Rethinking mortality rates in men and women: do men age faster?

: Women on average live longer than men, which seems to suggest that women also age slower than men. However, the potential difference in the pace of aging between the sexes is a relatively controversial topic, and both positions, i.e. “men age faster” and “men and women age at the same pace”, have found some support. We therefore employ parametric models previously established in model organisms as well as two nonparametric approaches to compare the pace of aging between the sexes using freely available mortality data from 13 developed countries. Our results support the hypothesis that men age faster than women while also suggesting that the difference is small and that from a practical standpoint male mortality rates behave similarly to the mortality rates of women approximately eight years their senior.

rate increase by means of mortality rate doubling time (MRDT), a parameter commonly used as an estimate of the rate of aging. 12,13 On the other hand, it does not distinguish between intrinsic and extrinsic mortality rates, where intrinsic mortality is assumed to be the result of aging and increases over time while extrinsic mortality is assumed to be caused by environmental hazards and is thus constant over time. 14 However, this inability to distinguish between intrinsic and extrinsic mortality rates is to some extent alleviated by the fact that mortality within the chosen interval of 30 to 60 years of age is mainly influenced by intrinsic causes. 9 The Gompertz-Makeham model extends the Gompertz model to include mortality rate independent of age. This partitioning of mortality rates into an age-related and a constant component is clearly helpful when analyzing the rates of aging.
In this study we used mortality data obtained from the Human Mortality Database 15 to calculate MRDTs using the Gompertz and Gompertz-Makeham model for male and female populations in 13 developed countries. Furthermore, we have also employed two non-parametric approaches to compare the pace of aging between sexes. However, it must be said that mortality rates are affected by a great variety of external influences unrelated to aging. One extreme example of such external influences was undoubtedly World War II, which dramatically altered mortality rates both directly through the deaths of millions of soldiers and civilians and indirectly through the late effects of injuries, starvation, psychological trauma, etc. It is known that mortality rates during the early life of a cohort influence its mortality rates later in life 16 which makes cohorts affected by a WWII unsuitable for comparing the pace of aging between sexes. Because most countries in the Human Mortality Database were more or less heavily involved in WWII, we analyzed mortality patterns only in people born at least five years after the end of this conflict. To be more specific, we analysed cohorts of people born from 1950 to 1954 using their mortality rates in periods starting . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint from 1980 to 1984 to the newest available data in the Human Mortality Database. In other words, investigated mortality rates were calculated using periods starting with the subjects' 30 th birthdays and ending with the end of records.

Methods
Mortality rate data were acquired from www.mortality.org on 12 July 2017. The Human Mortality Database (HMD) contained data about mortality rates for 39 sovereign countries and several others smaller areas and populations. In our analysis we focused on 13 developed, western (plus Japan), stable countries with populations exceeding 8 million. The analysed countries are: Australia, Belgium, Canada, France, Italy, Japan, the Netherlands, Portugal, Sweden, Switzerland, the United Kingdom, the United States of America and West Germany.

Gompertz and Gompertz-Makeham model
The Gompertz model 10,12 of exponential hazard growth was used to model the relationship between age and mortality rate. The basic form of the Gompertz model is where a and b are constants, t is time (age), and h(t) is the hazard (mortality) rate. Using the logarithmic transformation, a simple linear model is obtained where log(a) signifies the intercept (overall shift of the line in the direction of the y-axis) and b expresses the slope of the line. MRDT is subsequently calculated from the slope as = log (2) . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint and expresses the time it takes for the mortality rate to double.
The Gompertz-Makeham model is a natural extension of the Gompertz model obtained by adding a constant: 17 The constant c expresses the part of mortality that does not depend on age. Focusing only on the age-dependent part of the equation, the mortality rate doubling time can be obtained in the same manner as in the Gompertz model, using the value of parameter b.
We fitted the above described on data for each individual country using an age interval beginning at 30 years of age. We fitted one model for both male and female data with sex as a dummy variable in order to compare them. Due to the exponential nature of models, we used numerical fitting using non-linear least squares. Both models accurately fit human mortality dynamics roughly between 30 and 80, 9,11 which we subsequently confirmed using an exploratory analysis of HMD data.

