of any time-dependent exposure process and the event time process to ensure that linear or generalized linear mixed models and generalized estimating equations provide valid estimates. We provide theoretical and empirical evidence that if these conditions are not satisfied, then an independence estimating equation should be used for consistent estimation of association. We conclude with the recommendation that analysts carefully explore both the exposure and event time processes prior to implementing a repeated measures analysis of recurrent marked point process data.     

Socioeconomic Position and Low Birth Weight among Mothers Exposed to Traffic-Related Air Pollution

Background

Atmospheric pollution is a major public health concern. It can affect placental function and restricts fetal growth. However, scientific knowledge remains too limited to make inferences regarding causal associations between maternal exposure to air pollution and adverse effects on pregnancy. This study evaluated the association between low birth weight (LBW) and maternal exposure during pregnancy to traffic related air pollutants (TRAP) in São Paulo, Brazil.

Methods and findings

Analysis included 5,772 cases of term-LBW (<2,500 g) and 5,814 controls matched by sex and month of birth selected from the birth registration system. Mothers’ addresses were geocoded to estimate exposure according to 3 indicators: distance from home to heavy traffic roads, distance-weighted traffic density (DWTD) and levels of particulate matter ≤10 µg/m³ estimated through land use regression (LUR-PM₁₀). Final models were evaluated using multiple logistic regression adjusting for birth, maternal and pregnancy characteristics. We found decreased odds in the risk of LBW associated with DWTD and LUR-PM₁₀ in the highest quartiles of exposure with a significant linear trend of decrease in risk. The analysis with distance from heavy traffic roads was less consistent. It was also observed that mothers with higher education and neighborhood-level income were potentially more exposed to TRAP.

Conclusions

This study found an unexpected decreased risk of LBW associated with traffic related air pollution. Mothers with advantaged socioeconomic position (SEP) although residing in areas of higher vehicular traffic might not in fact be more expose to air pollution. It can also be that the protection against LBW arising from a better SEP is stronger than the effect of exposure to air pollution, and this exposure may not be sufficient to increase the risk of LBW for these mothers.     

Estimating the acute health effects of coarse particulate matter accounting for exposure measurement error

In air pollution epidemiology, there is a growing interest in estimating the health effects of coarse particulate matter (PM) with aerodynamic diameter between 2.5 and 10 μm. Coarse PM concentrations can exhibit considerable spatial heterogeneity because the particles travel shorter distances and do not remain suspended in the atmosphere for an extended period of time. In this paper, we develop a modeling approach for estimating the short-term effects of air pollution in time series analysis when the ambient concentrations vary spatially within the study region. Specifically, our approach quantifies the error in the exposure variable by characterizing, on any given day, the disagreement in ambient concentrations measured across monitoring stations. This is accomplished by viewing monitor-level measurements as error-prone repeated measurements of the unobserved population average exposure. Inference is carried out in a Bayesian framework to fully account for uncertainty in the estimation of model parameters. Finally, by using different exposure indicators, we investigate the sensitivity of the association between coarse PM and daily hospital admissions based on a recent national multisite time series analysis. Among Medicare enrollees from 59 US counties between the period 1999 and 2005, we find a consistent positive association between coarse PM and same-day admission for cardiovascular diseases.     

Delays in Appropriate Antibiotic Therapy for Gram-Negative Bloodstream Infections: A Multicenter,Community Hospital Study

Background

Gram-negative bacterial bloodstream infection (BSI) is a serious condition with estimated 30% mortality. Clinical outcomes for patients with severe infections improve when antibiotics are appropriately chosen and given early. The objective of this study was to estimate the association of prior healthcare exposure on time to appropriate antibiotic therapy in patients with gram-negative BSI.

Method

We performed a multicenter cohort study of adult, hospitalized patients with gram-negative BSI using time to event analysis in nine community hospitals from 2003-2006. Event time was defined as the first administration of an antibiotic with in vitro activity against the infecting organism. Healthcare exposure status was categorized as community-acquired, healthcare-associated, or hospital-acquired. Time to appropriate therapy among groups of patients with differing healthcare exposure status was assessed using Kaplan-Meier analyses and multivariate Cox proportional hazards models.

