![MathJax Logo](/templates/jsp/_style2/_tandf/pb2/images/math-jax.gif)
Abstract
Asthma is a global public health problem and the most common chronic disease among children. The factors associated with the condition are diverse, and environmental factors appear to be the leading cause of asthma exacerbation and its worsening disease burden. However, it remains unknown how changes in the environment affect asthma over time, and how temporal or environmental factors predict asthma events. The methodologies for forecasting asthma and other similar chronic conditions are not comprehensively documented anywhere to account for semistructured noncausal forecasting approaches. This paper highlights and discusses practical issues associated with asthma and the environment, and suggests possible approaches for developing decision-making tools in the form of semistructured black-box models, which is relatively new for asthma. Two statistical methods which can potentially be used in predictive modeling and health forecasting for both anticipated and peak events are suggested. Importantly, this paper attempts to bridge the areas of epidemiology, environmental medicine and exposure risks, and health services provision. The ideas discussed herein will support the development and implementation of early warning systems for chronic respiratory conditions in large populations, and ultimately lead to better decision-making tools for improving health service delivery.
Introduction
Asthma is a global public health problem and the most common chronic disease among children. It is underdiagnosed and undertreated, and constitutes a huge burden on individuals, societies, and institutions.Citation1–Citation5 Current estimates suggest that as many as 300 million people are affected worldwide,Citation1,Citation6,Citation7 and the burden of this chronic respiratory condition is rising, particularly among children.Citation1,Citation3,Citation5,Citation8,Citation9 Recent reviews on asthma reaffirm the highly heterogeneous nature of the disease, which is also influenced by a number of complex genetic and environmental factors.Citation10 Many of these reviews have comprehensively addressed key factors which contribute to the manifestation and progression of asthma in individuals, as well as laboratory-based experiments.Citation11–Citation13 However, there is little information on the forecasting of asthma events with the purpose of providing early warning systems to help in the management of the condition at the population level.Citation14
Asthma has a predictable prognosis.Citation15 However, its diagnosis remains a challenge because the disease is not clearly defined by a particular set of conditions, but by a mix of several dynamic factors.Citation2,Citation5,Citation16 These include numerous and quite unpredictable underlying genetic and environmental factors,Citation5,Citation17–Citation19 as well as occupational factors.Citation20,Citation21 As a result of the complex nature of the condition, some of the diagnostic techniques commonly used range from history and patterns of symptoms, physical examination, and lung function measurements including spirometry, through to skin test identification of allergens.Citation22
Several studies have shown changes in the global epidemiology of asthma. Developed countries have consistently shown dramatic increases in prevalence, and this change has more recently been observed in some less developed countries as well.Citation3,Citation17,Citation23,Citation24 The United Kingdom National Asthma CampaignCitation25 reported that asthma affected over five million people, ie, about one in every five households. Subsequent reports indicated that the United Kingdom had one of the highest prevalence rates, at over 15%.Citation4 In England, 67,077 people were hospitalized for asthma between April 2006 and March 2007, of whom more than 40% were children under the age of 15 years.Citation26 According to the Hospital Episode Statistics of the Department of Health (January 2001–December 2006), London, which is the busiest and most densely populated area in the United Kingdom, recorded about 57,000 asthma-related hospital admissions over that period, giving a crude annual rate of around 9500 (ie, an absolute estimate).Citation9 This situation presents asthma as an important condition of public health concern, with dimensions not just limited to the individual(s) affected, but also posing a significant burden on health care resources as well as society at large, and therefore a need for preparedness. A significant factor in making preparation is the capacity to forecast what to expect in terms of health systems demands.
The use of algorithms in forecasting, also known as black-box forecasting, provides a novel approach to achieve a better outcome compared with most traditional structural/causal modeling techniques.Citation27 Black-box forecasting involves a theoretical association of predictors with outcomes, the utility of which is strictly based on forecasting performance.Citation28 Because it is theoretical, and can be a computationally exhaustive process, this sometimes leads to overfitting and poor performance on unseen datasets.Citation27,Citation28 On the other hand, structural models account for specific indicators/variables and require substantive knowledge of the subject matter in order to construct an intelligent model.Citation27 They also overemphasize specific causes in an environment in which the complete causal process is poorly understood. Given the two approaches, a balanced semistructured black-box approach can be useful mid path in developing predictive models for health forecasting, where there is some prior knowledge of the relationship between a health condition and its environmental mediators.
We provide a brief overview of asthma and its environmental causes, with perspectives from the United Kingdom pertinent to other countries with similar populations. One of the key aims of the review is the association between asthma and environmental factors which have potential roles in health forecasting. The other is on developing semistructured black-box approaches that are predictive and can hypothetically forecast asthma events.
