In the USA, more deaths happen in the winter than the summer. But when deaths occur varies greatly by sex, age, cause of death, and possibly region. Seasonal differences in death rates can change over time due to changes in factors that cause disease or affect treatment.

Analyzing the seasonality of deaths can help scientists determine whether interventions to minimize deaths during a certain time of year are needed, or whether existing ones are effective. Scrutinizing seasonal patterns in death over time can also help scientists determine whether large-scale weather or climate changes are affecting the seasonality of death.

Now, Parks et al. show that there are age and sex differences in which times of year most deaths occur. Parks et al. analyzed data on US deaths between 1980 and 2016. While overall deaths in a year were highest in winter and lowest in summer, a greater number of young men died during summer – mainly due to injuries – than during winter. Seasonal differences in deaths among young children have largely disappeared and seasonal differences in the deaths of older children and young adults have become smaller. Deaths among women and men aged 45 or older peaked between December and February – largely caused by respiratory and heart diseases, or injuries. Deaths in this older age group were lowest during the summer months. Death patterns in older people changed little over time. No regional differences were found in seasonal death patterns, despite large climate variation across the USA.

The analysis by Parks et al. suggests public health and medical interventions have been successful in reducing seasonal deaths among many groups. But more needs to be done to address seasonal differences in deaths among older adults. For example, by boosting flu vaccination rates, providing warnings about severe weather and better insulation for homes. Using technology like hands-free communication devices or home visits to help keep vulnerable elderly people connected during the winter months may also help.

It is well-established that death rates vary throughout the year, and in temperate climates there tend to be more deaths in winter than in summer (Campbell, 2017; Fowler et al., 2015; Healy, 2003; McKee, 1989). It has therefore been hypothesized that a warmer world may lower winter mortality in temperate climates (Langford and Bentham, 1995; Martens, 1998). In a large country like the USA, which possesses distinct climate regions, the seasonality of mortality may vary geographically, due to geographical variations in mortality, localized weather patterns, and regional differences in adaptation measures such as heating, air conditioning and healthcare (Davis et al., 2004; Braga et al., 2001; Kalkstein, 2013; Medina-Ramón and Schwartz, 2007). The presence and extent of seasonal variation in mortality may also itself change over time (Bobb et al., 2014; Carson et al., 2006; Seretakis et al., 1997; Sheridan et al., 2009).

A thorough understanding of the long-term dynamics of seasonality of mortality, and its geographical and demographic patterns, is needed to identify at-risk groups, plan responses at the present time as well as under changing climate conditions. Although mortality seasonality is well-established, there is limited information on how seasonality, including the timing of minimum and maximum mortality, varies by local climate and how these features have changed over time, especially in relation to age group, sex and medical cause of death (Rau, 2004; Rau et al., 2018).

In this paper, we comprehensively characterize the spatial and temporal patterns of all-cause and cause-specific mortality seasonality in the USA by sex and age group, through the application of wavelet analytical techniques, to over three decades of national mortality data. Wavelets have been used to study the dynamics of weather phenomena (Moy et al., 2002) and infectious diseases (Grenfell et al., 2001). We also used centre of gravity analysis and circular statistics methods to understand the timing of maximum and minimum mortality. In addition, we identify how the percentage difference between death rates in maximum and minimum mortality months has changed over time.

Table 1 presents number of deaths by cause of death and sex. Deaths from cardiorespiratory diseases make up nearly half of all deaths (48.1%), with most deaths in that group from cardiovascular diseases. Next highest during the study period were deaths from cancers (23.2%), followed by injuries (6.8%), with two thirds of those being from unintentional injuries.

All-cause mortality in males had a 12 month seasonality in all age groups, except ages 35–44 years, for whom there was periodicity at 6 months (Figure 1). In females, there was 12 month seasonality in all groups except 5–14 and 25–34 years (p-values=0.21 and 0.25, respectively) (Figure 2). While seasonality persisted throughout the entire analysis period in older ages, it largely disappeared after the late 1990s in children aged 0–4 years in both sexes and in women aged 15–24 years.

