Abstract
Background
Shortterm fluctuations of ambient air pollution have been associated with exacerbation of cardiovascular disease. A multicity study was designed to assess the probability of recurrent hospitalization in a cohort of incident myocardial infarction survivors in five European cities. The objective of this paper is to discuss the methods for analyzing shortterm health effects in a cohort study based on a caseseries.
Methods
Three methods were considered for the analyses of the cohort data: Poisson regression approach, casecrossover analyses and extended Cox regression analyses. The major challenge of these analyses is to appropriately consider changes within the cohort over time due to changes in the underlying risk following a myocardial infarction, slow time trends in risk factors within the population, dynamic cohort size and seasonal variation.
Results
Poisson regression analyses, casecrossover analyses and Extended Cox regression analyses gave similar results. Application of smoothing methods showed the capability to adequately model the complex time trends.
Conclusion
From a practical point of view, Poisson regression analyses are less timeconsuming, and therefore might be used for confounder selection and most of the analyses. However, replication of the results with Cox models is desirable to assure that the results are independent of the analytical approach used. In addition, extended Cox regression analyses would allow a joint estimation of longterm and shortterm health effects of timevarying exposures.
Background
Ambient air pollution has been associated with increases in acute morbidity and mortality [1]. Patients with underlying chronic diseases such as for example diabetes, ischemic heart disease or heart failure may be at particular risk for the effects of ambient air pollution. Series of incident cases may be followed over time to assess the impact of shortterm fluctuation on recurrent disease exacerbation. These studies deviate from the classical cohort as well as timeseries designs. The major statistical challenge in these studies is the control for changes within the cohort over time due to changes in the underlying risk following disease inception, slow time trends in risk factors within population, dynamic cohort size and seasonal variation. The impact of time is particular important when effects of air pollution are considered, because concentrations of air pollutants vary by season and yearly averages of pollutants change due to weather, air pollution control measures and changes in sources.
In order to evaluate the impact of air pollution on patients with preexisting diseases, previous hospitalization might be used to define a potentially susceptible subgroup [24]. Poisson regression analyses and casecrossover analyses have been used to estimate the impact of variations in daily average air pollution concentrations on the risk of death in previously hospitalized subgroups of the population [58].
A multicity study was designed to follow cohorts of myocardial infarction (MI) survivors in five European cities: Augsburg, Barcelona, Helsinki, Rome and Stockholm (HEAPSSStudy). For entry into the cohort, incident first myocardial infarction cases were considered. The outcomes considered were reinfarctions and other related rehospitalization or death. Ambient air pollution was characterized based on existing air monitoring networks. In addition, condensation particle counters were set up in each location to measure the ambient particle number concentrations (PNC) and to retrospectively estimate PNC for the entire study period in each location.
This paper describes and compares different statistical approaches for analyzing shortterm air pollution health effects in a cohort with ongoing recruitment during the followup. Three different methods to analyze the cohort data were considered: (a) Poisson regression analyses on the calendartime axis, (b) casecrossover analyses and (c) extended Cox regression analyses. As an example the analyses of the association between NO_{2 }and any cardiac readmission of MI survivors are presented.
Methods
Data collection
Incident myocardial infarction survivors were recruited in five European cities (Augsburg, Barcelona, Helsinki, Rome, and Stockholm) during 1992 to 2000 as has been described elsewhere [9]. Briefly, data sources were AMI Registries in Augsburg and Barcelona, administrative databases of hospital admissions in Helsinki, Rome and Stockholm. Enrollment was restricted to residents of the above cities, aged 35 years or more (35–74 in Augsburg, 35–79 in Barcelona) who had their first AMI (index AMI) during the recruitment period. Subsequent first cardiac rehospitalizations of cohort members within the study area were recorded from day 29 after the index AMI until the individual end of followup period defined by death, migration out of the study area, or center specific end of the study. Readmissions of interest were those with primary diagnoses of reinfarctions (ICD9: 410; ICD10: i21, i22), acute angina pectoris (ICD9: 411, 413; ICD10: i20–i22, i24, i25), dysrhythmia (ICD9: 427; i46.0, I46.9, i47–i49, r00.1, r00.8) and heart failure (ICD9:428; ICD10: i50). Vital status and place of residence at the end of the followup period were ascertained for all cohort members.
Statistical analyses
In the study, MI survivors entered the cohort during an extended period. Once the cohort was complete at least one year of followup without recruitment was added. As a consequence the following issues had to be considered in the statistical analyses: (a) the number of subjects at risk increases over the recruitment period, (b) the risk of the cohort for a recurrent event on the calendartime axis varies based on the proportion of recent MI survivors in the entire cohort. In the following we refer to calendar time when we number the dates during followup and to cohorttime when we number the persontime followed.
