Parametric Estimation of Minimum Mortality Temperature with Over-dispersion: Using Non-linear Generalized Linear Model

Abstract

Background: The minimum mortality temperature (MMT) is an important concept in ecology studies for explaining how temperature affects mortality. Piecewise regression and generalized additive models (GAMs) with spline methods are generally used to find the MMT

however, these methods have difficulty in estimating variance in the MMT. For instance, piecewise regression cannot reflect the nonlinear relationship between temperature and mortality, and it is computationally very intensive to estimate variance in spline methods. Therefore it is necessary to develop a new method that can tackle both problems in the MMT. Method: We use a parametric method based on a generalized linear model (GLM). We consider nonlinear parameters to estimate MMTs and their variances are estimated by using the Delta method. The proposed method can estimate the relative risks (RRs) and their differences can be reflected by the relationship between temperature and non-accidental mortality. The proposed methodology, we use data on five Asian cities during 1992?2010 (Seoul), 1972?2010 (Tokyo, Osaka, Nagoya), and 1994?2007 (Taipei). Result: We find that the nonlinear model detected by our methodology represents the temperature effect on mortality well. Our results show that all estimates of MMTs are located from 22?29°C and their standard errors other than that for Seoul are less than 0.4. These results are similar or more stable with those using a B-spline method and previous epidemiological studies. We also estimate RRs to detect the extreme heat effect (differences in the 90% and 99% quantile temperatures) and estimate suitable RRs and their confidence intervals. Conclusions: Our methodology can be an useful alternative to piecewise regression or GAMs.