Literature search and study approach
In preparing this discussion paper, a scoping of the literature on asthma and associated environmental factors, as well as approaches adopted for managing the condition, was conducted using medical-related databases including PubMed (Medline), Web of Science, and Google Scholar. In addition, citation mapping was used to search and retrace the literature from the initially selected key papers and documents. All the papers and documents identified were synthesized and summarized according to the objective of this paper.
The paper presents reviewed literature on asthma, with a focus on environmental triggers which have been reported, particularly for their effects on respiratory health, including highlights from studies that support the links between environment and health. It further illustrates a wider scope of factors associated with asthma and the manifestation of its symptoms in a framework. The second part of the paper focuses on describing proposed statistical approaches for developing predictive forecasting models. One of these approaches (the negative binomial regression predictive model) is exemplified using data on daily admissions for asthma in London (2001–2006) as well as synthetically generated temporal dummy variables. The paper also briefly discusses a variety of selection strategies for predictive modeling.
Asthma and the environment
Local environmental conditions are important in determining the impact or manifestation of asthma. Factors such as temperature, humidity, and air pressure, as well as air pollutants, all interact to affect the occurrence of asthma, but do not have exclusively independent effects on the condition.Citation12,Citation29–Citation32 The impact of these complex environmental factors and their interrelationships in health has never been fully understood, even though understanding the key pathways of some individual factors has played an important role in developing a number of therapies.Citation11,Citation12 The Department of Health and the then Health Protection Agency in the United Kingdom published a review of the health effects of climate change in 2008.Citation33 In the report, two component issues of the environment, which are principally of interest, are weather and air quality, and these were both considered. It is noted that the constituent indicators of temperature, humidity, vapor/atmospheric pressure, wind, and atmospheric aerosols can produce polluted environments, which are usually recognized as mist, fog, or smog.Citation34 Hence, environmental pollution and dynamics can exacerbate asthma in many ways,Citation35,Citation36 and some of the mechanisms involved in this have been discussed subsequently.
Health conditions triggered by local environmental changes, including indoor conditions, as well as occupational exposures vary considerably in their effects and symptoms. These effects are known to depend primarily on the individual’s susceptibility and level of exposure to environmental conditions.Citation20,Citation21,Citation37–Citation40 Vulnerable groups within given populations, particularly childrenCitation41,Citation42 and the elderly, tend to be the hardest hit, with the former experiencing both direct and indirect effects of these environmental changes.Citation39,Citation43 The evidence for environmental effects on health is based on five main types of study:Citation44
health impacts associated with extreme events (eg, heat waves/extreme cold, floods, storms, droughts)
spatial studies where climate is an explanatory variable in the distribution of the disease or the disease vector
temporal studies assessing the health effects of change in climate or weather
experimental laboratory and field studies of vector, pathogen, or plant (allergen) biology
intervention studies that investigate the effectiveness of public health measures to protect people from environmental exposures.Citation45
These types of studies have demonstrated the need to understand fully the health effects of weather and air quality.Citation46 Thus, dynamic states of weather and air pollutants, which have demonstrated some effect(s) on asthma and its severity in the past, are useful in predicting future occurrences of the condition. Various quantitative procedures have been used to estimate some of these known relationships between a given health condition, such as asthma, and its potential effects.Citation47,Citation48
Climate generally affects health,Citation49 and there is ample evidence of the effect of temperature changes, barometric pressure, and relative humidity on the worsening of asthma symptoms.Citation50–Citation58 Many of these studies have used the association between weather and disease incidence, hospitalization, or mortality to examine the relationship. For instance, the effect of temperature on general practitioner consultations for respiratory disease was observed, and it was found that there could be up to 15 days of delayed effect of cold temperatures on the incidence of respiratory illness.Citation59 Also, constant seasonal variability in asthma admissions among children was found in Athens, Greece, where relative humidity and atmospheric pressure were established as key determinants.Citation60
The relationship between asthma and environmental conditions is affected in complex ways, and it is worth noting that these effects have different associations depending on location. Asthma events in Mexico, for instance, are associated with the rainy season, whilst in England and Wales, asthma events are more strongly associated with seasonal temperature change rather than rainfall.Citation54,Citation57 Furthermore, it has been observed in the United Kingdom and Taiwan that peaks in asthma events occur in the winter and autumn seasons, but not in summer.Citation59,Citation61,Citation62 Given the importance of context, it becomes critical to understand local relationships between asthma, weather, air quality, and season. However, even when local relationships are well understood, it remains difficult to predict extreme asthma events, ie, unusual peaks in asthma events that fall outside the usual fluctuations associated with seasonal changes and variations in weather and air quality. Forecasting these risks is complex and uncertain, but also requires specific data on a very long-term basis.Citation63 Meanwhile, the use of semistructured black-box approaches in forecasting routine and/or extreme asthma events has not been comprehensively explored.