Poisson regression analyses
Epidemiological studies in air pollution research have developed techniques using Poisson regression analyses on the calendartime axis [10]. In a time series analysis the daily counts of events are regressed on the daily predictor variables such as trend, season, weather, and air pollution. This design assumes that the events are independent and that the event rate is changes only slowly over time. The event rate λ_{t }at the time point t is modeled as follows
ln(λ_{t}) = α + ∑β_{i}x_{it}
With λ_{t }= y_{t}/N_{t }being the number of cases y observed at time t divided by the number of subjects N at risk at time t. The model can be rewritten as
ln(y_{t}) = ln(N_{t}) + α + ∑β_{i}x_{it}
In timeseries analyses it is sometimes assumed that the underlying population at risk does not change, and therefore the population at risk is not modeled explicitly in the regression analyses. However, when applied to a cohort the number of subjects at risk can be explicitly modeled as given in the equation above. In the cohort setting, when analyzing the data on the calendar time axis, the trend captures three different underlying reasons for changes in the rate of MI over time: (a) longterm underlying trends in the study base due to lifestyle changes, changes in health care or aging of the population, (b) seasonal variation and (c) changing composition of the cohort. Therefore, in the cohort setting proper trend control is very important because it is likely that the effect estimates will be biased if the trend is not correctly specified. Recent discussions on modeling in timeseries analyses [11,12] have lead to a broader use of different smoothing techniques in these analyses and different approaches have been used to assess the trend over time [13]. We selected three approaches to model the trend: (a) natural splines, (b) penalized splines and (c) locally weighted least square (loess) smoothers.
In a hierarchical approach potential confounders were selected, including long term trend, season, days of the week, holidays and meteorology, before adding air pollution concentration as independent variable. Generalized additive models were used to allow for nonparametric functions of the confounders in R (The R Foundation for Statistical Computing Version 1.8.1) using the package "mgcv" (version 0.9–6) [1416]. All models included the natural logarithm of the number of persons at risk each day as offset and the daily number of events as outcome variable. To allow for possible over or underdispersion the quasilikelihood family was used to estimate the parameters without specifying the underlying distribution function. Penalized regression splines were tested for the continuous confounder variables. The choice of degrees of freedom was left to the algorithm ("magic") in the "mgcv" – package that minimized the Generalized Cross Validation (GCV) criterion. The default of 10 knots as starting value was adjusted to higher values if necessary due to the structure of the data. If the smooth function was not significant or the estimated degrees of freedom were less than two, a linear term was tested instead. Decisions for keeping a covariate in a model were based on judgment using the p value (<.1), GCV score (the smaller the better), and the autocorrelation function (ACF) (the nearer to zero the better).
Trend was included in the model as an obligatory variable with a penalized spline starting with 6 knots per year to control for long term trends, seasonality and changes in the baseline risk. Then current day temperature and the deviation of the current day temperature from the mean temperature of lag day 1–3 were tested as penalized splines. At least one temperature term had to remain in the model. Thereafter penalized splines of air pressure and relative humidity, and then dummies for days of the week and the city specific indicators (holidays, population decrease) were tested one after the other. Finally the model was "fine tuned" changing the parameters where the decision had not been clear and comparing ACF plots and GCVscore to choose the final covariates to include for the further analyses.
Sensitivity analyses were performed to compare the results of the final models with the estimates obtained when modifying the smoothingfunctions used or the confounders entered in the Poisson model. Thus the analyses were repeated using natural cubic splines or loess instead of the penalized splines, with comparable effective degrees of freedom to those in the final model with penalized splines. Temperature was replaced by apparent temperature [17] and dew point temperature. Instead of temperature difference the mean of lag day 1 to 3 was used. The sensitivity of the results to the choice made when selecting the confounders was tested by excluding or including borderline significant confounders that had or had not entered the model. At the same time, those that had been included with a linear term were considered with a smooth function in the sensitivity analyses.
Casecrossover analyses
Casecrossover analyses have been developed to study transient effects of acute exposures using a caseonly design. This design samples information on exposure status from case and referent periods selected from the persontime of the cases. The period of exposure of the cases is selected as a plausible hazard period immediately preceding the event. Referent periods are chosen to represent the exposure distribution in the noncase time periods at risk.