Figure 1

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Figure 2

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Deaths from all causes of death were seasonal in older adults (above 65 or 75 years depending on cause, p-values<0.06) (Figures 1–10 and respective figure supplements), except for intentional injuries and substance use disorders. Deaths from cardiorespiratory diseases, and within it respiratory infections, exhibited seasonality throughout the life-course (p-values<0.06) except for males aged 5–24 years and females aged 15–24 years (p-values>0.11). In addition to older ages, injury deaths were seasonal from childhood through 44 years in women and through 64 years in men (p-values<0.09). Unintentional injuries drove the seasonality of injury deaths for females, whereas both unintentional and intentional injuries were seasonal in males in most ages, with the exception of below 15 years and above 85 years when intentional injuries were not seasonal (Figure 7—figure supplement 1). Consistent seasonality in cancer deaths (Figures 3,4) only appeared after 55 years of age (p-values<0.05). No consistent seasonality was evident in substance use disorders (Figure 9—figure supplement 1 and Figure 10—figure supplement 1) or maternal conditions (Figure 10—figure supplement 2).

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Centre of gravity analysis showed that death rates in men aged ≥45 years and women aged ≥35 years peaked in December, January or February and were lowest in June to August, for all-cause mortality as well as for all non-injury and non-maternal causes of death (Figure 11 and respective figure supplements). Deaths from cardiorespiratory diseases, including cardiovascular diseases, chronic respiratory diseases and respiratory infections, were also consistently highest in January and February and lowest in July and August across all ages, except for chronic respiratory diseases in ages 5–24 years where there are few deaths from this cause leading to unstable estimates (p-values for seasonality from wavelet analysis ranged from 0.35 to 0.48 for these ages). A similar temporal pattern was seen for all-cause and non-injury mortality in children younger than five years of age, whose all-cause death rate was highest in February and lowest in August. In contrast, among males aged 5–34 years, all-cause mortality peaked in June or July, as did deaths from injuries, which generally had a summer peak in males and females below 45 years of age.

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From 1980 to 2016, the proportional (percent) difference in all-cause death rates between peak and minimum months declined little for people older than 45 years of age (by less than eight percentage points with p-values for declining trend >0.1) (Figure 12). In contrast, the difference between peak (summer) and minimum (winter) death rates declined in younger ages, by over 25 percentage points in males aged 5–14 years and 15–24 years (p-values<0.01), largely driven in the declining difference between summer and winter injury deaths. Under five years of age, percent seasonal difference in all-cause death rates declined by 13 percentage points (p-value<0.01) for boys but only five percentage points (p-value=0.12) for girls. These declines in seasonality of child deaths were a net effect of declining winter-summer difference in cardiorespiratory diseases deaths and increasing summer-winter difference in injury deaths, itself driven by increasing difference in non-intentional injuries (Figure 12—figure supplement 1). Within specific cardiorespiratory diseases in under-five children, percent difference declined for cardiorespiratory diseases, cardiovascular diseases, and chronic respiratory diseases while increasing for respiratory infections.

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The subnational centre of gravity analysis showed that all-cause mortality peaks and minima in different climate regions are consistent with the national ones (Figures 13–16), indicating that seasonality is largely independent of geography. The relative homogeneity of the timing of maximum and minimum mortality contrasts with the large variation in seasonal temperatures among climate regions. For example, in men and women aged 65–74 years, all-cause mortality peaked in February in the Northeast and Southeast, even though the average temperatures for those regions were different by over 13 degrees Celsius (9.3 in the Southeast compared with −3.8 in the Northeast). Furthermore, above 45 years of age, there was little inter-region variation in the percent seasonal difference in all-cause mortality, despite the large variation in temperature difference between the peak and minimum months (Figure 17).