The issues discussed above are quite global in many respects. The hypothetical flow diagram () illustrates the relationship between asthma symptoms and immediate or underlying causes. Asthma is manifested by an inflammation and/or subsequent obstruction of air flow within the respiratory system.Citation64,Citation65 It is known that inflammation of the airways in an individual can result in asthmatic symptoms. Alternatively, inflammation may lead to obstruction of air flow directly or indirectly by causing hyperresponsiveness of the airways, ie, a state characterized by easily triggered contraction of the small airways (spasm), which may then cause obstruction of the airways.
Predicting asthma episodes in an ideal situation would require that we account for all the “known” potential predictors/indicators, which of course includes all immediate and underlying mediating factors. However, the availability of data that is usable is a common limitation. These factors and interrelationships, as illustrated in , may present some clues to data sources that can be mined and used for forecasting asthma.
Semistructured black-box modeling
Among the many health issues that can be forecast, the need for emergency care is the commonest form of health forecasting.Citation66–Citation71 This is particularly related to hospital bed occupancy or number of visits to the emergency room. Although popular, there have been some challenges associated with forecasting the demand for emergency department services. However, this paper does not necessarily focus on these lapses, given that they have been discussed more elaborately elsewhere.Citation72
The number of daily asthma admissions or routine measures for similar health conditions can be presented as integer value indicators (also referred to as rate data). This type of count data is common in many disciplines, can form a time series, and thus be used for causal or predictive modeling and forecasting.
Causal models are constructed to provide an explanation of model parameters. Hence, for a given outcome variable, Y will be defined by a function of the variables (X) known to have causal links with the dependent (outcome) variable Y, plus random noise and then the parameter error (EquationEquation 1(1) ). In relation to asthma (), Y could be represented as “primary care provider visit” for affected individuals, whilst X could be any one or more underlying causes (eg, air quality, weather, and temporal factors) associated with the affected individuals. The autoregressive integrated moving average (ARIMA) is the commonest technique used in this kind of health forecasting.
In the black-box approach to modeling, formulation of the predictive model does not require prior knowledge of causal links. As illustrated in , the process of predicting an outcome involves generation of suitable predictors and models, which are then validated before use in predictions.
There are more studies on causal (structural) modeling than on predictive (black-box) modeling, but the focus of this paper is on semistructured black-box modeling. For the latter approach, even though selection of variables is based originally on prior knowledge, it may also include important predictive factors/variables that have no causal relationship merely because those that end up being used in forecasting are based on their predictive capacity and not just on conformance to a particular theoretical relationship(s). This means that the approach is data-driven. Although data-driven approaches have sometimes created quite tense disagreements between causal modelers and predictive modelers, both approaches have their roles, and in the empirical forecasting and data mining areas, data-driven approaches are generally regarded as superior for the purposes of forecasting and out-of-sample prediction.Citation28 In some specific context (as in the use of negative binomial models which is described subsequently), their outputs could still have an extended or additional use for describing relationships in past data.
In modeling, count regression models, such as the Poisson or negative binomial model, are most suitable. This is because they have the advantages of being able to handle time series data and their autocorrelations, whilst adjusting for any potential intercorrelation between dependent and independent predictors.Citation73 Generally, count models are estimated using the maximum likelihood, which computationally proceeds iteratively until there is a convergence of the log likelihood.Citation74,Citation75 The exact choice of an appropriate count model depends on many factors which are directly related to the properties of the primary variable, such as the skewness of the distribution (kernel density) and the proportion and distribution of “0s” within the dataset. illustrates two major pathways for selecting a suitable count model, ie, a step-by-step approach and a one-stop test selection criterion, which involves the likelihood approach suggested by Long and Freese,Citation75 and is also available as an application in Stata statistical software.Citation76
Using a sample of hospital admission data on asthma, two statistical methods are proposed, ie, a negative binomial model and a quantile regression model, for the development of predictive forecasting models that are aimed at predicting a future/anticipated event(s) and at predicting peak events. The asthma dataset has already been described elsewhere in the nationally recorded hospital episode statistics maintained by the National Health Service in the United Kingdom,Citation77 and has also been used in some preliminary studies.Citation9,Citation78 Other data sources from which potential predictors could be extracted or derived include environmental data containing routine measures of weather and air quality indicators. Such data are accessible from the databases of the United Kingdom Meteorological Office. Additional variables (eg, temporal effects like day of the week or month of the year) can also be generated in addition to these data, to help in further investigations.
