## 4. Excess of male mortality over age and time

The analysis conducted in the previous section shows that the relative difference between male and female mortality was not constant, neither over age nor time. Hence, a simple proportional hazard model [Note 4] of type:

 YEAR + AGE + SEX (2)

will not be appropriate to capture the differences in survival between the sexes. I therefore decided to split the entire data set into ten-year age and calendar year periods and to fit Model (2) separately to each of the smaller data segments.

Table 1 includes the estimates of the SEX parameter. It shows the ratio of male to female mortality adjusted for age- and period-specific differences in mortality. Consider, for example, the period 1921-29 and age group 80-89. The SEX estimate is 1.05, which means that the male death rates were on the average 5% higher than those of females in this period at these ages. I have also fitted a nested model YEAR + AGE and compared it with (2) using the likelihood ratio to check whether the estimate of the SEX parameter is significant. It turns out that the estimate is not significant only for the age group 40-49 in the period 1921-29. In all other cases the p-values are less than 0.001.

As follows from Table 1, the smallest differences in survival between the sexes are observed in the period 1921-1940. Females even experienced higher mortality in the age group 20-50, as is indicated by the table cells with a blue background. Starting with the 1940s, male mortality was higher than female mortality at virtually all ages, and this difference increased over time, especially at young adult ages. Male mortality is now more than double female mortality at these ages.

Trends in sex differences over age and time can be presented more clearly by plotting the data from Table 1 by age groups and periods (Figure 3). Figure 3a shows estimates of the sex ratio plotted by age group. Almost constant curves for the age groups 0 and 1-9 reflect the fact that mortality decline occurred almost parallel for boys and girls. This is consistent with the findings in the previous section (Figures 2a and 2b): although the death rates fell dramatically in these age groups, the pattern of decline was similar for both sexes. The second important finding is that the difference in death rates by sex rose until the mid-1980s and then started to decline. This is indicated by the almost bell-shaped patterns of most of the curves. The only exceptions from this pattern are ages 30-39 and 80-89. For them the relative difference between males and females increased continuously over the entire period.

Figure 3b makes it easier to follow changes in the age pattern of mortality differences over time. We can see, for example, that there were dramatic changes in the pattern of the sex ratio at ages 10-40. During the period 1921-49 the death rates for males and females were fairly close but in the later years the sex ratio dramatically increased and reached a level of 2.5 and higher for the age group 20-29. This means that male death rates in this age group have been more than 2.5 times higher than for females over the last four decades.

Another important feature of Figure 3b is the convergence of male and female death rates at advanced ages. For virtually all the time periods analyzed, the curves drop towards the end of the age range. Thus, the relative difference in death rates is declining over age for all years included in the analysis. In addition, we can see that this decline is more pronounced in recent decades than in the earlier periods.

 Sex differentials in survival in the Canadian population, 1921-1997: A descriptive analysis with focus on age-specific structure Kirill Andreev © 2000 Max-Planck-Gesellschaft ISSN 1435-9871 http://www.demographic-research.org/Volumes/Vol3/12