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120 | www.epidem.com Epidemiology • Volume 30, Number 1, January 2019
Background: Several epidemiologic designs allow studying fecund-
ability, the monthly probability of pregnancy occurrence in noncon-
tracepting couples in the general population. These designs may, to
varying extents, suffer from attenuation bias and other biases. We
aimed to compare the main designs: incident and prevalent cohorts,
pregnancy-based, and current duration approaches.
Methods: A realistic simulation model produced individual repro-
ductive lives of a fictitious population. We drew random population
samples according to each study design, from which the cumulative
probability of pregnancy was estimated. We compared the abilities of
the designs to highlight the impact of an environmental factor influ-
encing fecundability, relying on the Cox model with censoring after
12 or 6 months.
Results: Regarding the estimation of the cumulative probability
of pregnancy, the pregnancy-based approach was the most prone
to bias. When we considered a hypothetical factor associated with
a hazard ratio (HR) of pregnancy of 0.7, the estimated HR was in
the 0.78–0.85 range, according to designs. This attenuation bias was
largest for the prevalent cohort and smallest for the current duration
approach, which had the largest variance. The bias could be limited
in all designs by censoring durations at 6 months.
Conclusion: Attenuation bias in HRs cannot be ignored in fecund-
ability studies. Focusing on the effect of exposures during the first 6
months of unprotected intercourse through censoring removes part of
this bias. For risk factors that can accurately be assessed retrospec-
tively, retrospective fecundity designs, although biased, are not much
more strongly so than logistically more intensive designs entailing
follow-up.
Keywords: Cohort; current duration; fecundability; fecundity; preg-
nancy; prevalent cohort; simulation; time to pregnancy.
(Epidemiology 2019;30: 120–129)
Fecundity, the biologic ability to obtain a live birth, is mark-
edly less efficient in humans than in most other mamma-
lian species.1,2 Studies reported a temporal decrease in sperm
parameters in some areas of industrialized countries,3–6 to an
extent that may impact couples’ fecundability, the probability
for a pregnancy to start during a menstrual cycle with inter-
course.7 Toxicologic and epidemiologic studies suggest that
specific environmental8–11 lifestyle and behavioral factors can
influence fecundity,12–14 but evidence from human studies is
missing for many environmental factors. Therefore, there is
a need for efficient approaches allowing monitoring of time
trends in human fecundity and characterization of the influence
of environmental and sociodemographic factors on fecundity.
The assessment of couples’ fecundity can rely on sev-
eral epidemiologic designs,15–18 and to our knowledge, no
quantitative comparison of their efficiency is available. The
case–control design has strong limitations when it comes to
studying fecundability,19,20 and will not be considered further
here. The remaining designs can be distinguished accord-
ing to the time when couples are sampled with respect to the
period of unprotected intercourse (eFigure 1; http://links.lww.
com/EDE/B404 and Table 1): if recruitment takes place after
the end of this period, then the design usually corresponds
to a pregnancy-based approach (if only periods of unpro-
tected intercourse followed by a pregnancy are identified and
recruited, as would be done in a study conducted in a mater-
nity clinic).21 If recruitment takes place before the start of the
period of unprotected intercourse and if couples are followed
up, then the design corresponds to an incident cohort.22 From
a cross-sectional sample of couples recruited during the period
of unprotected intercourse, one can collect the time elapsed
between the start of the period of unprotected intercourse and
inclusion, from which the distribution of the underlying total
duration of unprotected intercourse and the effect of covari-
ates on fecundity can be estimated, which corresponds to the
current duration approach, an approach that does not require
follow-up.17,18,23 From the same population, if couples are
Submitted December 25, 2017; accepted September 3, 2018.