The referent period selection poses the main challenge to the casecrossover analyses. Different sampling designs for referent periods have been proposed to estimate the effects of air pollution. Exposures that do not change in association with the casestatus, such as air pollution can be sampled also from persontime after the case occurred [18]. The stratified approach by Lumley and Levy [19] controls time trends by design.
Casecrossover analyses were performed as an alternative to the Poisson regression using conditional logistic regression models in the SPlus statistical package version 6.0. We used the "coxph" function with a strata statement. The date of each case contributed a hazard period that was matched with referent periods selected with the stratified approach (stratifying criteria were year, month and weekday). It controls for weekday by design. The same confounder variables were included as in the Poisson regression in order to obtain maximum comparability of the models. PSplines were used as smoothing method for meteorology variables. The effective degrees of freedom of the smoothers in the Poisson models were translated by adjusting the smoothing parameter of the Psplines.
Proportional hazard models
An alternative possibility is to model the data as cohort data using Cox proportional hazard models. Time t now denotes the time since MI. Extended Cox regression allows for timevarying covariates in survival analyses [20]. The hazard h at time t is given as
where X(t) = (X_{1}, X_{2},....., X_{p1}, X_{1}(t), X_{2}(t),....., X_{p2}(t)) and X_{1}, X_{2},....., X_{p1 }are timeinvariant variables such as for example age or gender, and X_{1}(t), X_{2}(t),....., X_{p2}(t) are timevarying variables such as weather or air pollution.
The model makes no assumption about the baseline hazard, and therefore is suitable for the analyses proposed here because the risk for cardiac readmission changes during the followup of the MI survivors. While X_{j}(t) is varying over time, the hazard model provides only one regression coefficient δ_{j }for each timevarying variable in the model. Thus at time t, there is only one value of the variables X_{j}(t) that has an effect on the hazard: the value being measured at time t. The model therefore assumes a uniform relative risk for all time points and consequently does not per se address the possibility of effect modification of the air pollution effects by length of followup.
The association with daily pollution levels was analyzed in SAS statistical software (SAS Institute Inc., Cary, NC, USA, Release 8.02) PROC PHREG using the counting process style of input. For each subject one record for each day at risk was created. All models included the same covariates as the Poisson models, but instead of smooth functions quadratic functions were used. Trend entered as a linear term. As constant covariates age at entry (in years as quadratic function), diabetes, hypertension and sex (as dummy variables) were considered, since they were identified as predictors of survival in a classical Cox regression.
Results
Data from Rome is used to illustrate the properties of the data. Rome was selected because it had one of the larger data sets and had clear evidence for seasonal variation. In Rome between 1998 and 2000, 7384 subjects survived at least 28 days after their first MI (Table 1). Between 1998 and 2001, 1916 readmissions for any cardiac disease defined as readmission for angina pectoris, myocardial infarction, congestive heart failure or arrhythmia were observed. Figure 1 describes various aspects of the cohort data for any cardiac readmission of MI survivors in Rome displayed on the calendar timeaxis. During the followup, the size of the cohort changed daily (figure 1a). In addition, the composition with respect to the distribution of length of follow also changes constantly if considered on the calendartime axis. Consequently, the number of cases observed at each timepoint of the calendartime axis of the followup reflects the size of the cohort and its composition (figure 1b). For each MI survivor, the risk of hospitalization for any cardiac disease is elevated during the first half year of followup and thereafter stabilizes (figure 1c). Figure 2 shows the number of subjects followed considering the time of followup as timeaxis. The number of subjects followed over time steadily decreases due to the occurrence of an event, loss to followup or end of the observational period (figure 2a). The number of events (figure 2b) and the incidence rate (figure 2c) observed is greatest at the beginning of the followup due to the vulnerability of the patients in the time immediately after the index event. The incidence rate observed after two or three years of followup is low (figure 2c).
Table 1. Description of the HEAPSS Study population, cardiac readmission as a selected outcome, and NO_{2 }concentrations in 5 European cities.
Figure 1. Number of MI survivors followed (a), the number of readmissions to the hospitals due to any cardiac disease during the followup (b) and incidence rate during the followup in Rome (c) as part of the HEAPSS study on the calendartime axis.
Figure 2. Number of MI survivors followed (a), the number of readmissions to the hospitals due to any cardiac disease during the followup (b) and incidence rate during the followup in Rome (c) as part of the HEAPSS study on the cohort timeaxis.