Predictive modeling with negative binomial models
Negative binomial models are applicable in developing both univariate and multivariate forecasting models. Given an expected number of daily admissions for asthma, the negative binomial regression can be presented in the form:
where λ is the mean of the distribution, α is the over dispersion parameter, y is the number of daily asthma admissions, and Γ is the gamma function.
A positive coefficient in the regression output indicates that a factor will increase the number of daily asthma admissions relative to its reference category. Conversely, a negative coefficient will decrease the number of daily asthma admissions relative to its reference category. The exponent of the coefficient can be interpreted, all other things being equal, as the proportionate increase (for values > 1) or decrease (for values between 0 and 1) in number of daily asthma admissions associated with a one unit increase in the explanatory variable.Citation9,Citation79 Obtaining an improved fit for a model in this situation can be established by inspecting the Akaike information criterion.Citation9,Citation14,Citation80–Citation82
To exemplify this proposed approach, we present an analysis and outputs based on hospital episode statistics data on asthma in London, which have been described elsewhere.Citation9 The dataset, which contains nonidentifiable individual records of asthma patients visiting their general practitioner or the emergency department, was transposed by daily sums to provide a time series dataset of total daily attendance. For the purpose of convenience, and also because of the lack of compatible and adequate data on other potential predictors of asthma already mentioned in the literature above (), we only illustrate with a temporal predictive model (ie, multivariable model based on temporal factors). The temporal factors we considered included seasons (spring, summer, autumn, and winter), month of the year (January, February through December) and day of the week (Sunday, Monday through Saturday), which were synthetically generated from the date of attendance record using statistical software.Citation76
A hold-in sample of the data was used in model development, and validation was done with a hold-out sample of the data from January 1, 2006 to December 31, 2006. Three bivariate and four multivariate predictive models were generated ( and , Appendix 1) and compared based on their Akaike information criterion (). These models were cross-validated with the hold-out dataset. For instance, in , the light blue (or gray) time series plot shows total daily asthma admissions in the London area, and the red (or dark) plot shows the predicted multivariate model based on month and week day. However, shows the validation output. The predicted plot reasonably tracks the real distribution of asthma admissions, although it misses out on extreme variations. Even though the focus of the work is on predictive modeling and not causal modeling, the negative binomial regression outputs for these models are also presented ( and ).
Figure 4 Asthma daily admissions and predictive model based on month and week day. (A) Model development sample (hold-in dataset). (B) Model validation sample (hold-out dataset).
![Figure 4 Asthma daily admissions and predictive model based on month and week day. (A) Model development sample (hold-in dataset). (B) Model validation sample (hold-out dataset).](/cms/asset/6d5b3643-d3c5-4b1b-b20a-7884b587aeab/dijg_a_34647_f0004_c.jpg)
Figure 5 Asthma daily admissions and predictive model based on season month and week day. (A) Model development sample (hold-in dataset). (B) Model validation sample (hold-out dataset).
![Figure 5 Asthma daily admissions and predictive model based on season month and week day. (A) Model development sample (hold-in dataset). (B) Model validation sample (hold-out dataset).](/cms/asset/be25c79b-6e49-4e43-a54d-969b9f8c6bc5/dijg_a_34647_f0005_c.jpg)
Table 1 Bivariate temporal models of daily asthma admissions in London for 2001–2005
Table 2 Multivariable temporal models of asthma daily admissions in London, 2001–2005
Table 3 Comparison of model fitness using the Akaike information criterion
Findings from the Akaike information criterion model fitness tests () show that the “day of the week model” (III) was the least performing model, whilst the VI and VII multivariate models outperformed all the others, and by as much as 2.4% of III in the hold-in data and over 6.6% in the holdout dataset. Model V was slightly better than both II and IV in the hold-in dataset, and conversely less fit than the latter in the hold-out dataset. Temporal factors have been used to predict exacerbations of chronic respiratory diseases, such as asthma and chronic obstructive pulmonary disease.Citation83 In addition to temporal factors, other studies have used allergens, weather, and air quality factors in specific areas to predict asthma hospital admissions.Citation84–Citation86 Hence our findings should be interpreted with caution because the dataset used represents a large and diverse population for London, and does not account for other important predictors of asthma, such as weather and air quality. Nonetheless, predicting asthma events can have policy implications for planning and executing health care delivery. This may then produce some indirect benefits pertaining to health budgets and resource allocation.
