The Authors Respond.

Abstract

To the Editor: We thank Michael Joffe for his letter1 pertaining to our article on selection bias due to parity conditioning in studies of time trends in fertility.2 We agree that studying the first pregnancy or attempt in a population that is representative of all women is appropriate, and were happy to see that Michael Joffe shared our view on the direction of causality from fertility to parity. However, in our opinion, he makes incorrect conclusions regarding the existence and direction of the selection bias2 in the referenced studies.3–6 Our arguments are as follows: First, and most importantly, Michael Joffe ignores the key issue behind parity-conditioning bias in this context, namely the definition of a study population with a wide age range at a cross section of time. The Swedish study consisted of all nulliparous women living in Sweden on December 31, 1982, who subsequently gave birth to their first child in 1983–2002.4 The two conditions (nulliparous on December 31, 1982 and reproduced in 1983–2002) resulted in a major difference in eligibility between different birth cohorts, with inclusion varying from 3% (birth cohort 1945–1949) to 91% (1965–1969), and further to 24% (1975–1979).4 Moreover, eligibility was strongly related to parity at the cross section, and thus also to fertility—a finding that is indicative of selection bias. Women with first birth at a younger age were excluded from the earlier birth cohorts, but included in the later birth cohorts. The opposite was true for women with first birth at an older age. This selection by parity is illustrated in the Lexis diagram (Figure). The most extreme difference in eligibility was between women born in 1945 and 1979. The 1945 cohort members should have had their first child at the age of 37 years or over to be included, whereas the 1979 cohort members should have reproduced before 24 years old. This comparison is simply not reasonable. The ultimate factors behind the selection bias are heterogeneity in fertility and differential success in at-risk cycles before the study period (earlier birth cohorts) or during the study period (later birth cohorts).FIGURE: Lexis diagram for 1945–1975 birth cohorts and the follow-up periods of three example studies. Arrow 1 A study without any restriction on age or parity includes first at-risk cycles of women during ~1960–2020. Two other studies examine study populations with broad age ranges at a cross section of time and condition on parity. Arrow 2 A study with a prospective follow-up including only women who gave birth during the study period 1983–2002 (area B)4 excludes women who were parous on 31.12.1982 (gray area A), and those who remained nulliparous after the study period (gray area C).4 A part of the included women from earlier birth cohorts 1945–1960 supposedly have experienced unsuccessful prior at-risk cycles, and thus are less fertile than those who reproduced before 1983. By contrast, some of the excluded women in the later birth cohorts ~1962–1975 supposedly have experienced unsuccessful at-risk cycles during the study period, and thus are less fertile than those who reproduced. Arrow 3 A study with a retrospective follow-up excluding women who remain nulliparous at the cross section3 suffers from the latter selection problem unless information on prior infertile phases or at-risk cycles have been collected.Second, the Finnish study5 did not include more than one pregnancy per woman. The study addressed primary infertility defined as an attempt to become pregnant that lasted 12 months or more before the first birth. Five-year age group-specific primary infertility increased from that of the 1938–1949 birth cohort through that of the 1950–1959 cohort to that of the 1960–1967 cohort. As indicated earlier, the findings of that study5 may be biased toward decreased fertility over time due to infertility misclassification.7 Instead of only including births that occurred during a common, arbitrary study period independent of the year of birth, a follow-up of all the birth cohorts should start at menarche and last until first pregnancy or until menopause. Otherwise the findings may suffer from parity-conditioning bias. In conclusion, as regards the existence and direction of parity-conditioning bias, we firmly maintain our original stand.2 Markku Sallmén Finnish Institute of Occupational Health Centre of Expertise for Health and Work Ability Helsinki, Finland [email protected] Jens Peter Bonde Department of Occupational and Environmental Medicine Bispebjerg Hospital University of Copenhagen Copenhagen, Denmark Marja-Liisa Lindbohm Finnish Institute of Occupational Health Centre of Expertise for Health and Work Ability Helsinki, Finland Petter Kristensen Department of Occupational Medicine and Epidemiology National Institute of Occupational Health Oslo, Norway Institute of Health and Society University of Oslo Oslo, Norway