Figure 3 shows the smooth timetrend in the Poisson regression analyses using three different smoothing techniques: (a) penalized splines, (b) natural splines and (c) locally weighted least square smoothers (loess). Here the timeaxis is the calendartime axis and the functions shown in figure 3 correspond to the descriptive data in incidence rates in figure 1c. All functions suggest a decreased probability to observe hospitalizations due to any cardiac disease over time overlaid by seasonal variation. Thereby, they are able to capture the trend components discussed above remarkably well. The different smoothing approaches render quite comparable functions.
Figure 3. Exposure response function of the number of hospital readmissions occurring over time based on Possion regression analyses for Rome.
The Effect of NO_{2}
Table 2 compares the regression coefficients and standard errors for the different modeling approaches for a selected pollutant, (NO_{2}) with the average between current and previous day concentrations. For the Poisson regression analyses sensitivity analyses are presented to assess the sensitivity of the results with respect to the confounder modeling. The selected models are shown in table 3. It is important to note that the same degrees of freedom were not required for exposure response functions in all cities, but that the number of cases observed determined the ability to model timevarying confounders.
Table 2. Comparison of the regression coefficients (beta) and standard errors (se) in the analyses of NO_{2 }concentrations (average of current and previous day) and any cardiac readmission applying different statistical models and assessing the sensitivity of the results for confounder selection as listed in table 3.
Table 3. Confounders included in the different models with the following abbreviations: S: penalized spline (* k = 30, otherwise k = 10), Poly: Polynomial with order in brackets, L: linear term, X: dummies, D: by design.
The different smoothing approaches show comparable air pollution effect estimates in the Poisson regression analyses. The pooled estimates for NO_{2 }after confounder control by natural splines or loess functions are somewhat reduced, but one would still draw the same conclusions. Removing confounders overall increases the estimates whereas adding more confounders slightly decreases the regression coefficients. In the casecrossover analyses, the estimates are sometimes slightly higher (Augsburg) and sometimes slightly lower (Barcelona, Helsinki, and Rome) than the Poisson model estimates. The pooled estimate would suggest smaller regression coefficients and larger standard errors than Poisson regression analyses. The results of the extended Cox regression analyses were consistent with the results of the Poisson regression analyses in Augsburg, Stockholm and Helsinki. Slightly smaller effect estimates were obtained for Barcelona and Rome. Overall, the pooled estimates were slightly smaller than those obtained with Poisson regression analyses, but would also suggest an association between NO_{2 }and hospital readmissions in MI survivors (figure 4). For extended Cox regression analyses individual characteristics were also considered as confounders in the analyses and the results were nearly identical to those obtained without consideration of individual characteristics. No strong evidence for heterogeneity of the cityspecific effect estimates was observed and pooled random effect estimates were identical to the pooled fixed effect estimates (data not shown).
Figure 4. Effect estimates for the association between NO_{2 }(8 μg/m^{3}) hospital readmissions in MI survivors obtained in Poisson regression analyses and Extended Cox regression analyses of all five cities within the HEAPSS study and the pooled estimates based on a fixed effect model.
Discussion
The major challenge of analyzing shortterm health effects of air pollution in a cohort of diseased subjects is to consider simultaneously other timevarying confounders and the changes in the probability of a recurrent event due to the individual characteristics. In the case of myocardial infarction survivors, a major determinant of individual vulnerability is the time since index event due to the underlying healing of the heart tissue.
Three different approaches were considered in the analyses. The first one, Poisson regression analysis summarizes the events on a calendar timeaxis. The data in this study demonstrate an example where the underlying probability of observing an event changes with the composition of the cohort. Therefore, time is not only a measure for slow trends and seasonal variation, but also represents the changing fractions of persons at high risk over time. Smoothing methods were used to attempt to model these three different components in the time trend. The recent discussion on smoothing techniques [11,12] was considered by the selection of three different approaches, namely natural splines, penalized splines and locally weight least square smoothers. All three methods gave quite comparable results and their function is consistent with a decreased risk of hospital readmission as the cohort ages and a seasonal variation in hospital readmissions. In the sensitivity analyses, results were robust to changes in the confounders selected in the final model.
The casecrossover method was chosen because it was designed to control for temporal changes by design. More specifically, the stratified referent period selection approach considered here controls for trends by design [19]. However, it has been noted that casecrossover analyses have reduced power compared to Poisson regression analyses [19]. In this study we observed slightly smaller effect estimates with larger standard errors. The case of a cohort with ongoing recruitment and dynamically changing composition has not been methodologically considered before. One may assume that the underlying changes in rates are constant within each stratum [21]. However, as observed in figure 1, panel C this assumption might be violated at the beginning of the study. Therefore, the changing number of subjects at risk might be responsible for the small differences observed between Poisson regression analyses, which explicitly consider the varying number of subjects at risk on a given day, and the casecrossover analyses. Nevertheless, casecrossover analyses were considered for these analyses because they quite elegantly allow analyses of subgroups.