Forecasting extreme events with quantile regression models
This paper also proposes the use of quantile regression models in forecasting peak events as a more ideal approach compared with others. Quantile regression is an extension of the linear model, and is better equipped to characterize the relationship between a response distribution and explanatory variable(s) for selective quintiles.Citation87–Citation89 It has been used more extensively in other areas of forecasting, but has yet to be fully tapped in health forecasting. Quantile regression models can be considered as fitting a linear model to a cross-section of the data/distribution within the anticipated range.
Using the asthma data as an example, for a peak number of daily admissions, the quantile regression model is presented in the form:
where Yi is asthma hospital admissions for a given day, β0 (p) is a constant term, β1 (p) is a coefficient of exposure term, xi is the exposure term, ɛi (p) is the error term, and p is the quantile. Further illustration of the quantile regression model equation above is available elsewhere.Citation88,Citation89
The pseudo R2 (comparable with the R2 for least-squares procedures)Citation14 is the coefficient of determination for quantile regression, and it represents the goodness-of-fit statistic, which is most appropriate for comparing models of specific quantiles.Citation90,Citation91 It is based on change in the deviance statistic, and ranges between 0 and 1. The pseudo R2 is thus estimated as:
Variable selection approaches
The variable selection approach is critical in modeling because it determines the final functional form, which is subsequently used for forecasting. As discussed earlier, there is a wide range of environment-related variables known to influence the incidence and/or exacerbation of asthma and other respiratory illnesses. However, common limitations in using environmental measures to forecast a wide population health issue like asthma include a reliable data source and its quality, as well as the extent to which these measures can represent an individual’s level of exposure. The inclusion of temporal components as independent factors in a predictive model (eg, day of the week, month, season), accounts for any temporal kinetics and also allows for the identification of lag times, which may improve predictions.Citation78,Citation92
There are equally unlimited approaches that can be adopted for the selection of variables in predictive modeling. Citation27 These approaches range from selection by convenience to computationally exhaustive searches for the best combination of predictors.Citation27,Citation28 The selection of potential predictors can also be biased by our common understanding of the mechanisms by which environmental agents cause diseases, particularly for respiratory illnesses. However, the ultimate goal is that one obtains a reliable and parsimonious forecasting model.
Backward elimination is one of the commonest approaches utilized to select an appropriate model. This method involves a systematic and/or automatic procedure of reducing a base model, ie, a multivariable model consisting of all possible predictors that are either independently strongly correlated with the dependent variable, or are of already known importance (ie, removing variables that are not statistically significant), while ensuring that the fit (ie, with either AIC or pseudo-R2) is improved or at least maintained.
Another strategy of variable selection in modeling is to conduct an exhaustive search of the best fitting model using all possible combinations of the available predictors. This approach is however computationally intensive and has a very high chance of over fitting the model. Nonetheless, such computationally exhaustive approaches are most adapted to the novel idea of semistructured black-box models.Citation28
Conclusion
Asthma poses a great burden to populations. Discrete measures of the incidence of the disease can be used for forecasting. Though environmental factors have specific effects on the disease, and these effects often vary by location, they may still provide supplementary variables for developing a forecast.
Two methods for developing predictive models as well as variable selection strategies, which have potential roles in semistructured black-box forecasting models, have been discussed. Both negative binomial models and quantile regression models are applicable to integer value health indicators (eg, total daily hospital admissions records). The negative binomial models predict anticipated events, whilst quantile regression models are designed to predict peculiar events. These kinds of forecast models vary in their complexity and methods, depending on the specific health condition and population data. The idea of semistructured black-box predictive modeling may stimulate further research on asthma and, possibly, health forecasting.
Disclosure
The authors declare they have no competing interests in this work.
