Table 3 Advantages and disadvantages of approaches used to assess changes in susceptibility to temperature effects over time

Compare minimum mortality temperature or thresholds above or below which heat/cold effects occur over time.

Simple metric for comparison.

Can be determined from models using maximum likelihood estimation.

Does not give information on how the RR is changing over time - an important factor in determining deaths attributable to heat or cold. The slope of the regression line is often related to the MMT or threshold. For heat effects, steeper slopes are often seen with higher thresholds. Quoting only the MMT/threshold would not include this relevant information.

MMTs/thresholds can be difficult to establish with data, especially for cold – models may not always select the most appropriate threshold.

It would be helpful to quote changes in MMT along with changes in RR. For example, when modelling heat effects, if there is both an increase in MMT over time and a decrease in RR despite the higher heat threshold, then this would give convincing evidence of a shift in susceptibility over time.

No included study used this approach in isolation, Carson et al. [44]. and Donaldson et al. [45] both give report MMT changes over time in addition to the changes in RR.

Compare the RR for heat or cold effects over time allowing:

a) Fixing the thresholds above/below which effects are modelled over time

b) Allowing thresholds above/below which effects are modelled to vary with time (e.g. allow for a shit in MMT)

Approach a:

If the threshold is fixed then the changes in RR are simple and easy to interpret – i.e. allows comparison of 1 parameter only. Fixing the threshold whilst fitting a linear relationship, however, may influence results: If the threshold is fixed at a lower temperature than that at which it actually occurs, the modelled heat slope may be biased towards being more shallow.

If thresholds are fixed, then giving information on how they have varied over time could help capture some information (as Carson et al. did).

Approach b:

Allows a better fit with the data series. However, this may lead to results which are difficult to interpret:

If both measures vary then interpreting the two measures is difficult, as they are inherently related.

Further, if thresholds vary by time period and only the RR is reported, this will not capture the full change in susceptibility occurring. For example, a situation may arise where both the threshold and slope have increased in a later period, but it is unclear whether the slope is artificially raised due to the higher threshold placement.

Conversely, if the shape of the temperature-mortality relationship remained the same but the threshold /MMT shifted to the right over time, reporting only the RR would under-estimate the change in vulnerability. This could be misinterpreted as there being no change in susceptibility over time.

Approach a) used by Carson et al. [44]

Approach b) used by Ekamper et al. [42]

Compare the RR for heat or cold effects at two defined temperatures (e.g.

a) At 29 DC vs 22 DC or b) At a given percentiles of the temperature distribution.

Allows for risk from relationships modelled non-linearly to be compared.

Gives information on how the population are responding to more ‘extreme’ temperatures.

If RR compared are derived from percentiles of the temperature distribution then these can be calculated relative to the whole time period of data (in which case similar to fixing an exact temperature as in a) or allowed to shift (defined relative to each time period analysed). If the percentiles shift according to the time period analysed, this will implicitly include some information about changing susceptibility or ‘adaptation’.

If the temperatures used for comparison of RR across the time period are fixed then interpretation of the results is simpler. Results would need to be interpreted with this choice in mind. For example, if the RR at the 98^th percentile compared to the average temperature has not changed over time, but the 98^th percentile has been calculated according to each time period (i.e. if temperatures have risen, the 98^th percentile temperature increases) then this demonstrates some decrease in susceptibility despite no change in RR.

Approach a) fixed temperatures or temperatures fixed at a given percentile relative to the entire time period, allows changes in susceptibility to heat/cold to be more easily judged as only one parameter is changed. If approach b) is taken and percentiles used are allowed to vary by time period, then care should be taken in interpreting results. A sensitivity analysis could be undertaken either using approach a) for comparison or by allowing the percentiles used for approach b) both to be fixed across the entire period and allowed to vary.

Approach a) used by Petkova et al. [36]

Approach b) used by Astrom et al. [39] who included sensitivity analysis allowing for percentiles at which RR were compared to either vary by time period or be defined relative to the whole time period of data analysis.

Compare deaths attributable to heat or cold over time.

The calculation of attributable deaths takes into account both the threshold above/below which effects are seen and the RR for each temperature above/below the threshold.

The calculation of deaths attributable to heat/cold also uses number of days at which the temperature was above/below the threshold for the given period and the baseline mortality for each time period. Therefore the change in outcome could be related to any of these factors which are independent of the temperature-mortality relationship. For example, the RR of heat related mortality may have decreased over time, but the number of days above the threshold increased with as temperatures warm. This may lead to the number of attributable deaths staying constant or increasing over time, despite a decrease in susceptibility compared to the earlier time period.

Providing information on the number of days above/below the given threshold or on temperature trends and on trends in baseline mortality may ease interpretation – for example, if the temperature has been increasing but there is a decreasing trend in excess heat-related deaths this gives more weight to evidence of decreasing population susceptibility to heat.

Bobb et al. [37], Carson et al. [44]

Use transfer function (e.g. RR from modelled relationship between temperature and mortality) from later or earlier years with the weather series from whole time period to assess whether there has been a change in attributable deaths.

This approach gives results which are easy to interpret. However, it would need to be made clear whether both the changed RR and potentially changed threshold above/below which effects have been modelled have been used to calculate the burdens.

Although using the temperature-mortality relationship from each time period with the same series of weather data seems to give an easily comparable result, clarity should be provided on whether the baseline mortality used for calculations has also been consistent. As for any of the above scenarios, the modelled RR may be influenced by outlying extreme temperatures and therefore taking a number of years as a basis for ‘transfer’ functions may be more reliable.

Christidis et al. [41]