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We used wavelet and centre of gravity analyses, which allowed systematically identifying and characterizing seasonality of total and cause-specific mortality in the USA, and examining how seasonality has changed over time. We identified distinct seasonal patterns in relation to age and sex, including higher all-cause summer mortality in young men (Feinstein, 2002; Rau et al., 2018). Importantly, we also showed that all-cause and cause-specific mortality seasonality is largely similar in terms of both timing and magnitude across diverse climatic regions with substantially different summer and winter temperatures. Insights of this kind would not have been possible analysing data averaged over time or nationally, or fixed to pre-specified frequencies.

Prior studies have noted seasonality of mortality for all-cause mortality and for specific causes of death in the USA (Feinstein, 2002; Kalkstein, 2013; Rau, 2004; Rau et al., 2018; Rosenwaike, 1966; Seretakis et al., 1997). Few of these studies have done consistent national and subnational analyses, and none has done so over time, for a comprehensive set of age groups and causes of death, and in relation to regional temperature differences. Our results on strong seasonality of cardiorespiratory diseases deaths and weak seasonality of cancer deaths, restricted to older ages, are broadly consistent with these studies (Feinstein, 2002; Rau et al., 2018; Rosenwaike, 1966; Seretakis et al., 1997), which had limited analysis on how seasonality changes over time and geography (Feinstein, 2002; Rau et al., 2018; Rosenwaike, 1966). Similarly, our results on seasonality of injury deaths are supported by a few prior studies (Feinstein, 2002; Rau et al., 2018; Rosenwaike, 1966), but our subnational analysis over three decades revealed variations in when injury deaths peaked and in how seasonal differences in these deaths have changed over time in relation to age group which had not been reported before.

A study of 36 cities in the USA, aggregated across age groups and over time, also found that excess mortality was not associated with seasonal temperature range (Kinney et al., 2015). In contrast, a European study found that the difference between winter and summer mortality was lower in colder Nordic countries than in warmer southern European nations (Healy, 2003; McKee, 1989) (the study’s measure of temperature was mean annual temperature which differed from the temperature difference between maximum and minimum mortality used in our analysis although the two measures are correlated). The absence of variation in the magnitude of mortality seasonality indicates that different regions in the USA are similarly adapted to temperature seasonality, whereas Nordic countries may have better environmental (e.g. housing insulation and heating) and health system measures to counter the effects of cold winters than those in southern Europe. If the observed absence of association between the magnitude of mortality seasonality and seasonal temperature difference across the climate regions also persists over time, the changes in temperature as a result of global climate change are unlikely to affect the winter-summer mortality difference.

The cause-specific analysis showed that the substantial decline in seasonal mortality differences in adolescents and young adults was related to the diminishing seasonality of (unintentional) injuries, especially from road traffic crashes, which are more likely to occur in the summer months (Liu et al., 2005) and are more common in men. The weakening of seasonality in boys under five years of age was related to two phenomena: first, the seasonality of death from cardiorespiratory diseases declined, and second, the proportion of deaths from perinatal conditions, which exhibit limited seasonality (Figure 9—figure supplement 2 and Figure 10—figure supplement 3), increased (MacDorman and Gregory, 2015).

In contrast to young and middle ages, mortality in older ages, where death rates are highest, maintained persistent seasonality over a period of three decades (we note that although the percent seasonal difference in mortality has remained largely unchanged in these ages, the absolute difference in death rates between the peak and minimum months has declined because total mortality has a declining long-term trend). This finding demonstrates the need for environmental and health service interventions targeted towards this group irrespective of geography and local climate. Examples of such interventions include enhancing the availability of both environmental and medical protective factors, such as better insulation of homes, winter heating provision and flu vaccinations, for the vulnerable older population (Katiyo et al., 2017). Social interventions, including regular visits to the isolated elderly during peak mortality periods to ensure that they are optimally prepared for adverse conditions, and responsive and high-quality emergency care, are also important to protect this vulnerable group (Healy, 2003; Lerchl, 1998; Katiyo et al., 2017). Emergent new technologies, such as always-connected hands-free communications devices with the outside world, in-house cameras, and personal sensors also provide an opportunity to enhance care for the older, more vulnerable groups in the population, especially in winter when the elderly have fewer social interactions (Morris, 2013). Such interventions are important today, and will remain so as the population ages and climate change increases the within- and between-season weather variability.