Extended Cox regression analyses, on the other hand, were formulated to consider the present study design in the correct way. Here, the underlying risk is modeled by a hazard function h_{0}(t) which is variable over time and considers both the changing hazard due to the recovery from the incident MI as well as changes in the composition of the cohort with respect to season and calendar year. The results are remarkably consistent with those obtained in the Poisson regression analyses. The practical disadvantage of the method is that the analyses are timeconsuming, in particular if these models are used for the selection of timevarying confounders. Consideration of individual confounders did not change the association between NO_{2 }and hospital readmissions. In contrast to a recently published similar approach, we chose time of followup instead of subject's age as time axis [22]. While these two approaches should give similar effect estimates we favor the model on the followup time axis as it more appropriately considers the changing risk levels within the cohort.
A recent review by the American Heart Association has highlighted the emerging evidence for the biological plausibility between ambient air pollution concentrations in urban areas and cardiovascular disease exacerbation [23]. However, effect estimates obtained from the general population might underestimate the risk of susceptible subpopulations, which have also higher baseline risks [24]. Cohort studies assessing the risk of susceptible populations are highly recommended to provide better estimates for risk assessment. For example, the age at first MI, socioeconomic status as well as the time since the first MI might modify the risk of shortterm air pollution exposures for an individual. All three methods might be used to assess the susceptibility of subgroups. The extended Cox regression analysis is the only method that would allow the estimation of the main effect of the considered effect modifier, but computation of the models is timeconsuming.
Recent research indicated that spatial and temporal variability of longterm exposures to ambient particles may be important factors to consider [25,26]. Furthermore, future research might consider shortterm fluctuations as well as individualized estimates of longterm exposures to ambient particles in assessing the health impact of environmental exposures. For these studies, Extended Cox regression analyses would be the method of choice. In its most simplistic version, one may estimate jointly the effect of homes exposed to high traffic together with air pollution concentrations from a central monitoring side. However, also more sophisticated approaches of exposure assessment building on spatiotemporal models such as for example described by Gulliver and Briggs [27] or Sahu and colleagues [28] can be foreseen.
Conclusion
Of the three methods considered for the analyses of the HEAPSS Study, the Poisson regression approach and the extended Cox regression analyses gave similar results. Casecrossover analyses might underestimate the strength of the association in this specific setting, but the differences were small. Further methodological investigation may be warranted. From a practical point of view, Poisson regression analyses are less timeconsuming, and therefore might be used for confounder selection and most of the analyses. However, replication of the results with Cox models is desirable to assure that the results are independent of the analytical approach used. For the identification of susceptible subgroups within a cohort of susceptible populations, casecrossover analyses might be the least time consuming approach, however, Extended Cox regression analyses would allow a joint estimation of the main effects and the effect modification.
Competing interests
The authors declare that they do not have any competing interests. Fredrik Nyberg, employed by AstraZeneca, is also Lecturer in Epidemiology at Karolinska Institutet. Astra Zeneca did not contribute any direct financing to this study.
Authors' contributions
AP wrote the first complete draft of the manuscript, has made substantial contributions to the design and the analysis, SvK conducted the analyses, made substantial contributions to the collection and analysis of the data and helped to draft the manuscript, NB made substantial contributions to design and data acquisition (Stockholm), AH made substantial contributions to data acquisition and validation (Augsburg), HL made substantial contributions to design and data acquisition (Augsburg), FN made substantial contributions to design and data acquisition (Stockholm), JP made substantial contributions to design and data acquisition (Helsinki); CAP made substantial contributions to data acquisition (Rome), MS made substantial contributions to data acquisition (Rome), JS made substantial contributions to design and data acquisition (Barcelona), PT made substantial contributions to design and statistical analyses, FF coordinated the project and conceived the design of the study. All authors contributed to the interpretation of the data, helped revising the manuscript, read and approved the final version of the manuscript.
References

