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On the estimation of heat-intensity and heat-duration effects in time series models of temperature-related mortality in Stockholm, Sweden

Joacim Rocklov1*, Adrian G Barnett2 and Alistair Woodward3

Author Affiliations

1 Department of Public Health and Clinical Medicine, Epidemiology and Global Health, Umeå University, Umeå, Sweden

2 Institute of Health and Biomedical Innovation & School of Public Health, Queensland University of Technology, Brisbane, Australia

3 School of Population Health, University of Auckland, Auckland, New Zealand

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Environmental Health 2012, 11:23  doi:10.1186/1476-069X-11-23

Published: 10 April 2012



We examine the effect of heat waves on mortality, over and above what would be predicted on the basis of temperature alone.


Present modeling approaches may not fully capture extra effects relating to heat wave duration, possibly because the mechanisms of action and the population at risk are different under more extreme conditions. Modeling such extra effects can be achieved using the commonly left-out effect-modification between the lags of temperature in distributed lag models.


Using data from Stockholm, Sweden, and a variety of modeling approaches, we found that heat wave effects amount to a stable and statistically significant 8.1-11.6% increase in excess deaths per heat wave day. The effects explicitly relating to heat wave duration (2.0–3.9% excess deaths per day) were more sensitive to the degrees of freedom allowed for in the overall temperature-mortality relationship. However, allowing for a very large number of degrees of freedom indicated over-fitting the overall temperature-mortality relationship.


Modeling additional heat wave effects, e.g. between lag effect-modification, can give a better description of the effects from extreme temperatures, particularly in the non-elderly population. We speculate that it is biologically plausible to differentiate effects from heat and heat wave duration.