A general conceptual and statistical framework to model non-linear and delayed exposure-response relationships and combi

Lead Research Organisation: London School of Hygiene & Tropical Medicine
Department Name: Public Health and Policy


Scientific studies which assess the health effects of various risk factors usually depend on statistical models, used to quantify the relationship between the dose people are exposed to, and the health outcome. This relationship should concisely and reliably summarize the association, in order to correctly inform about the health consequences of specific risk factors. This association is usually estimated in multiple comparable studies, whose evidence needs then to be combined in order to improve the knowledge about related health risks.

Researchers at the London School of Hygiene and Tropical Medicine, in collaboration with the MRC-Cambridge and the University of Southern California, have promoted a project to provide the statistical tools suitable to describe complex relationships and combine them across studies. These methodologies will be implemented in statistical software, freely available and usable by all the researchers working in different biomedical fields. The aim of the project is to improve the analytical method to study the association between risk factors and human health.

Technical Summary


Epidemiological multi-city studies on the health effects of environmental factors, such as air pollution and temperature, have known an intense development in the last few years. Within this study design, two methodological issues are prominent among those that need to be addressed: how to specify exposure-response relationships describing potentially non-linear and delayed effects in each city, and how to combine such complex associations across different cities.
Interestingly, the same problems apply in different research areas involving different study designs and data structures. The extension and further development of statistical methodologies already proposed in time series analysis would provide a valuable tool in a wide range of research fields.


The aim of this project is to develop a general conceptual and statistical framework to model non-linear and delayed exposure-response relationships, and to propose appropriate approaches to combine such complex associations across studies.

Specific objectives:
1. to define a general conceptual framework to formalize the idea of delayed effects.
2. to provide a unified statistical approach to model non-linear and delayed effects by extending existing methods developed in time series analysis.
3. to review, compare and extend meta-analytic techniques to synthesize non-linear and/or delayed associations.
4. to provide a complete software implementation of the methodologies described above in the R statistical software, together with detailed and comprehensive documentation.

Research plan

This research is comprised of sub-projects Sub-P1 and Sub-P2.
Sub-P1 addresses objectives 1-2-4. Existing methods in time series analysis, based on distributed lag non-linear models, will be improved and extended, algebraically and conceptually, to different designs such as cohort and longitudinal analysis. The framework will be implemented by extending the R package dlnm developed by the applicant.
Sub-P2 addresses objectives 3-4. In particular, two existing techniques, meta-smoothing and multivariate meta-analysis, will be compared and extended, assessing their flexibility, applicability, and reliability of their results through simulations and applications to real data. A specific R package will be developed to implement these models.


The research involves collaborations with high-calibre and experienced researchers across three different institutions (LSHTM, MRC-Cambridge and University of Southern California).

Research outputs

The research project aims to provide a unified methodological approach to model and pool non-linear and delayed dependencies, through a general conceptual and statistical framework. The research project emphasizes generality and usability, specifying a systematic and widely applicable methodology, which encompasses different study designs and data structures, and providing a comprehensive software implementation and documentation.


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