References
- Global Initiative for AsthmaGlobal Strategy for Asthma Management and Prevention2008 Available from: http://www.ginasthma.com/Guidelineitem.asp??l1=2&l2=1&intId=60Accessed February 1, 2009
- KaurBAndersonHRAustinJPrevalence of asthma symptoms, diagnosis, and treatment in 12–14 year old children across Great Britain (international study of asthma and allergies in childhood, ISAAC UK)BMJ199831671251181249462318
- PearceNAit-KhaledNBeasleyRWorldwide trends in the prevalence of asthma symptoms: Phase III of the International Study of Asthma and Allergies in Childhood (ISAAC)Thorax200762975876617504817
- MasoliMFabianDHoltSBeasleyRThe global burden of asthma: executive summary of the GINA Dissemination Committee reportAllergy200459546947815080825
- SubbaraoPMandhanePJSearsMRAsthma: epidemiology, etiology and risk factorsCMAJ20091819E181E19019752106
- FantaCHAsthmaN Engl J Med2009360101002101419264689
- DoughertyRHFahyJVAcute exacerbations of asthma: epidemiology, biology and the exacerbation-prone phenotypeClin Exp Allergy200939219320219187331
- NevilleRGMcCowanCHoskinsGThomasGCross-sectional observations on the natural history of asthmaBr J Gen Pract20015146636136511360699
- SoyiriINReidpathDDSarranCAsthma length of stay in hospitals in London 2001–2006: demographic, diagnostic and temporal factorsPLoS One2011611e2718422073282
- EditorialA fresh perspective on asthmaNat Med201218563122561801
- HoltPGSlyPDViral infections and atopy in asthma pathogenesis: new rationales for asthma prevention and treatmentNat Med201218572673522561836
- HolgateSTInnate and adaptive immune responses in asthmaNat Med201218567368322561831
- RodrigoGJRodrigoCHallJBAcute asthma in adults: a reviewChest200412531081110215006973
- SoyiriINReidpathDDEvolving forecasting classifications and applications in health forecastingInt J Gen Med20125138138922615533
- PanettieriRAJrCovarRGrantEHillyerEVBacharierLNatural history of asthma: persistence versus progression – does the beginning predict the end?J Allergy Clin Immunol2008121360761318328890
- FishwickDCurranADVariability in the diagnosis of occupational asthma and implications for clinical practiceCurr Opin Allergy Clin Immunol20088214014418317022
- HolgateSTThe epidemic of asthma and allergyJ R Soc Med200497310311014996954
- GalantSPCrawfordLJRMorphewTJonesCABassinSPredictive value of a cross-cultural asthma case-detection tool in an elementary school populationPediatrics20041143e307e31615342891
- GaffinJMPhipatanakulWThe role of indoor allergens in the development of asthmaCurr Opin Allergy Clin Immunol20099212813519326507
- DarbyACWaterhouseJCStevensVChronic obstructive pulmonary disease among residents of an historically industrialised areaThorax2012 Epub 2012 Jun 28
- FishwickDBarberCMDarbyACChronic obstructive pulmonary disease and the workplaceChron Respir Dis20107211312220185481
- British Thoracic Society Scottish Intercollegiate Guidelines NBritish guideline on the management of asthmaThorax200863Suppl 4iv1iv12118463203
- HolgateSTLessons learnt from the epidemic of asthmaQJM200497524725715100418
- NowakDSuppli UlrikCvon MutiusEAsthma and atopy: has peak prevalence been reached?Eur Respir J200423335936015065820
- National Asthma CampaignOut in the open: a true picture of asthma in the United Kingdom todayAsthma Journal20016Suppl 3314
- AsthmaUKWish you were here2008 Available from: http://www.asthma.org.uk/media/141047/wish_you_were_here__-_uk_report.pdfAccessed July 29, 2012
- ChatfieldCThe Analysis of Time Series: An Introduction6th edLondon, UKCRC Press2004
- BreimanLStatistical modeling: the two culturesStat Sci2001163199215
- MaLShimaMYodaYEffects of airborne particulate matter on respiratory morbidity in asthmatic childrenJ Epidemiol20081839711018490839
- ParkerJDAkinbamiLJWoodruffTJAir pollution and childhood respiratory allergies in the United StatesEnviron Health Perspect2009117114014719165401
- DietteGBMcCormackMCHanselNNBreyssePNMatsuiECEnvironmental issues in managing asthmaRespir Care200853560261518426614
- GentJFTricheEWHolfordTRAssociation of low-level ozone and fine particles with respiratory symptoms in children with asthmaJAMA2003290141859186714532314
- Department of Health, Health Protection AgencyHealth effects of climate change in the UK 2008: An update of the Department of Health report 2001/2002Department of Health, Health Protection Agency12292008 Available from: http://www.dh.gov.uk/en/Publicationsandstatistics/Publications/PublicationsPolicyAndGuidance/DH_080702Accessed July 29, 2012