Brunekreef B, Holgate ST: Air pollution and health. [Review] [147 refs].
Lancet 2002, 360:12331242. PubMed Abstract  Publisher Full Text

Zanobetti A, Schwartz J, Dockery DW: Airborne particles are a risk factor for hospital admissions for heart and lung disease.
Environ Health Perspect 2000, 108:10711077. PubMed Abstract  PubMed Central Full Text

Zanobetti A, Schwartz J, Gold DR: Are there sensitive subgroups for the effects of airborne particles?
Environ Health Perspect 2000, 108:841845. PubMed Abstract

AnnesiMaesano I, Agabiti N, Pistelli R, Couilliot MF, Forastiere F: Subpopulations at increased risk of adverse health outcomes from air pollution. [Review] [53 refs].
Eur Respir J Suppl 2003, 40:57s63s. PubMed Abstract  Publisher Full Text

Sunyer J, Schwartz J, Tobias A, Macfarlane D, Garcia J, Anto JM: Patients with chronic obstructive pulmonary disease are at increased risk of death associated with urban particle air pollution: a casecrossover analysis.

Goldberg MS, Burnett RT, Bailar JCIII, Tamblyn R, Ernst P, Flegel K, Brook J, Bonvalot Y, Singh R, Valois MF, Vincent R: Identification of persons with cardiorespiratory conditions who are at risk of dying from the acute effects of ambient air particles.

Kwon HJ, Cho SH, Nyberg F, Pershagen G: Effects of ambient air pollution on daily mortality in a cohort of patients with congestive heart failure.
Epidemiology 2001, 12:413419. PubMed Abstract  Publisher Full Text

Bateson TF, Schwartz J: Who is Sensitive to the Effects of Particulate Air Pollution on Mortality?: A CaseCrossover Analysis of Effect Modifiers.
Epidemiology 2004, 15:143149. PubMed Abstract  Publisher Full Text