From the aJulius Center for Health Sciences and Primary Care, Department of
Biostatistics and Research Support, University Medical Center, Utrecht,
The Netherlands; bDepartment of Public Health, Erasmus MC, University
Medical Center, Rotterdam, The Netherlands; cINED (French Institute for
Demographic Studies) and French Academy of Sciences, Paris, France;
dDepartment of Biostatistics, University of Copenhagen, Copenhagen,
Denmark; and eTeam of Environmental Epidemiology Applied to Repro-
duction and Respiratory Health, U1209, Inserm, CNRS and University
Grenoble-Alpes Joint Research Center (IAB), Grenoble, France.
The authors report no conflicts of interest.
The computing code can be obtained by request to the first author.
Supplemental digital content is available through direct URL citations
in the HTML and PDF versions of this article (www.epidem.com).
Correspondence: Rémy Slama, Inserm, IAB Research Center, Team of Envi-
ronmental Epidemiology, Allée des Alpes, Site Santé, 38700 La Tronche,
France. E-mail: Remy.slama@univ-grenoble-alpes.fr.
Copyright © 2018 Wolters Kluwer Health, Inc. All rights reserved.
ORIGINAL ARTICLE
ISSN: 1044-3983/19/3001-0120
DOI: 10.1097/EDE.0000000000000916
A Systematic Comparison of Designs to
Study Human Fecundity
Marinus J. C. Eijkemans,a,b Henri Leridon,c Niels Keiding,d and Rémy Slamae
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Epidemiology • Volume 30, Number 1, January 2019 Comparison of Four Designs to Assess Fecundity
© 2018 Wolters Kluwer Health, Inc. All rights reserved. www.epidem.com | 121
followed up to monitor the time from inclusion until a pos-
sible pregnancy, then this corresponds to a prevalent cohort
design, which is for fecundability studies generally restricted
to couples who have initiated the period of unprotected inter-
course a few months before inclusion.24–26
These designs differ in many aspects. First, regarding
the targets of inference, the pregnancy-based design can be
considered as being biased in terms of estimation of fecund-
ability, in that infertile couples are not included. The current
duration approach targets the duration of the period of unpro-
tected intercourse, corresponding to the minimum of time to
pregnancy (TTP) and time to stop the period of unprotected
intercourse. Second, the designs also strongly differ in terms of
eligibility rates.18,22,23 Third, because the sampling takes place
at different times with respect to the start of the at-risk period
for various designs, the proportions of subjects with long dura-
tions (e.g., 1 year or more) differ between designs. This may
have consequences in terms of attenuation bias if no censoring
is applied.27,28 In our context, attenuation bias relates to the fact
that, in a population that is heterogeneous in terms of fecundity,
at each time, the most fecund couples are more likely to con-
ceive a pregnancy, and hence to exit the population at risk of
pregnancy, than less fecund couples. Consequently, in a study
of the effect of a factor decreasing fecundability, as times goes
by, the group not or least exposed to the factor (where fecund-
ability is initially higher than in the exposed group) is more
strongly depleted than the most exposed group. This leads to
an attenuation over time of the time-specific ratio of the prob-
ability of pregnancy between the exposed and the unexposed
groups.27 Because of these and other differences between these
designs, they may differ in terms of bias.
So far, comparisons between designs only considered
the pregnancy-based and the incident cohort designs.29,30 They
indicate that the pregnancy-based and the incident cohort
designs differ in terms of ability to highlight the impact of a
factor on fecundity.30 To our knowledge, there is no system-
atic comparison taking into account more recently proposed
approaches such as the prevalent cohort25,31 and current dura-
tion17,18,32,33 designs.
Our aim was to systematically investigate the amount
of bias in the four designs mentioned, in terms of estima-
tion of the cumulative probability of pregnancy and also in
terms of ability to highlight the impact of an exposure factor
influencing fecundity. We used a realistic simulation of the
general population with age dependency and heterogeneity in
fecundability.