The ERA-Interim temperature data are available at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim. The US Census Populations With Bridged Race Categories data for 1990-2016 are available at https://wonder.cdc.gov/bridged-race-population.html. Pre 1990, the County Intercensal Tables are available at https://www.census.gov/data/tables/time-series/demo/popest/1980s-county.html. The Vital statistics data are available at https://www.cdc.gov/nchs/nvss/dvs_data_release.htm through a request to NAPHSIS (https://www.naphsis.org/).

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Thank you for submitting your article "National and regional seasonal dynamics of all-cause and cause-specific mortality in the USA from 1980 to 2013" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by Eduardo Franco as a Reviewing Editor and Prabhat Jha as the Senior Editor. The Reviewing Editor has drafted this decision to help you prepare a revised submission. As is common in eLife, decision narratives are an amalgamation of the essential points of the reviewers' critiques after eliminating redundancies in comments and suggestions.

Summary:

This paper examines the seasonality in age- and disease-specific mortality in the US using geocoded data analyzed via wavelet statistical modelling and Poisson regression techniques. The key results indicate mortality increases in adults over 45 years old in winter from cardiorespiratory causes and injuries. Injuries, attributable mainly to road traffic crashes were seen to rise in the summer months among young men. No variation in seasonality was found by climate region, indicating no apparent disparities in adaptation by geographic location. This study provides insights as to whether climate changes could have an impact on the mortality patterns observed in the US as a model. The findings could assist in planning surveillance mechanisms and in projecting workforce requirements in primary and emergency healthcare.

Essential revisions:

1) By choosing only 4 disease groups the authors seem to have missed a key opportunity to investigate seasonal patterns in finer subgroups despite possessing a large sample size (n = 77,771,264), Furthermore, the rationale for choosing the subgroups presented is unclear. For example, the authors chose to group cardiorespiratory diseases into one large outcome when cardiovascular and respiratory outcomes have differing mechanisms in their association with heat or cold exposure. Within respiratory diseases itself, it makes sense to separate acute and chronic causes because the mechanisms vary so starkly and are related to seasonal patterns, i.e. the incidence of pneumonia and acute respiratory outcomes are likely heightened in the winter and this observation may differ to how/why the incidence of chronic respiratory deaths vary seasonally. Furthermore, the mechanisms for how heat is associated with elevated respiratory deaths is understudied and knowing more about seasonal patterns here would be a useful addition to the literature.

I believe it's important to investigate seasonal patterns of deaths from infectious disease, maternal and neonatal causes, endocrine disorders, genitourinary conditions and neuropsychiatric conditions (which are all associated with temperature) to add valuable insight into understudied but important disease groups, but these have been excluded from the present analysis. Considering the tragic opioid epidemic in USA, it would be a valuable contribution to the literature to understand whether seasonal patterns (at least in more recent years) are observed with deaths related to substance use disorders.

2) The authors pointed out in the Introduction that global warming may impact on excess cold weather death rates. Presumably a major part of the rationale for testing the differences in regions over time was to help inform our understanding of what the impact may be. However no conclusions were reached with regard to the implications of the findings. Clearly any such conclusions would need to be appropriately and heavily caveated but as this is a major reason for the analysis. Please expand the Discussion to include these points.

3) Methodology:

A) Wavelet power spectra are not always easy to interpret, and the uncertainty in estimated wavelet coefficients is difficult to quantify. The wavelet analysis makes for an interesting exploratory tool, showing that for the most part cycles have a duration of 12 months and are reasonably stable over time. It does not seem possible to draw firm conclusions about the research hypothesis using wavelets, however. All cause male mortality for 15-24 year olds appears to be less cyclical in recent years, although how to quantify this effect and assign a statistical significance to it is not apparent from the power spectrum shown.