Results

The cohort included 578 patients with gram-negative BSI, including 320 (55%) healthcare-associated, 217 (38%) community-acquired, and 41 (7%) hospital-acquired infections. 529 (92%) patients received an appropriate antibiotic during their hospitalization. Time to appropriate therapy was significantly different among the groups of healthcare exposure status (log-rank p=0.02). Time to first antibiotic administration regardless of drug appropriateness was not different between groups (p=0.3). The unadjusted hazard ratios (HR) (95% confidence interval) were 0.80 (0.65-0.98) for healthcare-associated and 0.72 (0.63-0.82) for hospital-acquired, relative to patients with community-acquired BSI. In multivariable analysis, interaction was found between the main effect and baseline Charlson comorbidity index. When Charlson index was 3, adjusted HRs were 0.66 (0.48-0.92) for healthcare-associated and 0.57 (0.44-0.75) for hospital-acquired, relative to patients with community-acquired infections.

Conclusions

Patients with healthcare-associated or hospital-acquired BSI experienced delays in receipt of appropriate antibiotics for gram-negative BSI compared to patients with community-acquired BSI. This difference was not due to delayed initiation of antibiotic therapy, but due to the inappropriate choice of antibiotic.     

A measurement error model for time-series studies of air pollution and mortality

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.     

Evaluation of two methods for assessing gene-environment interactions using data from the Danish case-control study of facial clefts

BACKGROUND: Epidemiological investigations have begun to consider gene-environment (GE) interactions as potential risk factors for many diseases, including several different birth defects. However, traditional methodological approaches for the analysis of case-control data tend to have low power for detection of interaction effects. A log-linear approach that can impose the assumption that the genotype and exposure of interest occur independently in the population has been proposed as a potentially more powerful method for assessing GE interactions but has not been widely applied in the published literature. METHODS: The present analyses were undertaken to compare the results obtained when stratified analyses and a log-linear approach were used to assess potential GE interactions. The analyses were conducted using data from a population-based, case-control study conducted in Denmark and considered associations between nonsyndromic cleft lip with or without cleft palate (CL+/-P), infant genotype for variants of RAR-alpha, TGF-alpha, TGF-beta3, and MSX1, and maternal exposure to smoking, alcohol, and multivitamins. RESULTS: Neither the stratified nor the log-linear analyses provided evidence that that risk of CL+/-P is influenced by any of the GE interactions that were evaluated, despite the potential increase in power offered by the latter approach. Further, the analyses highlight concerns regarding the power to reject the assumption of independence of the genetic and environmental factor of interest in the controls and related concerns regarding the validity of results obtained using the log-linear approach when the underlying assumption is violated. CONCLUSIONS: The potential increase in power offered by the log-linear approach is offset by concerns regarding the validity of this approach when the independence assumption is violated.     

Time-varying coefficient models for the analysis of air pollution and health outcome data

In this article a time-varying coefficient model is developed to examine the relationship between adverse health and short-term (acute) exposure to air pollution. This model allows the relative risk to evolve over time, which may be due to an interaction with temperature, or from a change in the composition of pollutants, such as particulate matter, over time. The model produces a smooth estimate of these time-varying effects, which are not constrained to follow a fixed parametric form set by the investigator. Instead, the shape is estimated from the data using penalized natural cubic splines. Poisson regression models, using both quasi-likelihood and Bayesian techniques, are developed, with estimation performed using an iteratively re-weighted least squares procedure and Markov chain Monte Carlo simulation, respectively. The efficacy of the methods to estimate different types of time-varying effects are assessed via a simulation study, and the models are then applied to data from four cities that were part of the National Morbidity, Mortality, and Air Pollution Study.     

Exposure to moderate air pollution during late pregnancy and cord blood cytokine secretion in healthy neonates

Background/Objectives

Ambient air pollution can alter cytokine concentrations as shown in vitro and following short-term exposure to high air pollution levels in vivo. Exposure to pollution during late pregnancy has been shown to affect fetal lymphocytic immunophenotypes. However, effects of prenatal exposure to moderate levels of air pollutants on cytokine regulation in cord blood of healthy infants are unknown.

Methods

In a birth cohort of 265 healthy term-born neonates, we assessed maternal exposure to particles with an aerodynamic diameter of 10 µm or less (PM₁₀), as well as to indoor air pollution during the last trimester, specifically the last 21, 14, 7, 3 and 1 days of pregnancy. As a proxy for traffic-related air pollution, we determined the distance of mothers'' homes to major roads. We measured cytokine and chemokine levels (MCP-1, IL-6, IL-10, IL-1ß, TNF-α and GM-CSF) in cord blood serum using LUMINEX technology. Their association with pollution levels was assessed using regression analysis, adjusted for possible confounders.

