Page 68 - GHES-1-2

Global Health Econ Sustain Stochastic modeling of age at menopausal

considered as the proportion of survival. The following Table 1. Observed and expected value of the number of
procedures were used to construct the menopausal life table. women by different distributions (2005)
Thus, from the fitted results of the logistic and RGLLog Age group Observed Expected number of women by
models, it was assumed that F is the empirical result of the Normal Weibull LLog Logistic
x
proportion of women having menopause at age x year or Below 35 1 0.256 2.358 0.476 0.411
less and S = 1−F is the survived proportion or not reached 35–37 2 0.943 2.614 1.002 1.995
x
x
menopause at age x. From the concept of the actuarial life
table technique, let l be the cohort of women, followed 37–39 5 3.147 4.988 2.776 3.294
0
by the number of women not having menopause at age x 39–41 7 7.940 8.898 6.894 7.279
(l ) using the equation l = l S . The probability of reaching 41–43 11 15.157 14.504 14.384 14.240
x
x
x
x
menopause from age x to x+1 year (q ) was computed as: 43–45 24 21.887 20.743 22.760 22.217
x
F − F 45–47 25 23.911 24.321 24.951 24.832
q = x+1 − F x (15) 47–49 18 19.763 20.983 18.974 19.240
x
1
x
49–51 10 12.358 11.308 11.065 11.101
Other symbols such as L is the total number of
x
women-years having menopause by the cohort at age x, T 51–53 6 5.846 2.998 5.595 5.347
x
is the total number of women-years having menopause by 53–55 5 2.793 0.284 5.123 4.043
the cohort above age x, and e is the mean expected age α - 13.638 20.562 -
x
of menopause at age x were calculated using the following β 3.742 46.478 45.679 2.241
formula as in the actuarial life table: γ 45.634 - 0.000 45.598
k(l + l ) n χ 2 2.601 5.811 2.379 1.661
x ∑
+
L = x x k , T = L + L X1 +…+ L X n (16) NLL −43.027 −41.016 −40.989 −39.086
+
x
+
X
2
x
AIC 90.054 86.033 85.977 82.172
Where k is the number of years between years n to n+k. BIC 90.849 86.829 86.773 82.968
T
T x+1 = T − L , and e = l x (17) Table 2. Descriptive statistics of age at menopause data of
x
x
x
x
2018 according to their occupation
4. Results and discussion
Occupation of Mean No. of Standard
The distributional pattern of age at menopause of Nepalese respondents women deviation
women was fitted using the four probability models and the Service 49.667 6 0.516
fitted results along with different test statistics results are Business 50.667 12 1.969
presented in Table 1 for the first data set and Table 2 for the Agriculture 49.968 31 2.273
second data set. The logistic distribution was significantly Housemaker 49.653 98 1.663
better fitted with the menopause data as compared to other
distributions. The observed value of AIC, BIC, SSQ, and χ Others 49.000 7 0.817
2
were found as the lowest for logistic distribution, and the Total 49.766 154 1.785
result of NLL was found as the highest for logistic distribution
as compared to other distributions used in this research. considered when girls have menarche. If the average age of
The graphical representation between the observed and menarche was considered as 15 years then the expected age
expected frequencies of women at the age of menopause of menopause was after 30.507 years of menarche.
is shown in Figure 1. From the analysis and graphical If the woman was 30 years old, the expected age of
presentation, the logistic distribution was found to be a menopause was estimated as after 15.565 years. The
good fit so it was recommended to use this distribution for probability of having menopause when the age of women was
describing the age pattern of women at menopause.
35 years is 0.018 (1.8%) whereas when the age of women was
After fitting the logistic distribution, the fitted value 45 years the chances of having menopause is 0.484 (48.4%).
of cumulative distribution was used to compute the
other components of the menopausal life table which Several parameter probability distributions were also
are shown in Table 3. From the analysis, the expected computed to better predict the waiting time for menopause
age of menopause at the birth of girls was estimated as and the probability of having menopause at a particular
45.511 years. However, the expected age of menopause was age (Table 4).
Volume 1 Issue 2 (2023) 5 https://doi.org/10.36922/ghes.1239