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      Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis


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          The time stratified case cross-over approach is a popular alternative to conventional time series regression for analysing associations between time series of environmental exposures (air pollution, weather) and counts of health outcomes. These are almost always analyzed using conditional logistic regression on data expanded to case–control (case crossover) format, but this has some limitations. In particular adjusting for overdispersion and auto-correlation in the counts is not possible. It has been established that a Poisson model for counts with stratum indicators gives identical estimates to those from conditional logistic regression and does not have these limitations, but it is little used, probably because of the overheads in estimating many stratum parameters.


          The conditional Poisson model avoids estimating stratum parameters by conditioning on the total event count in each stratum, thus simplifying the computing and increasing the number of strata for which fitting is feasible compared with the standard unconditional Poisson model. Unlike the conditional logistic model, the conditional Poisson model does not require expanding the data, and can adjust for overdispersion and auto-correlation. It is available in Stata, R, and other packages.


          By applying to some real data and using simulations, we demonstrate that conditional Poisson models were simpler to code and shorter to run than are conditional logistic analyses and can be fitted to larger data sets than possible with standard Poisson models. Allowing for overdispersion or autocorrelation was possible with the conditional Poisson model but when not required this model gave identical estimates to those from conditional logistic regression.


          Conditional Poisson regression models provide an alternative to case crossover analysis of stratified time series data with some advantages. The conditional Poisson model can also be used in other contexts in which primary control for confounding is by fine stratification.

          Electronic supplementary material

          The online version of this article (doi:10.1186/1471-2288-14-122) contains supplementary material, which is available to authorized users.

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          Most cited references19

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          Case-crossover analyses of air pollution exposure data: referent selection strategies and their implications for bias.

          The case-crossover design has been widely used to study the association between short-term air pollution exposure and the risk of an acute adverse health event. The design uses cases only; for each individual case, exposure just before the event is compared with exposure at other control (or "referent") times. Time-invariant confounders are controlled by making within-subject comparisons. Even more important in the air pollution setting is that time-varying confounders can also be controlled by design by matching referents to the index time. The referent selection strategy is important for reasons in addition to control of confounding. The case-crossover design makes the implicit assumption that there is no trend in exposure across the referent times. In addition, the statistical method that is used-conditional logistic regression-is unbiased only with certain referent strategies. We review here the case-crossover literature in the air pollution context, focusing on key issues regarding referent selection. We conclude with a set of recommendations for choosing a referent strategy with air pollution exposure data. Specifically, we advocate the time-stratified approach to referent selection because it ensures unbiased conditional logistic regression estimates, avoids bias resulting from time trend in the exposure series, and can be tailored to match on specific time-varying confounders.
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            Referent selection in case-crossover analyses of acute health effects of air pollution.

            The case-crossover design was proposed for the study of a transient effect of an intermittent exposure on the subsequent occurrence of a rare acute-onset disease. This design can be an alternative to Poisson time series regression for studying the health effects of fine particulate matter air pollution. Characteristics of time-series of particulate matter, including long-term time trends, seasonal trends, and short-term autocorrelations, require that referent selection in the case-crossover design be considered carefully and adapted to minimize bias. We performed simulations to evaluate the bias associated with various referent selection strategies for a proposed case-crossover study of associations between particulate matter and primary cardiac arrest. Some a priori reasonable strategies were associated with a relative bias as large as 10%, but for most strategies the relative bias was less than 2% with confidence interval coverage within 1% of the nominal level. We show that referent selection for case-crossover designs raises the same issues as selection of smoothing method for time series analyses. In addition, conditional logistic regression analysis is not strictly valid for some case-crossover designs, introducing further bias.
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              On the equivalence of case-crossover and time series methods in environmental epidemiology.

              The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.

                Author and article information

                BMC Med Res Methodol
                BMC Med Res Methodol
                BMC Medical Research Methodology
                BioMed Central (London )
                24 November 2014
                24 November 2014
                : 14
                : 1
                [ ]Department of Social and Environmental Health Research, London School of Hygiene and Tropical Medicine (LSHTM), 15-17 Tavistock Place, London, WC1H 9SH UK
                [ ]Department of Medical Statistics, London School of Hygiene and Tropical Medicine (LSHTM), Keppel Street, London, WC1E 7HT UK
                [ ]Institute of Environmental Assessment and Water Research (IDAEA), Spanish Council for Scientific Research (CSIC), C/Jordi Girona 18-26, 08031 Barcelona, Spain
                © Armstrong et al.; licensee BioMed Central Ltd. 2014

                This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

                Research Article
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                © The Author(s) 2014

                statistics,conditional distributions,poisson regression,time series regression,environment


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