METHODS
Study Population
We adapted a simulation model previously developed
by Leridon.34
The model simulates life histories of 1,000,000 women
by randomly generating events during their life following real-
istic distributions. For each woman, age at onset of permanent
sterility is drawn, and fecundability is assumed to vary with
age (eFigure 2; http://links.lww.com/EDE/B404).34
Starting from the age of 18 years, the model draws for
each subject the emergence of a stable relationship, the start
of attempts to become pregnant among those in a relation-
ship, conception following the attempts and the pregnancy
outcome, which can be a live birth or a miscarriage. Monthly
TABLE 1. Characteristics of the Main Study Designs Considered
Study Design Timing of Inclusion
Conditioning
of Inclusion Follow-up Outcome of Interest Censoring
Handling of Infertility
Treatments
1) Incident cohort Before the start of the
PUI
Couple starts a PUI Yes Time until pregnancy min(C, treatment,
time gives up)
Censoring of duration at
the treatment start
2) Prevalent cohort During PUI Couple is currently
during a PUI
Yes Time until pregnancy min(C, treatment,
time gives up)
Censoring of duration at
the treatment start
3) Prevalent cohort
with delayed entry
limited to 6 months
During PUI 2) + PUI started <6
months ago
Yes Time until pregnancy min(C, treatment,
time gives up)
Censoring of duration at
the treatment start
4) Current duration During PUI 2) No Time until end of PUI At time C
5) Current duration,
treatments excluded
During PUI 4) + Couple has not
started treatment at
inclusion
No Time until end of PUI min(C, time
gives up)
Couples with treatment
before inclusion are
excluded
6) Pregnancy-based
design
After pregnancy
detection
A pregnancy started
and was detected
No Time until pregnancy in
fecund couples
min(C, treatment) Censoring of duration at
the treatment start
7) Pregnancy-based
design, treatments
excluded
After pregnancy
detection
A pregnancy started
without treatment
and was detected
No Time until pregnancy in
fecund couples not
resorting to medical
treatments
min(C) Exclusion of couples with
treatment
C was set to 12 months in the main analysis and to 6 months in the secondary analysis.
C indicates censoring duration; PUI, period of unprotected intercourse.
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Eijkemans et al. Epidemiology • Volume 30, Number 1, January 2019
122 | www.epidem.com © 2018 Wolters Kluwer Health, Inc. All rights reserved.
chances of these events, of the number of desired children
and the distribution of birth spacing intervals, were drawn
from distributions based on demographic data from France.
Intervening events are also modeled: becoming widowed or
becoming divorced.34 Fertility treatments were also incorpo-
rated into the simulations. We assumed that couples start treat-
ment in a deterministic way when they were not pregnant after
a duration depending on the woman’s age: 48 months before
age 30 (i.e., an assumption that 100% of couples not pregnant
within 4 years resort to infertility treatment), declining to 36
months at age 35, 24 months at age 40, and 12 months at 45.
Irrespective of age, the duration before treatment start was 12
months for women sterile when trying to become pregnant,
assuming that a clinical examination would be performed and
would allow diagnosing sterility.35
The main extensions to the original demographic simu-
lation model34,35 were (1) couples would not persist indefi-
nitely in their pregnancy attempt. A 10% yearly stopping
rate (including divorce, modeled separately, see above) was
assumed, independently of age.36 (2) For each woman, date of
birth has been defined, drawn uniformly between 1 January
1955 and 31 December 1999.
The reproductive life of each woman was divided into
consecutive episodes, which were saved. Each episode was
characterized by five attributes: its end-date; the matrimo-
nial situation (single, married/having a stable relationship,
widowed, divorced); the intention with respect to reproduc-
tion (not trying to become pregnant: no partner; not trying:
enough children; not trying: too soon; trying; pregnant); the
outcome in case of pregnancy (miscarriage or live birth); and
the treatment status (yes/no). For each woman, a new episode
is created when any one of these attributes changes owing to a
randomly drawn variable.
Sampling According to the Compared Designs
From the simulated population of 1,000,000 individu-
als, we drew women according to each of the four study
designs that we considered (eFigure 1; http://links.lww.com/
EDE/B404 and Table 1). The actual sampling was supposed to
take place or start on one specific day.