The second analysis is more appropriate, although the details of this analysis are sparse. It appears that the model used is something like the following, where Yit is the count of deaths in age group i at time t.

--------------------- -------------------------------------

Yit∼ Poisson(Nit ⋅ λit)log(λit)= μi + βit + Mit ⋅ [α1i ⋅ cos(2πt/12)

+α2i ⋅ sin(2πt/12)+α3i ⋅ cos(2πt/6)

+α4i ⋅ sin(2πt/6)]

Mit= ρi + γit

--------------------- -------------------------------------

A model of this could answer the following questions, with p-values produced from a likelihood ratio test.

- Is γi negative? If so the seasonal effect is becoming less severe for age group i.

- Does it look like all age groups have the same trend, with γi = γ₀ for all i?

- Do all age groups have the same cycle, with αpi = αp0?

- Does γ vary by region (negative in cold-climate regions?)

- Do the cycles, given by the α, vary by region or is a nation-wide cycle sufficient?

The above model is easier to interpret than the wavelet analysis. The quantity 1 − exp(120γ) is the change per decade in the seasonality effect, which could be reported with a 95% confidence interval.

B) The approach is different to a number of those referenced (particularly the standard measure of excess winter deaths). It would be helpful to have some comment on this, particularly the generalisability to other studies. The focus has been on peak months in this analysis, but the standard assessment of excess winter deaths is to compare December to March months to the rest of the year.

C) Appropriate rationale was given to the regional splits used in the analysis. However no description was given of the characteristics of these regional areas other than subsequent information on temperatures. As pointed out there could be a number of factors that are important. I would expect some reference to their differing characteristics.

4) Interpretation:

A) No table is presented with descriptive statistics, i.e. on the sample size of cases that fall into each disease category.

B) I may be misreading the paper (in which case it would be helpful to clarify so others do not make the same mistake), however the analysis in Figure 6 compares the difference in temperature experienced in those regions between the warmest and coldest months versus the% seasonal difference in death. In the Discussion this in contrasted with findings from Europe where countries with a more temperate winter have, paradoxically, higher rates of excess winter mortality. However this is not an appropriate direct comparison, regional extremes in variation were not looked at when comparisons between countries are made. This does not invalidate the comparison but it would be helpful to explicitly summarise if there are any differences between regions and examine what those are.

C) One option for this paper would be to be admittedly exploratory, avoiding the use of the word 'significant' and simplifying the analysis. Simple monthly averages and testing for the months having the same mean could replace the wavelet analysis. A second option would be to focus on a specific research hypothesis, explain carefully how the model estimates relate to this research hypothesis, and adjust the p-values for multiple testing.

Essential revisions:

1) By choosing only 4 disease groups the authors seem to have missed a key opportunity to investigate seasonal patterns in finer subgroups despite possessing a large sample size (n = 77,771,264), Furthermore, the rationale for choosing the subgroups presented is unclear. For example, the authors chose to group cardiorespiratory diseases into one large outcome when cardiovascular and respiratory outcomes have differing mechanisms in their association with heat or cold exposure. Within respiratory diseases itself, it makes sense to separate acute and chronic causes because the mechanisms vary so starkly and are related to seasonal patterns, i.e. the incidence of pneumonia and acute respiratory outcomes are likely heightened in the winter and this observation may differ to how/why the incidence of chronic respiratory deaths vary seasonally. Furthermore, the mechanisms for how heat is associated with elevated respiratory deaths is understudied and knowing more about seasonal patterns here would be a useful addition to the literature.

I believe it's important to investigate seasonal patterns of deaths from infectious disease, maternal and neonatal causes, endocrine disorders, genitourinary conditions and neuropsychiatric conditions (which are all associated with temperature) to add valuable insight into understudied but important disease groups, but these have been excluded from the present analysis. Considering the tragic opioid epidemic in USA, it would be a valuable contribution to the literature to understand whether seasonal patterns (at least in more recent years) are observed with deaths related to substance use disorders.

