**6. Summary and Implications**

The above review allows us to draw several broad conclusions. Across space, temperature–mortality ERFs for both heat and cold effects differ substantially in ways that appear to depend strongly on prevailing temperatures. In relatively cool climates, the MMT is shifted to the left on the temperature axis, with a shallow cold slope and steep hot slope. In relatively warm climates, the MMT is shifted to the right (higher temperatures), with a steep cold slope and a shallow hot slope. Over time, there is strong evidence that MMTs are rising and that hot slopes are declining, with the particular finding being somewhat dependent on the analytical methods used in individual studies, which are not standardized. There is relatively little evidence for changes in cold slopes over time, in contrast to the cross sectional evidence noted above. Projections of future heat-related mortality that do not take adaptation into account very likely overestimate future heat impacts.

What information can we draw from the current literature to guide future mortality projection studies? There are several possible approaches. As a simple way to incorporate uncertainty regarding adaptation trends, future projections could incorporate sensitivity analyses that apply adjustments to the hot slope ranging from −20% to −80%, a range that is supported by the literature. However, such adjustments would remain somewhat arbitrary, and also would not explicitly take elapsed time into account, which ought to matter in projecting risks of the future.

Alternatively, one could apply a simple time-dependence adjustment by drawing quantitative information on trends in heat slopes based on longitudinal studies such as in [28,29]. The average decadal decline in the heat slope in Petkova's analysis of the past four decades in NYC was about 31% [28]. Nordio's analysis over five decades nationally suggested a decadal decline of about 45% on average per decade [29]. Thus, a range of between 30% and 45% decline in the heat ERF per decade could be applied to projections over the next several decades. This approach has the appeal that it is tied to empirical evidence for trends over time. Additional data to support this approach are available from the supplemental materials provided by Nordio et al., where ERFs by cluster and time period are given, along with corresponding climate data. A recent study applied this approach to project future mortality across the U.S. in a changing climate [57].

Another adaptation model that would be supported by the literature is to adjust the MMT upwards as a function of MST, either keeping the hot slope constant or allowing it to be reduced with rising temperatures. Todd and Valleron [18] provided quantitative backing for this approach in France, although A/C is not yet prevalent in this country. [Their study suggests that the temporal change in MMT vs. MST is about 60% of the magnitude of the spatial change in MMT vs. MST, which hints at the pace of adaptation in a changing climate; in other words, we observe about a 60% adjustment to new climate conditions compared to the observed cross sectional differences.] These findings warrant replication using other national datasets. Heat wave-based mortality models are also amenable to simple adaptation adjustments, as in [49].

More generally, international datasets that include mortality and temperature data observed over multiple decades and locations could be further analyzed to better quantify spatial and temporal patterns in heat-related ERF parameters [57], perhaps using simple parameterizations that include a hot slope and a threshold as in [17]. Cold effects could be similarly modeled. The parameters of city-specific fits could then be analyzed in second stage models that relate them to both time per se, and to spatial and temporal differences in mean temperatures.

Finally, it is important to emphasize that this review has focused on trends in heat-related mortality analyzed at the city scale using administrative data in high-income countries, because that is where the literature has focused until now. While these data are of high relevance to public health planning in the context of a changing climate, they miss important aspects of the problem, which should be a priority for research moving forward. In particular, there is an urgent need for studies focusing on low-income countries, and on vulnerable population subgroups such as agricultural and other outdoor workers [20], for whom adaptation options will be much more limited. New study designs and data sources could also help advance the science of heat adaptation, taking advantages of new health and exposure sensors, citizen science, GIS, and big data.

**Funding:** This work was partially supported by contract # EP-D-14-031 from the U.S. Environmental Protection Agency.

**Conflicts of Interest:** The authors declare no conflict of interest.