The pregnancy-based approach focused on all women
who had had a planned pregnancy (leading to a live birth
or a spontaneous abortion) in the 15-year period before the
inclusion date (assumed to be 1 July 2015); the outcome
was TTP of the most recent pregnancy, defined as the dura-
tion elapsed between the start of the period of unprotected
intercourse and date of conception. We did not consider
unplanned pregnancies because their TTP is not defined.
Some couples would retrospectively describe these preg-
nancies as planned in a pregnancy-based study, and possibly
assign them a (short) TTP, which corresponds to pregnancy
planning bias.37 By ignoring these unplanned pregnancies,
our model essentially assumes that there is no planning bias
that would occur if the probability of having an unplanned
pregnancy was related to fecundability, which would influ-
ence all designs.
The current duration design corresponded to a cross-
sectional sampling of all women having unprotected inter-
course at the inclusion date (eFigure 1; http://links.lww.com/
EDE/B404, and Table 1). The outcome was the current dura-
tion of unprotected intercourse, corresponding to the duration
elapsed between the start of the pregnancy attempt and the
inclusion date.
The prevalent cohort design relied on the population
sampled in the current duration design, except that in this
case it was followed up; the outcome was time to pregnancy,
defined as the time elapsed between the start of the period
of unprotected intercourse and the date of conception. We
also implemented a prevalent cohort approach in which only
couples with a current duration of less than 6 months at inclu-
sion (the “recent initiators”) were eligible, a restriction used in
several prevalent cohort fecundity studies.25,38
The incident cohort study sampled all women wishing
to start a period of unprotected intercourse within an accrual
period of 12 months starting from the sampling date. For the
prevalent cohort and incident cohort designs, length of fol-
low-up was assumed to be 12 months, or less if a pregnancy
occurred before this duration.
We assumed a lack of any measurement error for all
four designs.
Estimation of the Cumulative Probability of
Pregnancy
The eligibility rate of each design was defined as the
ratio of the number of eligible women to the total number of
women 18–44 years of age in the population (here, 1,000,000).
The cumulative probability of pregnancy was estimated
using the Kaplan-Meier approach for the pregnancy-based
and incident cohort designs, and Kaplan-Meier approach with
left truncation (i.e., delayed entry) at the date of inclusion for
the prevalent cohort design. For the current duration design,
we used a parametric approach assuming an underlying gen-
eralized gamma distribution with censoring at 36 months.39,40
TTP was in addition right censored at the date of occur-
rence of an infertility treatment in the pregnancy-based and
in the two cohort designs; for the current duration analysis,
we provide estimates in which couples with treatment were
either excluded or included, as previously done23; we have
also repeated the pregnancy-based analysis excluding couples
with treatment, instead of censoring them, to mimic what
would happen in a society where fecundity treatments are not
widespread. Pregnancy rates were provided at 3, 6, and 12
months and compared taking the incident cohort estimate as
a reference.
As a basic test of the validity of our approach, we also
simulated a population without fecundability heterogeneity,
age dependence of fecundity, sterility, and stopping behavior.
We estimated the corresponding survival curves, expecting
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Epidemiology • Volume 30, Number 1, January 2019 Comparison of Four Designs to Assess Fecundity
© 2018 Wolters Kluwer Health, Inc. All rights reserved. www.epidem.com | 123
that, in this homogeneous population, all sampling designs
would give identical results.
Estimation of the Impact of a Risk Factor on
Fecundity
We assumed the existence of a risk factor A that
impacted on fecundability without affecting the proportion of
sterile couples; fecundability was multiplied by 0.7 in sub-
jects exposed to A. The prevalence of exposure to factor A
was assumed to be independent of all characteristics of the
subjects and corresponded to 20% of the whole population.
We drew subjects from a new simulated population accord-
ing to each study design as indicated above, the probability of
inclusion being independent of exposure status.