Results

Mean (95%-CI) PM₁₀ exposure for the last 7 days of pregnancy was 18.3 (10.3–38.4 µg/m³). PM₁₀ exposure during the last 3 days of pregnancy was significantly associated with reduced IL-10 and during the last 3 months of pregnancy with increased IL-1ß levels in cord blood after adjustment for relevant confounders. Maternal smoking was associated with reduced IL-6 levels. For the other cytokines no association was found.

Conclusions

Our results suggest that even naturally occurring prenatal exposure to moderate amounts of indoor and outdoor air pollution may lead to changes in cord blood cytokine levels in a population based cohort.     

Regression Analysis with a Misclassified Covariate from a Current Status Observation Scheme

Summary Naive use of misclassified covariates leads to inconsistent estimators of covariate effects in regression models. A variety of methods have been proposed to address this problem including likelihood, pseudo‐likelihood, estimating equation methods, and Bayesian methods, with all of these methods typically requiring either internal or external validation samples or replication studies. We consider a problem arising from a series of orthopedic studies in which interest lies in examining the effect of a short‐term serological response and other covariates on the risk of developing a longer term thrombotic condition called deep vein thrombosis. The serological response is an indicator of whether the patient developed antibodies following exposure to an antithrombotic drug, but the seroconversion status of patients is only available at the time of a blood sample taken upon the discharge from hospital. The seroconversion time is therefore subject to a current status observation scheme, or Case I interval censoring, and subjects tested before seroconversion are misclassified as nonseroconverters. We develop a likelihood‐based approach for fitting regression models that accounts for misclassification of the seroconversion status due to early testing using parametric and nonparametric estimates of the seroconversion time distribution. The method is shown to reduce the bias resulting from naive analyses in simulation studies and an application to the data from the orthopedic studies provides further illustration.     

The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds

To analyse the dependence of a qualitative (dichotomous or polytomous) response variable upon one or more qualitative explanatory variables, log-linear models for frequencies are compared with log-linear models for odds, when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or unordered. The log-linear models for odds express the odds (or log odds) pertaining to adjacent response categories in terms of appropriate multiplicative (or additive) factors. These models include the 'null log-odds model', the 'uniform log-odds model', the 'parallel log-odds model', and other log-linear models for the odds. With these models, the dependence of the response variable (with ordered categories) can be analyzed in a manner analogous to the usual multiple regression analysis and related analysis of variance and analysis of covariance. Application of log-linear models for the odds sheds light on earlier applications of log-linear models for the frequencies in contingency tables with ordered categories.     

Modeling parasitism rate and parasitism risk: an illustration using a colonially nesting songbird, the red-winged blackbird Agelaius phoeniceus

Ornithologists interested in the drivers of nest success and brood parasitism benefit from the development of new analytical approaches. One example is the development of so-called "log exposure" models for analyzing nest success. However, analyses of brood parasitism data have not kept pace with developments in nest success analyses. The standard approach uses logistic regression which does not account for multiple parasitism events, nor does it prevent bias from using observed proportions of parasitized nests. Likewise, logistic regression analyses do not capture fine scale temporal variation in parasitism. At first glance, it might be tempting to apply log exposure models to parasitism data, but the process of parasitism is inherently different from the process of nest predation. We modeled daily parasitism rate as a Poisson process, which allowed us to correct potential biases in parasitism rate. We were also able to use our estimated parasitism rate to model parasitism risk as the probability of one or more parasitism events. We applied this model to red-winged blackbird Agelaius phoeniceus nesting colonies subject to parasitism by brown-headed cowbirds Molothrus ater . Our approach allowed us to model parasitism using a wider rage of covariates, especially functions of time. We found strong support for models combining temporal fluctuations in parasitism rate and nest-site characteristics. Similarly, we found that our annual predicted parasitism risk was lower on average than the risk estimated from observed parasitism levels. Our approach improves upon traditional logistic regression analyses and opens the door for more mechanistic modeling of the process of parasitism.     