We had selected the four cause groups to go beyond all-cause mortality and still have parsimonious presentation and sufficient number of events by sex, age group, year, month and geography. In the specific case of cardiorespiratory diseases, they are commonly analysed together when studying the effects of temperature and air pollution (Basu, 2009; Basu, Dominici, and Samet, 2005; Basu and Samet, 2002; Bennett et al., 2014; Braga, Zanobetti, and Schwartz, 2002; Curriero et al., 2002; Dockery et al., 1993; Gasparrini et al., 2015; Hoek et al., 2013; Pope et al., 2002), possibly because of their shared aetiology (e.g., death from cor pulmonale arising from COPD or death from pneumonia in patients with acute vascular events) and because assignment of cause of death may use them interchangeably. We now present a third layer of disaggregation following the above suggestions (figure supplements for Figures 6-13; Table 1; Materials and methods).

2) The authors pointed out in the Introduction that global warming may impact on excess cold weather death rates. Presumably a major part of the rationale for testing the differences in regions over time was to help inform our understanding of what the impact may be. However no conclusions were reached with regard to the implications of the findings. Clearly any such conclusions would need to be appropriately and heavily caveated but as this is a major reason for the analysis. Please expand the Discussion to include these points.

To quantitatively analyse the potential implications of global climate change, one would need to formally incorporate temperature in the analysis which would involve a distinct analytical framework and presentation. As correctly pointed out in this comment, the current analysis can nonetheless provide qualitative insights into such effects, which we have now discussed with appropriate caveats (Discussion, second, third and fourth paragraphs).

3) Methodology:

A) Wavelet power spectra are not always easy to interpret, and the uncertainty in estimated wavelet coefficients is difficult to quantify. The wavelet analysis makes for an interesting exploratory tool, showing that for the most part cycles have a duration of 12 months and are reasonably stable over time. It does not seem possible to draw firm conclusions about the research hypothesis using wavelets, however. All cause male mortality for 15-24 year olds appears to be less cyclical in recent years, although how to quantify this effect and assign a statistical significance to it is not apparent from the power spectrum shown.

Wavelet analysis is a formal analytical framework that can provide quantitative conclusions (Hubbard, 1996; Torrence and Compo, 1998), and has been applied in different areas of health and the environment, for example measles epidemics and El Niño oscillations, to quantitatively characterise their seasonality including.(Grenfell, Bjørnstad, and Kappey, 2001; Moyet al., 2002) A key advantage of wavelet analysis is that it does not assume a stationary time series, and hence can easily capture a decline/increase in or appearance/disappearance of seasonality. The uncertainty of wavelet spectra are also well-characterised (Hubbard, 1996). We follow wavelet analysis with a centre of gravity analysis to identify the months of maximum and minimum mortality (Figure 12 and respective figure supplements; subsection “Statistical methods"), and with a quantitative analysis of (percentage) difference in death rates from 1980 to 2016 (Figure 13 and respective figure supplements; subsection “Statistical methods").

We note that even in standard statistical comparisons, p-values and statistical significance are not apparent from figures but are a part of the analysis. We have added p-values to each of the wavelet analyses in Figures 2-11 and the respective figure supplements (subsection “Statistical methods").

The second analysis is more appropriate, although the details of this analysis are sparse. It appears that the model used is something like the following, where Yit is the count of deaths in age group i at time t.

--------------------- -------------------------------------

Yit∼ Poisson(Nit ⋅ λit)log(λit)= μi + βit + Mit ⋅ [α1i ⋅ cos(2πt/12)

+α2i ⋅ sin(2πt/12)+α3i ⋅ cos(2πt/6)

+α4i ⋅ sin(2πt/6)]

Mit= ρi + γit

--------------------- -------------------------------------

A model of this could answer the following questions, with p-values produced from a likelihood ratio test.

- Is γi negative? If so the seasonal effect is becoming less severe for age group i.

- Does it look like all age groups have the same trend, with γi = γ₀ for all i?