The impact of the risk factor was estimated using the
Cox proportional hazard model, with delayed entry for the
prevalent cohort analysis. The Cox model estimates hazard
ratios (HR) of pregnancy, a value below one indicating that
the probability of pregnancy is decreased in exposed com-
pared with nonexposed subjects. For the pregnancy-based,
incident, and prevalent cohort designs, we used a continuous
Cox model with the Efron method to handle ties. Note that
though the simulation is in units of months, the data are in
units of days, because we generated birth dates with a resolu-
tion at the level of days. For the current duration approach, we
used a modification of the “semiparametric” adaptation of the
Cox model proposed by McLain et al.41 Observations were
censored at 12 months for the incident and prevalent cohort
designs (which was the maximum length of follow-up we
assumed). The Cox proportional hazards model is known to
suffer from attenuation bias.27,28 We tried to limit the atten-
uation bias identified in early simulation runs by censoring
observations at 6 months. For the current duration design, this
was done by right-truncating the observed distribution at 6
months before applying the McLain algorithm. Models were
run without and with adjustment for age.
RESULTS
Study Population
The eligibility rate was highest for the pregnancy-based
design (35% of women 18–44 years of age were eligible,
Table 2) and lowest for the current duration and prevalent
cohort designs (about 2% of women). The current duration
and prevalent cohort designs over-represented sterile couples
(2.5% sterility for the current duration design), compared with
an incident cohort (1.0% of couples were sterile, Table 2),
an overrepresentation that is corrected for in the statistical
analyses.
Cumulative Probability of Pregnancy
In the situation without sterility, age dependency, or
any other source of heterogeneity in fecundability and with-
out stopping behavior, all four designs showed as expected
TABLE 2. Eligibility Rate, Sample Composition, and Number of Events in the Population Studied According to Each of the Four
Considered Study Designs: Simulation of 1,000,000 Women
Characteristics
Study Design
Incident
Cohort
Current
Duration
Prevalent
Cohort
Prevalent Cohort
<6 MonthsaPregnancy-based
Number of eligible women (%) 43,024 (4.3) 20,396 (2.0) 20,396 (2.0) 14,620 (1.5) 345,035 (35.0)
Age at start of attempt (years)b26.8 (24.3, 29.9) 27.5 (24.7, 30.9) 27.5 (24.7, 30.9) 27.4 (24.7, 30.7) 27.8 (25.1, 30.8)
Number of children at inclusion
No child 47.4% 49.1% 49.1% 48.3% 36.3%
1 38.7% 37.3% 37.3% 37.9% 44.9%
2 11.7% 11.4% 11.4% 11.6% 15.7%
>2 2.1% 2.2% 2.2% 2.2% 3.2%
Proportion of couples sterile
at start of pregnancy attempt (n)
1.0% (460) 2.5% (513) 2.5% (513) 1.9% (285) 1.0% (3,556)
Fecundability of nonsterile
couples at start of attemptb
0.22 (0.14, 0.31) 0.15 (0.08, 0.25) 0.15 (0.08, 0.25) 0.18 (0.11, 0.25) 0.22 (0.14, 0.29)
Exposure monthsb2.2 (0.9, 4.5) 3.3 (1.3, 6.5) 3.3 (1.4, 6.4) 4.0 (1.5, 7.7) 3.1 (1.2, 7.3)
Proportion of couples with a
pregnancy during follow-up (n)
60.0% (25,793) 0 (0) 57.1% (11,642) 69.6% (10,169) 85.0% (293,340)
Proportion of couples treated for
infertility (n)c
0.8% (337) 0.5% (109) 1.3% (273) 1.3% (197) 5.9% (20,499)
aPrevalent cohort approach restricted to recent initiators, i.e., to couples who have started the period of unprotected intercourse for less than 6 months at the time of inclusion.
bMedian and (25th–75th) percentiles.
cProportion of couples treated for involuntary infertility during the period “at risk of pregnancy”, i.e., between inclusion and end of follow-up (incident and prevalent cohorts);
between start and end of the last period of unprotected intercourse leading to a pregnancy (pregnancy-based design) or between the start of the current period of unprotected intercourse
and inclusion (current duration design).