北京市大气细颗粒污染物与老年呼吸系统疾病急诊就医关系的病例交叉研究

目的:探讨北京市大气细颗粒污染物对呼吸系统疾病急诊的影响。方法:收集2013年3月-2014年3月解放军305医院以及西三环的总参军训部北京第八干休所门诊部的临床病例急诊数据、北京市环境监测中心的大气细颗粒污染物和气象条件数据资料,应用病例交叉设计研究方法进行数据分析。结果:在控制气温、相对湿度的影响后,单向回顾性1:1配对病例交叉分析结果显示,滞后0天细颗粒物污染对慢性支气管炎、哮喘、慢性阻塞性肺病急诊影响的OR值最大,细颗粒物日平均浓度每升高10μg/m3,对应的OR值分别为1.032、1.033、1.035。结论:该研究区域内大气细颗粒物污染物浓度升高可以导致呼吸系统疾病相关的慢性支气管炎、哮喘、慢性阻塞性肺病疾病的急诊增加。     

A general approach to analyzing epidemiologic data that contain misclassification errors

Misclassification is a common source of bias and reduced efficiency in the analysis of discrete data. Several methods have been proposed to adjust for misclassification using information on error rates (i) gathered by resampling the study population, (ii) gathered by sampling a separate population, or (iii) assumed a priori. We present unified methods for incorporating these types of information into analyses based on log-linear models and maximum likelihood estimation. General variance expressions are developed. Examples from epidemiologic studies are used to demonstrate the proposed methodology.     

Biomarkers of Exposure to Polycyclic Aromatic Hydrocarbons and Cognitive Function among Elderly in the United States (National Health and Nutrition Examination Survey: 2001-2002)

Recent studies report a link between common environmental exposures, such as particulate matter air pollution and tobacco smoke, and decline in cognitive function. The purpose of this study was to assess the association between exposure to polycyclic aromatic hydrocarbons (PAHs), a selected group of chemicals present in particulate matter and tobacco smoke, and measures of cognitive performance among elderly in the general population. This cross-sectional analysis involved data from 454 individuals aged 60 years and older from the 2001–2002 National Health and Nutrition Examination Survey. The association between PAH exposures (as measured by urinary biomarkers) and cognitive function (digit symbol substitution test (DSST)) was assessed using multiple linear regression analyses. After adjusting for age, socio-economic status and diabetes we observed a negative association between urinary 1-hydroxypyrene, the gold standard of PAH exposure biomarkers, and DSST score. A one percent increase in urinary 1-hydroxypyrene resulted in approximately a 1.8 percent poorer performance on the digit symbol substitution test. Our findings are consistent with previous publications and further suggest that PAHs, at least in part may be responsible for the adverse cognitive effects linked to tobacco smoke and particulate matter air pollution.     

Respiratory health and air pollution: additive mixed model analyses

We conduct a reanalysis of data from the Utah Valley respiratory health/air pollution study of Pope and co-workers (Pope et al., 1991) using additive mixed models. A relatively recent statistical development (e.g. Wang, 1998; Verbyla et al., 1999; Lin and Zhang, 1999), the methods allow for smooth functional relationships, subject-specific effects and time series error structure. All three of these are apparent in the Utah Valley data.     

Bayesian distributed lag models: estimating effects of particulate matter air pollution on daily mortality

Summary .  A distributed lag model (DLagM) is a regression model that includes lagged exposure variables as covariates; its corresponding distributed lag (DL) function describes the relationship between the lag and the coefficient of the lagged exposure variable. DLagMs have recently been used in environmental epidemiology for quantifying the cumulative effects of weather and air pollution on mortality and morbidity. Standard methods for formulating DLagMs include unconstrained, polynomial, and penalized spline DLagMs. These methods may fail to take full advantage of prior information about the shape of the DL function for environmental exposures, or for any other exposure with effects that are believed to smoothly approach zero as lag increases, and are therefore at risk of producing suboptimal estimates. In this article, we propose a Bayesian DLagM (BDLagM) that incorporates prior knowledge about the shape of the DL function and also allows the degree of smoothness of the DL function to be estimated from the data. We apply our BDLagM to its motivating data from the National Morbidity, Mortality, and Air Pollution Study to estimate the short-term health effects of particulate matter air pollution on mortality from 1987 to 2000 for Chicago, Illinois. In a simulation study, we compare our Bayesian approach with alternative methods that use unconstrained, polynomial, and penalized spline DLagMs. We also illustrate the connection between BDLagMs and penalized spline DLagMs. Software for fitting BDLagM models and the data used in this article are available online.