- Do all age groups have the same cycle, with αpi = αp0?

- Does γ vary by region (negative in cold-climate regions?)

- Do the cycles, given by the α, vary by region or is a nation-wide cycle sufficient?

The above model is easier to interpret than the wavelet analysis. The quantity 1 − exp(120γ) is the change per decade in the seasonality effect, which could be reported with a 95% confidence interval.

Our current methods successfully answer the questions that the reviewer has posed. We have clarified our methods, especially those for Figures 12 to 17 and their respective figure supplements where applicable (referred to as the ‘second analysis’ above) in the revised manuscript and summarise the approach and its findings below.

- Is γi negative? If so the seasonal effect is becoming less severe for age group i.

- Does it look like all age groups have the same trend, with γi = γ₀ for all i?

We calculated change in percent difference between 1980 and 2016 by fitting a linear regression to the time series of seasonal differences in mortality within a year. We have reported the percentage point change in seasonality, with p-values, from 1980 to 2016 by age, sex, and cause of death (Figure 13 and respective figure supplements).

- Do all age groups have the same cycle, with αpi = αp0?

We calculated the timing of maximum and minimum mortality using centre of gravity analysis and circular statistics. We have reported the maximum and minimum values by age, sex, and cause of death (Figure 12 and respective figure supplements).

- Does γ vary by region (negative in cold-climate regions)?

We report percent difference in death rates between maximum and minimum months by region (Figure 18 and subsection “Statistical methods"). We have also calculated change in percent difference between 1980 and 2016 by region, shown in Author response image 1 for all-cause mortality, though not included in the main paper which is already dense with inclusion of a large number of results at the national level.

Author response image 1

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- Do the cycles, given by the α, vary by region or is a nation-wide cycle sufficient?

We calculated the timing of maximum and minimum mortality using centre of gravity analysis by region as well as nationally. We have reported the maximum and minimum values by age and sex for all-cause death (Figures 14-17 and subsection “Statistical methods").

Therefore, we have successfully answered all the questions posed by the reviewers with our current methods. The wavelet analysis allows greater flexibility when compared to the above model suggested because it does not require assuming only 6- and 12-month periodicity.

We have nonetheless implemented the above approach. We note that some the parameters of this model (e.g., the ρ, γ, and α terms) cannot be interpreted on their own, because the model includes involve interaction terms, for example (γ x α1i). In addition, the interpretation of γ is also dependent on the sign of α, as, for example, a negative value of α with a negative value of γ indicates the percentage difference between maximum and minimum mortality is increasing, whereas a positive value of α with a negative value of γ indicates that the percentage difference between maximum and minimum mortality is decreasing. For these reasons, interpretable results require predicting the outcomes in specific years and not simply the model parameters. We have done so for one of the outcomes presented in the paper, namely percent difference in death rates between maximum and minimum mortality months, with results presented in the table below. Conclusions were similar to those from the existing method.

We believe that our current approach has the dual advantage over the proposed method of using a more general and flexible framework and being more easily understandable. We welcome guidance on whether adding this additional method would improve the paper.

Author response table 1. Percent difference in death rates between the maximum and minimum mortality months for all-cause mortality in 2016 versus 1980 by sex and age group using the alternative method.

B) The approach is different to a number of those referenced (particularly the standard measure of excess winter deaths). It would be helpful to have some comment on this, particularly the generalisability to other studies. The focus has been on peak months in this analysis, but the standard assessment of excess winter deaths is to compare December to March months to the rest of the year.

We have avoided the term Excess Winter Deaths (EWDs) because the latter assumes higher deaths in winter than in the summer, and requires a priori decisions about which months to include in “winter” and “summer”. Our empirical results show that peak mortality not only varies from age group to age group or cause by cause, but also can in the extreme take place in summer, e.g., for young adult males. We have added a brief overview of EWDs, and why an empirical approach like ours is preferred to its strong assumptions (P. 19).