Klot S, Peters A, Aalto P, Bellander T, Berglind N, D'Ippoliti D, Elosua R, Hörmann A, Kulmala M, Lanki T, Löwel H, Pekkanen J, Picciotto S, Sunyer J, Forastiere F: Ambient air pollution is associated with increased risk of hospital readmissions of myocardial infarction survivors in European cities.
Circulation 2005, 112:30733079. PubMed Abstract  Publisher Full Text

Kwon HJ, Cho SH, Nyberg F, Pershagen G: Effects of ambient air pollution on daily mortality in a cohort of patients with congestive heart failure.
Epidemiology 2001, 12(4):413419. PubMed Abstract  Publisher Full Text

Dominici F, Zeger S, Samet J: A measurement error model for timeseries studies of air pollution and mortality.
Biostatistics 2000, 157175. PubMed Abstract  Publisher Full Text

Ramsay TO, Burnett RT, Krewski D: The effect of concurvity in generalized additive models linking mortality to ambient particulate matter.
Epidemiology 2003, 14:1823. PubMed Abstract  Publisher Full Text

Schwartz J, Zanobetti A, Bateson TF: Mortality and morbidity among eldery residents of cities with daily PM measurements. In Revised Analyses of TimeSeries Studies of Air Pollution and Health. Boston, Health Effects Institute; 2003:2558. [Special Report]

Wood SN, Augustin NH: GAMs with integrated model selection using penalized regression splines and applications to environmental modelling.
Ecological Modelling 2002, 157:157177. Publisher Full Text

Wood SN: Modelling and smoothing parameter estimation with multiple quadratic penalties.
J R Statist Soc B 2000, 62:413428. Publisher Full Text

Wood SN: Thin plate regression splines.
J R Statist Soc B 2003, 65:95114. Publisher Full Text

O'Neill MS, Zanobetti A, Schwartz J: Modifiers of the temperature and mortality association in seven US cities.
Am J Epidemiol 2003, 157:10741082. PubMed Abstract  Publisher Full Text

Navidi W: Bidirectional casecrossover designs for exposures with time trends.
Biometrics 1998, 54:596605. PubMed Abstract  Publisher Full Text

Lumley T, Levy D: Bias in the casecrossover design: implications for studies of air pollution.
Environmetrics 2000, 11:689704. Publisher Full Text

Janes H, Sheppard L, Lumley T: Casecrossover analyses of air pollution exposure data: referent selection strategies and their implications for bias.
Epidemiology 2005, 16:717726. PubMed Abstract  Publisher Full Text

Lepeule J, Rondeau V, Filleul L, Dartigues JF: Survival analysis to estimate association between shortterm mortality and air pollution.
Environ Health Perspect 2006, 114:242247. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Brook RD, Franklin B, Cascio WE, Hong Y, Howard G, Lipsett M, Luepker RV, Mittleman MA, Samet JM, Smith SCJ, Tager IB: Air Pollution and Cardiovascular Disease: A statement of the health care professionals from the expert panel on population and prevention science of the American Heart Association.
Circulation 2004, 109:26552671. PubMed Abstract  Publisher Full Text

Peters A: Susceptible subgroups: the challenge of studying interactions.
Epidemiology 2004, 15:131132. PubMed Abstract  Publisher Full Text

Laden F, Schwartz J, Speizer FE, Dockery DW: Reduction in Fine Particulate Air Pollution and Mortality: Extended Followup of the Harvard Six Cities Study.
Am J Respir Crit Care Med 2006, 173:667672. PubMed Abstract  Publisher Full Text

Jerrett M, Burnett RT, Ma R, Pope CAIII, Krewski D, Newbold KB, Thurston G, Shi Y, Finkelstein N, Calle EE, Thun MJ: Spatial analysis of air pollution and mortality in Los Angeles.
Epidemiology 2005, 16:727736. PubMed Abstract  Publisher Full Text

Gulliver J, Briggs DJ: Timespace modeling of journeytime exposure to trafficrelated air pollution using GIS.
Environ Res 2005, 97:1025. PubMed Abstract  Publisher Full Text

Sahu SK, Gelfand AE, Holland DM: Spatiotemporal modeling of fine particulate matter.
J Agricult Biol Environ Stat 2006, 11:6186. Publisher Full Text