Abstract
BackgroundRich literature has reported that there exists a nonlinear association between temperature and mortality. One important feature in the temperature-mortality association is the minimum mortality temperature (MMT). The commonly used approach for estimating the MMT is to determine the MMT as the temperature at which mortality is minimized in the estimated temperature-mortality association curve. Also, an approximate bootstrap approach was proposed to calculate the standard errors and the confidence interval for the MMT. However, the statistical properties of these methods were not fully studied.MethodsOur research assessed the statistical properties of the previously proposed methods in various types of the temperature-mortality association. We also suggested an alternative approach to provide a point and an interval estimates for the MMT, which improve upon the previous approach if some prior knowledge is available on the MMT. We compare the previous and alternative methods through a simulation study and an application. In addition, as the MMT is often used as a reference temperature to calculate the cold- and heat-related relative risk (RR), we examined how the uncertainty in the MMT affects the estimation of the RRs.ResultsThe previously proposed method of estimating the MMT as a point (indicated as Argmin2) may increase bias or mean squared error in some types of temperature-mortality association. The approximate bootstrap method to calculate the confidence interval (indicated as Empirical1) performs properly achieving near 95% coverage but the length can be unnecessarily extremely large in some types of the association. We showed that an alternative approach (indicated as Empirical2), which can be applied if some prior knowledge is available on the MMT, works better reducing the bias and the mean squared error in point estimation and achieving near 95% coverage while shortening the length of the interval estimates.ConclusionsThe Monte Carlo simulation-based approach to estimate the MMT either as a point or as an interval was shown to perform well particularly when some prior knowledge is incorporated to reduce the uncertainty. The MMT uncertainty also can affect the estimation for the MMT-referenced RR and ignoring the MMT uncertainty in the RR estimation may lead to invalid results with respect to the bias in point estimation and the coverage in interval estimation.
Highlights
Rich literature has reported that there exists a nonlinear association between temperature and mortality
The %Coverage probability (CP) is near or greater than 95% for Empirical1 and Empirical2’s in all scenarios except that the %CP was relatively lower for Empirical2moderate and Empirical2minimal in scenario 4
In scenario 4, the empirical distribution of the mortality temperature (MMT) was observed as highly right-skewed with the two empirical methods and an adjustment to percentiles in the CI as the 0th – 95th recovered over 95% coverage (98.6% and 98.3%, respectively)
Summary
Rich literature has reported that there exists a nonlinear association between temperature and mortality. The commonly used approach for estimating the MMT is to determine the MMT as the temperature at which mortality is minimized in the estimated temperature-mortality association curve. A recently proposed approach for estimating the MMT in a nonlinear temperature-mortality association is to determine the MMT as the temperature at which mortality is minimized in the estimated temperaturemortality association curve [1, 5]. This approach provides a point estimate but the corresponding uncertainty is not quantified. Another study [6] proposed an approximate bootstrap approach to calculate the standard errors and the confidence interval for the MMT. The study applied the method to the data for 52 cities in Spain and showed that the uncertainty can be small or large depending on the estimated association pattern which varies among cities
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