- Met OfficeClimate science explained, 2009Pope V, Haywood J, climate scientists discussants Available from: http://www.metoffice.gov.uk/climatechange/science/explained/index.htmlAccessed February 1, 2009
- LinSGomezMIHwangS-AMunsieJPFitzgeraldEFSelf-reported home environmental risk factors for childhood asthma: a cross-sectional study of children in Buffalo, New YorkJ Asthma200845432533218446598
- BecklakeMRErnstPEnvironmental factorsLancet1997350S10S13
- ZekaAEisenEAKriebelDGoreRWegmanDHRisk of upper aerodigestive tract cancers in a case-cohort study of autoworkers exposed to metalworking fluidsOccup Environ Med200461542643115090663
- FouilletAReyGWagnerVHas the impact of heat waves on mortality changed in France since the European heat wave of summer 2003? A study of the 2006 heat waveInt J Epidemiol200837230931718194962
- KovatsRSHajatSHeat stress and public health: a critical reviewAnnu Rev Public Health200829415518031221
- KoskelaHOCold air-provoked respiratory symptoms: the mechanisms and managementInt J Circumpolar Health20076629110017515249
- RaphozMGoldbergMSGarneauMHéguyLValoisM-FGuayFAssociations between atmospheric concentrations of spores and emergency department visits for asthma among children living in MontrealArch Environ Occup Health201065420121021186425
- HéguyLGarneauMGoldbergMSRaphozMGuayFValoisM-FAssociations between grass and weed pollen and emergency department visits for asthma among children in MontrealEnviron Res2008106220321118093580
- O’SheaSDTaylorNFParatzJDBut watch out for the weather: factors affecting adherence to progressive resistance exercise for persons with COPDJ Cardiopulm Rehabil Prev200727316617417558200
- MenneBKovatsSBellJClimate change and health: international research agendaEuropean Preparatory Meeting for the Global Ministerial Forum on Research for HealthCopenhagen, DenmarkApril 29–30, 2008
- Intergovernmental Panel on Climate Change, Andy Jorgensen, lead author IPCC Fourth Assessment Report, Working Group II: Chapter 8 Encyclopedia of EarthClevelandCJWashington, DC: Environmental Information Coalition, National Council for Science and the EnvironmentWashington, DCEncyclopedia of Earth2010
- SauerbornRClimate change: an agenda for research and teaching in public healthScand J Public Health200735656156318030648
- SchonwetterRSClarkLDLeedySAQuinnMJAzerMKimSPredicting emergency room visits and hospitalizations among hospice patients with cardiac diseaseJ Palliat Med20081181142115018980456
- TobiasASaezMGalanICampbellMJSensitivity analysis of common statistical models used to study the short-term effects of air pollution on healthInt J Biometeorol200347422722912687451
- Intergovernmental Panel on Climate ChangeAssessing the Health Impacts of Climate ChangeGeneva, SwitzerlandWorld Meteorological Organization/United Nations Environment Programme1995
- StorrJLenneyWSchool holidays and admissions with asthmaArch Dis Child19896411031072923458
- RossiOVKinnulaVLTienariJHuhtiEAssociation of severe asthma attacks with weather, pollen, and air pollutantsThorax19934832442488497823
- EptonMJMartinIRGrahamPClimate and aeroallergen levels in asthma: a 12 month prospective studyThorax19975265285349227719
- HalesSLewisSSlaterTCraneJPearceNPrevalence of adult asthma symptoms in relation to climate in New ZealandEnviron Health Perspect199810696076109722625
- WeilandSKHusingAStrachanDPRzehakPPearceNClimate and the prevalence of symptoms of asthma, allergic rhinitis, and atopic eczema in childrenOccup Environ Med200461760961515208377
- ChavarriaJFShort report: asthma admissions and weather conditions in Costa RicaArch Dis Child200184651451511369573
- IveyMASimeonDTMonteilMAClimatic variables are associated with seasonal acute asthma admissions to accident and emergency room facilities in Trinidad, West IndiesClin Exp Allergy200333111526153014616864
- KhotABurnREvansNLenneyWStorrJBiometeorological triggers in childhood asthmaClin Allergy19881843513583416418
- JohnstonNWSearsMRAsthma exacerbations. 1: EpidemiologyThorax200661872272816877691
- HajatSHainesAAssociations of cold temperatures with GP consultations for respiratory and cardiovascular disease amongst the elderly in LondonInt J Epidemiol200231482583012177030
- PriftisKNPaliatsosAGPanagiotopoulou-GartaganiPAssociation of weather conditions with childhood admissions for wheezy bronchitis or asthma in AthensRespiration200673678379016763383
- Hospital Episode Statistics onlineAsthma, Health and seasonsHealth and Social Care Information Centre2009 Available from: http://www.hesonline.nhs.uk/Ease/servlet/ContentServer?siteID=1937&categoryID=972Accessed January 1, 2009
