Extending distributed lag models to higher degrees.
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ABSTRACT:
SUBMITTER: Heaton MJ
PROVIDER: S-EPMC3944968 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundMeasures of attributable risk are an integral part of epidemiological analyses, particularly when aimed at the planning and evaluation of public health interventions. However, the current definition of such measures does not consider any temporal relationships between exposure and risk. In this contribution, we propose extended definitions of attributable risk within the framework of distributed lag non-linear models, an approach recently proposed for modelling delayed associations in either linear or non-linear exposure-response associations.MethodsWe classify versions of attributable number and fraction expressed using either a forward or backward perspective. The former specifies the future burden due to a given exposure event, while the latter summarizes the current burden due to the set of exposure events experienced in the past. In addition, we illustrate how the components related to sub-ranges of the exposure can be separated.ResultsWe apply these methods for estimating the mortality risk attributable to outdoor temperature in two cities, London and Rome, using time series data for the periods 1993-2006 and 1992-2010, respectively. The analysis provides estimates of the overall mortality burden attributable to temperature, and then computes the components attributable to cold and heat and then mild and extreme temperatures.ConclusionsThese extended definitions of attributable risk account for the additional temporal dimension which characterizes exposure-response associations, providing more appropriate attributable measures in the presence of dependencies characterized by potentially complex temporal patterns.
| S-EPMC4021419 | biostudies-literature
Project description:Distributed lag models (DLMs) have been widely used in environmental epidemiology to quantify the lagged effects of air pollution on a health outcome of interest such as mortality and morbidity. Most previous DLM approaches only consider one pollutant at a time. In this article, we propose distributed lag interaction model (DLIM) to characterize the joint lagged effect of two pollutants. One natural way to model the interaction surface is by assuming that the underlying basis functions are tensor products of the basis functions that generate the main-effect distributed lag functions. We extend Tukey's one-degree-of-freedom interaction structure to the two-dimensional DLM context. We also consider shrinkage versions of the two to allow departure from the specified Tukey's interaction structure and achieve bias-variance tradeoff. We derive the marginal lag effects of one pollutant when the other pollutant is fixed at certain quantiles. In a simulation study, we show that the shrinkage methods have better average performance in terms of mean squared error (MSE) across different scenarios. We illustrate the proposed methods by using the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) data to model the joint effects of PM10 and O3 on mortality count in Chicago, Illinois, from 1987 to 2000.
| S-EPMC6328049 | biostudies-literature
Project description:In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure-lag-response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others.
| S-EPMC4098103 | biostudies-literature
Project description:Distributed lag models are useful in environmental epidemiology as they allow the user to investigate critical windows of exposure, defined as the time periods during which exposure to a pollutant adversely affects health outcomes. Recent studies have focused on estimating the health effects of a large number of environmental exposures, or an environmental mixture, on health outcomes. In such settings, it is important to understand which environmental exposures affect a particular outcome, while acknowledging the possibility that different exposures have different critical windows. Further, in studies of environmental mixtures, it is important to identify interactions among exposures and to account for the fact that this interaction may occur between two exposures having different critical windows. Exposure to one exposure early in time could cause an individual to be more or less susceptible to another exposure later in time. We propose a Bayesian model to estimate the temporal effects of a large number of exposures on an outcome. We use spike-and-slab priors and semiparametric distributed lag curves to identify important exposures and exposure interactions and discuss extensions with improved power to detect harmful exposures. We then apply these methods to estimate the effects of exposure to multiple air pollutants during pregnancy on birthweight from vital records in Colorado.
| S-EPMC10724118 | biostudies-literature
Project description:Distributed lag models (DLMs) have been widely used in environmental epidemiology to quantify the lagged effects of air pollution on an outcome of interest such as mortality or cardiovascular events. Generally speaking, DLMs can be applied to time-series data where the current measure of an independent variable and its lagged measures collectively affect the current measure of a dependent variable. The corresponding distributed lag (DL) function represents the relationship between the lags and the coefficients of the lagged exposure variables. Common choices include polynomials and splines. On one hand, such a constrained DLM specifies the coefficients as a function of lags and reduces the number of parameters to be estimated; hence, higher efficiency can be achieved. On the other hand, under violation of the assumption about the DL function, effect estimates can be severely biased. In this article, we propose a general framework for shrinking coefficient estimates from an unconstrained DLM, that are unbiased but potentially inefficient, toward the coefficient estimates from a constrained DLM to achieve a bias-variance trade-off. The amount of shrinkage can be determined in various ways, and we explore several such methods: empirical Bayes-type shrinkage, a hierarchical Bayes approach, and generalized ridge regression. We also consider a two-stage shrinkage approach that enforces the effect estimates to approach zero as lags increase. We contrast the various methods via an extensive simulation study and show that the shrinkage methods have better average performance across different scenarios in terms of mean squared error (MSE).We illustrate the methods by using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) to explore the association between PM$_{10}$, O$_3$, and SO$_2$ on three types of disease event counts in Chicago, IL, from 1987 to 2000.