C) Appropriate rationale was given to the regional splits used in the analysis. However no description was given of the characteristics of these regional areas other than subsequent information on temperatures. As pointed out there could be a number of factors that are important. I would expect some reference to their differing characteristics.

A fair comment and addressed in the revised manuscript by providing an overview of the characteristics of the regions (subsection “Data”, second paragraph and Table 2).

4) Interpretation:

A) No table is presented with descriptive statistics, i.e. on the sample size of cases that fall into each disease category.

We have added a table of descriptive statistics (Table 1).

B) I may be misreading the paper (in which case it would be helpful to clarify so others do not make the same mistake), however the analysis in Figure 6 compares the difference in temperature experienced in those regions between the warmest and coldest months versus the% seasonal difference in death. In the Discussion this in contrasted with findings from Europe where countries with a more temperate winter have, paradoxically, higher rates of excess winter mortality. However this is not an appropriate direct comparison, regional extremes in variation were not looked at when comparisons between countries are made. This does not invalidate the comparison but it would be helpful to explicitly summarise if there are any differences between regions and examine what those are.

A fair comment and addressed in the revised manuscript in the Discussion. Specifically, the European papers that we had cited (Fowler et al., 2015; Healy, 2003; McKee, 1989) had based their comparison on annual mean temperature whereas ours was based on the temperature range. We have clarified this distinction in the revised Discussion, noting that the two temperature metrics are correlated (see Author response image 2).

Author response image 2

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C) One option for this paper would be to be admittedly exploratory, avoiding the use of the word 'significant' and simplifying the analysis. Simple monthly averages and testing for the months having the same mean could replace the wavelet analysis. A second option would be to focus on a specific research hypothesis, explain carefully how the model estimates relate to this research hypothesis, and adjust the p-values for multiple testing.

As above, wavelet analysis, the subsequent steps of centre-of-gravity analysis to identify peak and minimum mortality months, and estimation of changes in seasonal mortality range are all formal analyses.

We now quote p-values in results, as opposed to setting an explicit threshold for significance (as derived by comparing against a threshold on the p-value), hence removing the need for correction for multiple testing.

Author details

1. Robbie M Parks

   1. MRC-PHE Centre for Environment and Health, Imperial College London, London, United Kingdom
   2. Department of Epidemiology and Biostatistics, School of Public Health, Imperial College London, London, United Kingdom

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7916-1717

2. James E Bennett

   1. MRC-PHE Centre for Environment and Health, Imperial College London, London, United Kingdom
   2. Department of Epidemiology and Biostatistics, School of Public Health, Imperial College London, London, United Kingdom
   3. WHO Collaborating Centre on NCD Surveillance and Epidemiology, Imperial College London, London, United Kingdom

   Contribution

   Conceptualization, Visualization, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

3. Kyle J Foreman

   1. MRC-PHE Centre for Environment and Health, Imperial College London, London, United Kingdom
   2. Department of Epidemiology and Biostatistics, School of Public Health, Imperial College London, London, United Kingdom
   3. Institute for Health Metrics and Evaluation, University of Washington, Seattle, United States

   Contribution

   Data curation, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

4. Ralf Toumi

   Space and Atmospheric Physics, Imperial College London, London, United Kingdom

   Contribution

   Conceptualization, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

5. Majid Ezzati

   1. MRC-PHE Centre for Environment and Health, Imperial College London, London, United Kingdom
   2. Department of Epidemiology and Biostatistics, School of Public Health, Imperial College London, London, United Kingdom
   3. WHO Collaborating Centre on NCD Surveillance and Epidemiology, Imperial College London, London, United Kingdom

   Contribution

   Conceptualization, Resources, Data curation, Supervision, Funding acquisition, Visualization, Methodology, Writing—original draft, Project administration

   For correspondence

   majid.ezzati@imperial.ac.uk

   Competing interests

   Reports a charitable grant from the AstraZeneca Young Health Programme, and personal fees from Prudential, Scor, and Third Bridge, all outside the submitted work.

   "This ORCID iD identifies the author of this article:" 0000-0002-2109-8081

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