- YangC-YChenC-CChenC-YKuoH-WAir pollution and hospital admissions for asthma in a subtropical city: Taipei, TaiwanJ Toxicol Environ Health A200770211111717365571
- KimJHaJ-SJunSParkT-SKimHThe weather watch/warning system for stroke and asthma in South KoreaInt J Environ Health Res200818211712718365801
- Global Initiative for AsthmaGlobal Burden of Asthma2004 Available from: http://www.ginasthma.com/download.asp?intid=29Accessed February 1, 2009
- HolgateSTComminsBTAndersonHRAsthma and Outdoor Air PollutionLondon, UKDepartment of Health Committee on the Medical Effects of Air Pollutants1995 Available from: http://www.comeap.org.uk/documents/reports.htmlAccessed August 13, 2012
- JonesSAJoyMPPearsonJForecasting demand of emergency careHealth Care Manage Sci200254297305
- BoyleJJessupMCrillyJPredicting emergency department admissionsEmerg Med J201229535836521705374
- BibiHNutmanAShoseyovDPrediction of emergency department visits for respiratory symptoms using an artificial neural networkChest200212251627163212426263
- BlaisdellCJWeissSRKimesDSUsing seasonal variations in asthma hospitalizations in children to predict hospitalization frequencyJ Asthma200239756757512442946
- SchweiglerLMDesmondJSMcCarthyMLBukowskiKJIonidesELYoungerJGForecasting models of emergency department crowdingAcad Emerg Med200916430130819210488
- WilerJLGriffeyRTOlsenTReview of modeling approaches for emergency department patient flow and crowding researchAcad Emerg Med201118121371137922168201
- McCarthyMLZegerSLDingRAronskyDHootNRKelenGDThe challenge of predicting demand for emergency department servicesAcad Emerg Med200815433734618370987
- NovikovIKalter-LeiboviciOChetritAStavNEpsteinYWeather conditions and visits to the medical wing of emergency rooms in a metropolitan area during the warm season in Israel: a predictive modelInt J Biometeorol201156112112721267601
- LongJSFreeseJPredicted probabilities for count modelsStata J2001115157
- LongJSFreeseJRegression Models for Categorical Dependent Variables Using StataCollege Station, TXStata Press2003
- StataSERelease 11. Statistical SoftwareCollege Station, TXStataCorp LP2009
- Hospital Episode Statistics. HES User GuideHealth and Social Care Information Centre2008 Available from: http://www.hesonline.nhs.ukAccessed July 29, 2009
- SoyiriINReidpathDDPredicting extreme asthma events in London using quantile regression modelsEmerg Health Threats J201141623940
- HilbeJMNegative Binomial Regression2nd edCambridge, UKCambridge University Press2011
- BurgJGSeasonal activity and spatial distribution of host-seeking adults of the tick Dermacentor variabilisMed Vet Entomol200115441342111776460
- GrayBHaroRRogalaJAddressing among-group variation in covariate effects using multilevel modelsEnviron Ecol Stat2009174573591
- CameronACTrivediPKEssentials of Count Data RegressionMalden, MABlackwell Publishing Ltd2007
- MoineddinRNieJDombGLeongAUpshurRSeasonality of primary care utilization for respiratory diseases in Ontario: A time-series analysisBMC Health Services Res200881160
- SheppardLLevyDNorrisGLarsonTVKoenigJQEffects of ambient air pollution on nonelderly asthma hospital admissions in Seattle, Washington, 1987–1994Epidemiology199910123309888276
- RaphozMGoldbergMSGarneauMHéguyLValoisM-FGuayFAssociations between atmospheric concentrations of spores and emergency department visits for asthma among children living in MontrealArch Environ Occup Health201065420121021186425
- NastosPTWeather, ambient air pollution and bronchial asthma in Athens, GreeceThomsonMHerreraRGBenistonMSeasonal Forecasts, Climatic Change and Human Health. Health and Climate. Series: Advances in Global Change ResearchNew York, NYSpringer2006
- BarbosaSMQuantile trends in Baltic sea levelGeophys Res Lett200835L22704
- HaoLNaimanDQQuantile regressionQuantitative Applications in the Social SciencesThousand Oaks, CASage Publications Inc2007
- KoenkerRQuantile RegressionNew York, NYCambridge Press2005
- ZietzJZietzESirmansGDeterminants of house prices: a quantile regression approachJ Real Estate Finan Econ2008374317333
- BarnesMLHughesAWA quantile regression analysis of the cross section of stock market returnsEconPapers No 02-2, Working PapersFederal Reserve Bank of Boston2002 [updated June 6, 2012]. Available from: http://EconPapers.repec.org/RePEc:fip:fedbwp:02-2Accessed November 1, 2010
- RaclozVRamseyRTongSHuWSurveillance of dengue fever virus: a review of epidemiological models and early warning systemsPLoS Negl Trop Dis201265e164822629476