Is age at menopause decreasing? - The consequences of not completing the generational cohort

Abstract

Background: Due to contradictory results in current research, whether age at menopause is increasing or decreasing in Western countries remains an open question, yet worth studying as later ages at menopause are likely to be related to an increased risk of breast cancer. Using data from breast cancer screening programs to study the temporal trend of age at menopause is difficult since especially younger women in the same generational cohort have often not yet reached menopause. Deleting these younger women in a breast cancer risk analyses may bias the results. The aim of this study is therefore to recover missing menopause ages as a covariate by comparing methods for handling missing data. Additionally, the study makes a contribution to understanding the evolution of age at menopause for several generations born in Portugal between 1920 and 1970.

Methods: Data from a breast cancer screening program in Portugal including 278,282 women aged 45-69 and collected between 1990 and 2010 are used to compare two approaches of imputing age at menopause: (i) a multiple imputation methodology based on a truncated distribution but ignoring the mechanism of missingness; (ii) a copula-based multiple imputation method that simultaneously handles the age at menopause and the missing mechanism. The linear predictors considered in both cases have a semiparametric additive structure accommodating linear and non-linear effects defined via splines or Markov random fields smoothers in the case of spatial variables.

Results: Both imputation methods unveiled an increasing trend of age at menopause when viewed as a function of the birth year for the youngest generation. This trend is hidden if we model only women with an observed age at menopause.

Conclusion: When studying age at menopause, missing ages must be recovered with an adequate procedure for incomplete data. Imputing these missing ages avoids excluding the younger generation cohort of the screening program in breast cancer risk analyses and hence reduces the bias stemming from this exclusion. In addition, imputing the not yet observed ages of menopause for mostly younger women is also crucial when studying the time trend of age at menopause otherwise the analysis will be biased.

Keywords: Copula function; Distributional regression; GJRM; Incomplete data; Menopause; Smoothing.

Fig. 1

Age at menopause for the women with an observed value

Fig. 2

Histogram of the missing ages at menopause by birth year and points representing the mean age at menopause by birth year

Fig. 3

Missing ages at menopause by municipality

Fig. 4

Mean age at menopause by municipality

Fig. 5

Participation rate by municipality. The NA represent information not available

Fig. 6

Two overlayed histograms showing one random sample of 20 imputations after applying the gamlss methodology considering a truncated Weibull distribution to impute the missing menopause ages (light grey) and after applying the copula approach (dark grey)

Fig. 7

Results using gamlss to fit only the complete cases (CCA), i.e. without imputations. Results are plotted on the scale of the semiparametric predictor

Fig. 8

Results using gamlss to fit the completed cases, i.e. after the missing menopause ages have been replaced with the imputations considering a truncated Weibull distribution at the screening age to ensure that the imputed values are not lower than the actual woman’s age. Results are plotted on the scale of the semiparametric predictor

Fig. 9

Results using GJRM to fit only the CCA, i.e. without imputations, considering a marginal Gumbel distribution for the menopause age and a Joe copula rotated 270^o. Results are plotted on the scale of the semiparametric predictor

Fig. 10

Results obtained with gamlss after filling up the missing values with one imputation using the copula approach. A marginal Gumbel for the menopause age and a Joe copula rotated 270^o were considered. Results are plotted on the scale of the semiparametric predictor

Fig. 11

Boxplots for the menopause age considering only the set of women for whom menopause age was missing in 2010, but which was already observed in 2017: solely imputations without truncation in 2010 (0); solely imputations with a truncated Weibull in 2010 (1); solely imputations with a Copula approach in 2010 (2); true ages observed in 2017 (4)