| S-EPMC6454578 | biostudies-literature
Project description:Prolonged exposures can have complex relationships with health outcomes, as timing, duration, and intensity of exposure are all potentially relevant. Summary measures such as cumulative exposure or average intensity of exposure may not fully capture these relationships. We applied penalized and unpenalized distributed-lag nonlinear models (DLNMs) with flexible exposure-response and lag-response functions in order to examine the association between crystalline silica exposure and mortality from lung cancer and nonmalignant respiratory disease in a cohort study of 2,342 California diatomaceous earth workers followed during 1942-2011. We also assessed associations using simple measures of cumulative exposure assuming linear exposure-response and constant lag-response. Measures of association from DLNMs were generally higher than those from simpler models. Rate ratios from penalized DLNMs corresponding to average daily exposures of 0.4 mg/m3 during lag years 31-50 prior to the age of observed cases were 1.47 (95% confidence interval (CI): 0.92, 2.35) for lung cancer mortality and 1.80 (95% CI: 1.14, 2.85) for nonmalignant respiratory disease mortality. Rate ratios from the simpler models for the same exposure scenario were 1.15 (95% CI: 0.89, 1.48) and 1.23 (95% CI: 1.03, 1.46), respectively. Longitudinal cohort studies of prolonged exposures and chronic health outcomes should explore methods allowing for flexibility and nonlinearities in the exposure-lag-response.
| S-EPMC6030974 | biostudies-literature
Project description:Built environment factors constrain individual level behaviors and choices, and thus are receiving increasing attention to assess their influence on health. Traditional regression methods have been widely used to examine associations between built environment measures and health outcomes, where a fixed, prespecified spatial scale (e.g., 1 mile buffer) is used to construct environment measures. However, the spatial scale for these associations remains largely unknown and misspecifying it introduces bias. We propose the use of distributed lag models (DLMs) to describe the association between built environment features and health as a function of distance from the locations of interest and circumvent a-priori selection of a spatial scale. Based on simulation studies, we demonstrate that traditional regression models produce associations biased away from the null when there is spatial correlation among the built environment features. Inference based on DLMs is robust under a range of scenarios of the built environment. We use this innovative application of DLMs to examine the association between the availability of convenience stores near California public schools, which may affect children's dietary choices both through direct access to junk food and exposure to advertisement, and children's body mass index z scores.
| S-EPMC5065688 | biostudies-literature
Project description:BackgroundThe two-stage time series design represents a powerful analytical tool in environmental epidemiology. Recently, models for both stages have been extended with the development of distributed lag non-linear models (DLNMs), a methodology for investigating simultaneously non-linear and lagged relationships, and multivariate meta-analysis, a methodology to pool estimates of multi-parameter associations. However, the application of both methods in two-stage analyses is prevented by the high-dimensional definition of DLNMs.MethodsIn this contribution we propose a method to synthesize DLNMs to simpler summaries, expressed by a reduced set of parameters of one-dimensional functions, which are compatible with current multivariate meta-analytical techniques. The methodology and modelling framework are implemented in R through the packages dlnm and mvmeta.ResultsAs an illustrative application, the method is adopted for the two-stage time series analysis of temperature-mortality associations using data from 10 regions in England and Wales. R code and data are available as supplementary online material.Discussion and conclusionsThe methodology proposed here extends the use of DLNMs in two-stage analyses, obtaining meta-analytical estimates of easily interpretable summaries from complex non-linear and delayed associations. The approach relaxes the assumptions and avoids simplifications required by simpler modelling approaches.
| S-EPMC3599933 | biostudies-literature
Project description:In this article, we introduce the R package dLagM for the implementation of distributed lag models and autoregressive distributed lag (ARDL) bounds testing to explore the short and long-run relationships between dependent and independent time series. Distributed lag models constitute a large class of time series regression models including the ARDL models used for cointegration analysis. The dLagM package provides a user-friendly and flexible environment for the implementation of the finite linear, polynomial, Koyck, and ARDL models and ARDL bounds cointegration test. Particularly, in this article, a new search algorithm to specify the orders of ARDL bounds testing is proposed and implemented by the dLagM package. Main features and input/output structures of the dLagM package and use of the proposed algorithm are illustrated over the datasets included in the package. Features of dLagM package are benchmarked with some mainstream software used to implement distributed lag models and ARDLs.
| S-EPMC7034805 | biostudies-literature
Project description:Distributed lag non-linear models (DLNMs) represent a modeling framework to flexibly describe associations showing potentially non-linear and delayed effects in time series data. This methodology rests on the definition of a crossbasis, a bi-dimensional functional space expressed by the combination of two sets of basis functions, which specify the relationships in the dimensions of predictor and lags, respectively. This framework is implemented in the R package dlnm, which provides functions to perform the broad range of models within the DLNM family and then to help interpret the results, with an emphasis on graphical representation. This paper offers an overview of the capabilities of the package, describing the conceptual and practical steps to specify and interpret DLNMs with an example of application to real data.
| S-EPMC3191524 | biostudies-literature