Mortality Data Suggests that Men do age faster than women

Women on average live longer than men, which seems to suggest that women also age slower than men. However, the potential difference in pace of aging between sexes is a relatively controversial topic, and both positions “women age slower” and “women and men age at the same pace” have found some support. We thus employ mathematical methods previously established in model organisms to compare the pace of aging between the sexes using freely available mortality data from 13 countries. Our results support hypothesis that men age faster than women.

mortality rates at almost every age, i.e. that the reason for their shorter lifespan is that men are the less "robust" sex and as such exhibit higher background mortality 1,3 . On the other hand, researchers suggesting that women indeed age slower than men note that this line of reasoning may not be altogether valid since men die from different causes at different ages 2 . Interestingly both of these views fail to answer the existence of the mortality-morbidity paradox, in other words why women live longer but are sicker than men [3][4][5] . Regardless of theoretical arguments, aging is defined as an age-dependent increase in mortality 2,6,7 and therefore, the pace of aging of men and women may be empirically calculated using available mortality data. In this article, we present the results of an analysis of mortality data which suggests that men do age faster than women.
One method of quantifying aging relies on calculating the rate at which mortality increases with age 8 . The relationship between human age and mortality is usually modeled using a predefined distribution which explicitly defines the relationship between age and mortality rate.
Distributions most commonly used for this purpose include Gompertz or its extension Gompertz-Makeham, Weibull and logistic 9 . The choice of a specific distribution depends on the purpose of its use: the best fitting model is often desired when a prediction is sought while a different model may be more suitable for the interpretation of parameter values 10,11 . Since our objective was to test the difference between the pace of mortality rate increase in men and women, the Gompertz model 12 was selected as well-suited for this purpose. It is appropriate for accommodating human mortality data approximately between 30 and 80 years of age 11,13 and also offers a means for comparing mortality rate increase by means of mortality rate doubling time (MRDT), a parameter commonly used as an estimate of the rate of aging 14,15 . Its disadvantage, i.e. the inability to distinguish between intrinsic and extrinsic mortality rate, however this should be to some extend compensated by the fact that the chosen interval of 30 to 60 years of age is influenced mainly by intrinsic causes 11 . Furthermore, the Gompertz model may also be easily transformed and estimated as a linear model, which offers straightforward statistical tools for testing the difference between men and women. We have further employed Gompertz-Makeham model to verify results of Gompertz model and help us in interpretation of results.
In this study we used mortality data obtained from the Human Mortality Database 16 to calculate MRDTs by Gompertz model for male and female populations in 13 developed countries.
Furthermore, for each country, we also tested whether a statistically significant difference is to be found between the sexes in slopes of lines obtained by the log-linear Gompertz mortality rate model. Mortality rates may be affected by a great variety of external influences unrelated to aging. One extreme example of such external influences was undoubtedly the Second World War

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 population exceeding 8 million. Analysed countries are: Australia, Belgium, Canada, France, Italy, Japan, Netherlands, Portugal, Sweden, Switzerland, United Kingdom, United States of America and West Germany.

The Gompertz model
The Gompertz model 12,14 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 (in our case 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 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 18 : 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.
The above-described models were fitted on data for each individual country using an age interval beginning at 30 years of age. A separate model was fitted using male and female data in order to obtain parameters for both populations. Due to exponential nature of models, numerical fitting using non-linear least squares was used. Both models accurately fit human mortality dynamics roughly between 30 and 80 11,13 , which was subsequently confirmed during exploratory analysis of the data from HMD.

Results:
The Gompertz model: MRDTs calculated for people born in 1954 is longer for males in 10 out of 13 countries (Table 1)

Gompertz-Makeham
Contrary to the results of Gompertz     The opposing results of the Gompertz and Gompertz-Makeham models are most likely caused by different parametrization rather than different curve shape (Fig. 1). When the age-independent parameter c is not included like in the Gompertz model, the value of the other two parameters changes accordingly in order to provide best-fitting curve. If a roughly same mortality curve is described by the Gompertz and Gomperz-Makeham model, following applies: the growing c value of the Gompertz-Makeham corresponds to a decreasing b value in the Gompertz model and thus a increasing MRDT. We have found that the age-independent parameter c is universally higher in males (Table 3)

Discussion
In this study, we have investigated mortality data to test whether men age faster than women, as was previously suggested by several authors 2,19-21 . Interestingly, our calculations of MRDTs using Gompertz model do not show any consistent difference in pace of aging between sexes while results of Gompertz-Makeham model strongly suggests that men age faster than women. The diference between results of Gompertz and Gompertz-Makeham model may be explained by the fact that Gompertz-Makeham unlike Gompertz model, includes an age-independent parameter c which is almost universally higher in men. Furthemore, this also implies that Gompertz-Makeham model is beter suited to compare aging between sexes. Thus, overal our results suport hypothesis that men age faster than women.
The potential weakness of our work is that our analysis of mortality data does not distinguish between intrinsic and extrinsic sources of mortality. There is a great body of literature focusing on partitioning mortality to intrinsic and extrinsic mortality 22,23 . Partitioning of mortality remains the gold standard which can in some situations undoubtedly bring an important insight into the aging process. However, partitioning mortality to intrinsic and extrinsic is highly superficial, and the assumption that intrinsic sources of mortality are caused by aging while the extrinsic sources of mortality are caused by the environment and are thus constant over age is simply wrong 24 . Accordingly, even Bruce A. Carnes and S. Jay Olshansky arguably the two most influential authors studying mortality partitions sharply disagree with such naive assumption. This is probably best documented by the fact that both of them are among authors of a paper which clearly states "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 . In other words, biologically, older individuals have a higher risk of death from both intrinsic and extrinsic sources. Thus we believe that for our purpose using total mortality to compare the pace of aging should be sufficient or even preferable to using only intrinsic mortality.
Overall, our results indicate that men age faster than women. This may have a far-reaching implications for aging research as well as medicine.