Smoothing spline approach
We also used a nonparametric approach to model the relationship between age and mortality rate.
We approximated the death rate data by a smoothing spline 18   The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint The disparate outcomes of the Gompertz and Gompertz-Makeham models are most likely caused by different parametrization rather than by different curve shapes (Fig. 2). When the ageindependent parameter c is not included, like in the Gompertz model, the value of the other two parameters changes accordingly in order to provide a best-fitting curve. If a roughly similar mortality curve were to be described by the Gompertz and Gompertz-Makeham models, the following would apply: the growing c value of the Gompertz-Makeham corresponds to a decreasing b value in the Gompertz model and thus an increasing MRDT. We have found that the age-independent parameter c is higher in males in most cases (Table S2)   The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint

Smoothing spline approach
We employed a nonparametric approach to further test the difference in the pace of aging between the sexes without the constraint of parametric models. Results in the form of derivative curves, where the value of the derivative at each time point constitutes an increase of mortality rate per year, (Figure 3 and Table S3) clearly show that mortality rates increase faster in men than in . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint women in all studied countries and cohorts. These results are thus in agreement with the results of the Gompertz-Makeham model.    The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint

Mortality rate matching approach
Since the selected calculation methods may have influenced our results, we have decided to employ a second nonparametric approach. By comparing absolute mortality rate values rather than derivatives, we tested whether our results are robust enough to withstand various methodological approaches. When comparing the mortality rates of males and females, we found that the mortality rates of females aged 50 are on average equal to the mortality rates of males aged 41.9 years ( Figure 6 and Table S4). When we made the same comparison for the mortality rates of women aged 60 we found out that men had already achieved equal mortality rates at the average age of 51.2. In other words, the gap between female and male mortality rates increased on average by 0.7 years over the course of the decade ( Figure 6 and Table S4), suggesting that males age faster.
. CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/179846 doi: bioRxiv preprint Figure 6: Men achieve mortality rates equal to that of women aged 50 many years earlier. Equivalent mortality (EQ) at age X expresses how much earlier men achieve the same mortality rates as women aged X. For example, an EQ 50 of 10 means that men aged 40 exhibit the same mortality rates as women aged 50. The y axis captures how differences in age with the same mortality rates developed over a ten-yearlong period in the studied countries and cohorts.
On the other hand, when we compared the age difference between equal male and female mortality rates using longer timescales, it seems that the observed changes are rather small and that male

Discussion
We investigated mortality data to test whether men age faster than women, as previously suggested in several studies. 2,[19][20][21] While calculations MRDTs conducted using the Gompertz studying mortality partitions, sharply disagree with this naive assumption. This is probably best documented by the fact that both are among the authors of a paper which clearly states that "It is difficult to envision a cause of death for humans or any other species, either intrinsic or extrinsic, that does not exhibit age-dependence." 22 Furthermore, it is documented that even mortality caused by accidents such as falls, drowning, transport accidents and exposure to mechanical forces dramatically increases with age, as does the number of deaths caused by natural disasters, including excessive heat or cold, earthquakes, lightning, storms, and floods. 14 In other words, biologically older individuals are at a higher risk of death from both intrinsic and extrinsic sources.
We thus believe that using overall i.e. non-partitioned mortality to compare the pace of aging should be sufficient or even preferable to focusing purely on intrinsic mortality.
Though not entirely conclusive, our results support the hypothesis that men age faster than women.
This may be important since the faster aging of men could have far-reaching implications for aging research as well as for medicine. Furthermore, while the survival advantage of females has been reported in other primates, it is not typical of all mammals. 3 If we therefore assume that the longer lifespan of one sex should to some extent reflect differences in aging between the sexes, it also implies that the faster aging of men is a recent evolutionary development. In case this interpretation is correct, it then leads to an obvious question: what triggered the evolution of sex-specific aging rates?
On the other hand, our study demonstrates that a comparison of the paces of aging may yield vastly different results when different methods are employed (e.g., Gompertz vs. Gompertz-Makeham), which is an issue deserving of broader scientific attention. Furthermore, our results show that if men and women age at different paces, the difference is rather small and it seems that, from a