Distributed lag non-linear models

Environmental stressors often show effects that are delayed in time, requiring the use of statistical models that are flexible enough to describe the additional time dimension of the exposure–response relationship. Here we develop the family of distributed lag non-linear models (DLNM), a modelling framework that can simultaneously represent non-linear exposure–response dependencies and delayed effects. This methodology is based on the definition of a ‘cross-basis’, a bi-dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. In this way the approach provides a unified framework for a range of models that have previously been used in this setting, and new more flexible variants. This family of models is implemented in the package dlnm within the statistical environment R. To illustrate the methodology we use examples of DLNMs to represent the relationship between temperature and mortality, using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) for New York during the period 1987–2000. Copyright © 2010 John Wiley & Sons, Ltd

Distributed Lag Linear and Non-Linear Models in R: The Package dlnm.

: 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.<br/

Household Saving over the Life Cycle: International Evidence from Micro Data

In this paper I estimate age-saving profiles from micro data in six countries (Italy, Japan, Taiwan, Thailand, the UK, and the US) to verify whether households are saving as postulated by the life- cycle theory. The level of household savings depends on age, cohort and year effects, and the perfect collinearity among these effects is broken by applying a semiparametric regression model. In this model, the cohort effect is assumed to be an arbitrary smooth function, and the model is estimated by the generalized additive model with a penalized smoothing spline approach. Estimated saving-age profiles showed declining savings in the old age for the majority of examined countries. An interesting feature for Asian households was a double hump in savings, with a temporal dip for households in the age bracket at around mid-40s

Flexible distributed lag models and their application to geophysical data

Regression models with lagged covariate effects are often used in biostatistical and geo- physical data analysis. In the difficult and all-important subject of earthquake research, strong long-lasting rainfall is assumed to be one of many complex trigger factors that lead to earthquakes. Geophysicists interpret the rain effect with an increase of pore pressure due to the infiltra- tion of rain water over a long time period. Therefore, a sensible statistical regression model examining the influence of rain on the number of earthquakes on day t has to contain rain information of day t and of preceding days t − 1 to t − L. In the first part of this thesis, the specific shape of lagged rain influence on the number of earthquakes is modeled. A novel penalty structure for interpretable and flexible estimates of lag coefficients based on spline representations is presented. The penalty structure enables smoothness of the resulting lag course and a shrinkage towards zero of the last lag coefficient via a ridge penalty. This additional ridge penalty offers an approach to another problem neglected in previous work. With the help of the additional ridge penalty, a suboptimal choice of the lag length L is no longer critical. We propose the use of longer lags, as our simulations indicate that superfluous coefficients are correctly estimated close to zero. We provide a user-friendly implementation of our flexible distributed lag (FDL) ap- proach, that can be used directly in the established R package mgcv for estimation of generalized additive models. This allows our approach to be immediately included in com- plex additive models for generalized responses even in hierarchical or longitudinal data settings, making use of established stable and well-tested algorithms. We demonstrate the performance and utility of the proposed flexible distributed lag model in a case study on (micro-) earthquake data from Mount Hochstaufen, Bavaria with focus on the specific shape of the lagged rain influence on the occurrence of earthquakes in different depths. The complex meteorological and geophysical data set was collected and provided by the Geophysical Observatory of the Ludwig-Maximilians University Munich. The benefit of flexible distributed lag modeling is shown in a detailed simulation study. In the second part of the thesis, the penalization concept is extended to lagged non- linear covariate influence. Here, we extend an approach of Gasparrini et al. (2010), that was up to now unpenalized. Detailed simulation studies illustrate again the benefits of the penalty structure. The flexible distributed lag nonlinear model is applied to data of the volcano Merapi in Indonesia, collected and provided by the Geophysical Observatory in Fürstenfeldbruck. In this data set, the specific shape of lagged rain influence on the occurrence of block and ash flows is examined

Parametric and semi-parametric approaches in the analysis of short-term effects of air pollution on health

Since mid-1990s, Generalised Additive Models (GAM) became very popular for the analysis of short-term effects of air pollution on health. Such approach involves specification of non parametric functions to adjust for confounding effect of unobserved variables with a systematic temporal behaviour and to model weather variables and influenza epidemics. Recently critical points in using commercial statistical software for fitting GAMs were stressed (Dominici et al., 2002; Ramsey et al., 2003) and some reanalyses of time series data on air pollution and health were performed. This new attention to semi-parametric models has led researchers to consider alternative estimation methods for GAMs and to wonder whether simpler parametric models can be a better choice than GAMs (Lumley and Sheppard, 2003). The purpose of this work is to show by simulation analyses some of the problems which we could find using GAMs, and to discuss real advantages of semi-parametric approach with respect to a fully parametric alternative, based on specification of Generalized Linear Models with natural cubic splines (GLM + NS). Here we considered the situation in which only the smooth function for time trend is included in the model. Generalized Additive Models were fitted by the direct methods implemented in R software (Wood, 2000). Different simulation analyses were performed, varying the "true" number of degrees of freedom for the smooth function, the concurvity amount in data and the "true" size of air pollutant effect. Our simulations show that GAM provide biased estimates of air pollutant effect, the bias being not negligible for moderate concurvity amount and small effect size. We found also that using semi-parametric approach a certain amount of undersmoothing is needed to obtain appropriated estimation of risk. Good performance was obtained selecting the smoothing parameter by Generalized Cross Validation. On the contrary analysis of partial autocorrelation of residuals from GAM brings to inappropriate model selection. GLM+NS is a good alternative to semi-parametric approach, resulting robust to misspecification of degrees of freedom for the spline. However the applicability of such approach should be considered carefully in presence of particular local variations of seasonality or in presence of outliers, because results could be sensitive to knots placement. Moreover the choice of knots positions could be a very important problem in smoothing other covariates like temperature