## 5. Visualization of sex-specific differences in survival

There are a number of methods for visualizing demographic data [Vaupel et al. 1998] and in this section I am going to demonstrate how these methods can be applied to the analysis of Canadian mortality. Using death counts and exposure estimates we can compute death rates by single year and age, and then plot them as a Lexis map. In terms of intensity regression this is equivalent to fitting the YEAR*AGE model to each sex alone. Figure 4, for example, shows a Lexis map of Canadian male death rates computed this way [Note 5]. The scale on the right partitions all death rates into groups and the death rates included in a given group are assigned the same color. For example, all death rates which are less than 0.0005 are plotted in dark blue as indicated by the lowest scale rectangle. Similarly, all death rates which are higher than 0.0005 and lower than 0.002 are plotted in ordinary blue (second rectangle on the scale from the bottom) and so on.

The contour maps of Canadian mortality presented in Figures 4 and 5 permit us to see all death rates at a glance. The contour lines themselves help us to follow the development of mortality over age and time. If we look at contour line 0.016 (Figure 4), for example, which separates light blue from light magenta, we can see that it remains almost constant at age 58 up to the year 1980 and only after this year does it start to rise. This indicates that mortality in this age group did not undergo any significant changes until 1980 and only then began to decline. This observation confirms findings in death rates shown in Figure 2 for ages 50-80. For females, however, mortality developments at adult ages have been quite different. Contour lines have been steadily rising for virtually all ages over the whole period of observation. This is an indication of persistent progress made against mortality, a pattern very different from what we observe in the male data.

The dark blue area in Figures 4 and 5 shows the lowest levels of death rates ever reached in the Canadian population. We can see that, for females, this area started to emerge in the 1950s and over time it spread out to cover more ages. For males the region of lowest mortality is less pronounced, and it did not become evident until the mid-1960s. It, too, has spread out over time but in contrast to females only to young ages. Additionally, a light blue area in the year 1975 at age 20 shows the ages and years where mortality in the male population in fact increased (it is also visible, though less distinctly, in Figures 2c and 2d). Finally, to provide the reader with an overview of the amount of the information presented, let us state that Figures 4 and 5 include information on 13,860 death rates, displaying them in a concise and revealing manner.

In order to reveal age-specific differences in Canadian survival I divided the matrix of male death rates by the matrix of female death rates and then plotted the result as a Lexis map (Figure 6). In this map the elements that exceed 1 in the sex ratio matrix are colored in magenta hues and the elements less than 1 in blue. Thus, magenta shows the area with higher male mortality and blue with lower. We can see, for example, that females had a mortality excess at ages 20-50 in the years 1921-1940. This area of excessive female mortality completely disappeared before 1940, at which point the gap between male and female mortality started to emerge. It is apparent from Figure 6 that the gap started to form in two distinct age groups. The first group consists of the young ages: already in the 1950s male death rates at age 20 were twice as high as female death rates. Over time the difference only became aggravated and spread to cover older ages as well. Now male death rates at ages 17-35 are from 2 to 2.5 times higher than the corresponding female death rates.

Another age group which suffered from exceptionally high excess male mortality covers the senior ages (55-70). The difference in death rates shows quite a different pattern, however. It started to rise in the 1940s, reached a peak in 1980, and declined afterwards. The area of male death rates, which were more than twice as high as for females, appears on the map as a distinct, eye-catching ellipse which virtually disappears in the 1990s. In most recent years the difference between male and female death rates has continued to decline at these ages.

The World Health Report 1999 [WHO 1999] reports Canadian life expectancy at birth to be 71 for males and 78 for females in the year 1978 and 76 and 82 in 1998, respectively. As we just learned in this section, the convergence in life expectancy between the sexes is now driven mostly by the behavior of death rates at senior ages. This overall convergence is occurring despite the fact that at young ages the sex differences are increasing over time. The level of mortality at young ages is very low now and this diverging trend cannot affect the trends in life expectancy in any important way.

Finally, returning to Model (2) I would like to note that Figure 6 provides further evidence of the fact that a simple proportional model will not fit the whole data set appropriately. Such a model will try to catch the male-female difference by means of a single parameter, but the pattern is much more complicated.

 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