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very similar results (eFigure 3; http://links.lww.com/EDE/
B404). When we considered a more realistic population with
age dependence of fecundity, with additional heterogene-
ity in fecundability, with sterile couples and including stop-
ping behavior, the cumulative pregnancy rates after 6 and 12
months of unprotected intercourse were 68.3% (95% confi-
dence interval [CI], 67.9, 68.8) and 83.1% (95% CI, 82.7,
83.5, Table 3 and Figure 1) for the incident cohort design. The
absolute bias in the estimated rate of 12-month involuntary
infertility (the incident cohort being taken as a reference) was
close to or below 2% for most designs, but for the pregnancy-
based analysis in which couples with an infertility treatment
were excluded; in this case, the rate of 12-month involuntary
infertility was underestimated by 7% (estimated rate, 10%,
compared with 17% for the incident cohort). Including treated
couples (with censoring) limited the bias of the pregnancy-
based design (Table 3).
Impact of a Risk Factor on Fecundity
The HR associated with factor A tended to be attenu-
ated (biased toward one) in all designs, the bias being lowest
for the current duration design (age- and parity-adjusted HR,
0.78, 95% CI, 0.73, 0.84, compared with a theoretical value
among fecund couples of 0.70) and highest for the prevalent
cohort design (HR, 0.85, 95% CI, 0.81, 0.89, Table 4). The
plot of the hazard rates allowed investigating the origin of
this bias and showed that, both for the incident and prevalent
cohort designs, the hazard ratio associated with exposure to A
attenuated over time to reach a value close to 1.0 after 10–15
months of unprotected intercourse (Figure 2A). The number
of subjects still trying to become pregnant was, as expected,
maximum during the first month of unprotected intercourse in
the incident cohort design, whereas it was lowest during the
first month of unprotected intercourse and increased to reach
a maximum for a follow-up of about 6 months in the prevalent
cohort design, after which the number decreased because of
the restriction to recent initiators (Figure 2B).
Censoring at 6 months led to decreases in the num-
ber of observations in the current duration design and in the
prevalent cohort design without restriction to recent initiators
(in which many couples were included after more than 6
months of unprotected intercourse) but not for the other
designs (Table 4). HRs of pregnancy were all further away
from the null value and closer to the theoretical value of 0.70
after censoring at 6 months: for example, the HR of pregnancy
associated with factor A was 0.78 in the incident cohort design
after censoring at 6 months, compared with 0.79 when censor-
ing at 12 months (Table 4). The HR of pregnancy estimated
by the pregnancy-based design decreased from 0.82 to 0.79,
while that of the prevalent cohort decreased from 0.85 to 0.77,
reaching a value very close to the incident cohort estimate
TABLE 3. Bias of Estimates of the Cumulative Pregnancy
Rates at Various Follow-up Times for Each Study Design,
Including Couples Treated for Infecundity, Unless Stated
Otherwise: Simulation of 1,000,000 Women
Study Design
Proportion
Pregnant,
% (95% CI) Biasa
Incident cohort
At 3 months 48.1 (47.7, 48.6) 0 (ref)
At 6 months 68.3 (67.9, 68.8) 0 (ref)
At 12 months 83.1 (82.7, 83.5) 0 (ref)
Current durationb
At 3 months 49.1 (46.1, 53.2) 0.010
At 6 months 68.6 (66.9, 70.4) 0.003
At 12 months 83.6 (82.8, 84.4) 0.005
Current duration, excluding treated couplesb
At 3 months 49.4 (46.0, 52.6) 0.013
At 6 months 69.3 (67.3, 71.0) 0.009
At 12 months 84.8 (84.0, 85.6) 0.018
Prevalent cohort
At 3 months 47.7 (45.8, 49.6) −0.004
At 6 months 67.9 (66.6, 69.1) −0.005
At 12 months 83.2 (82.5, 83.9) 0.002
Prevalent cohort <6 monthsc
At 3 months 47.7 (45.8, 49.6) −0.004
At 6 months 67.9 (66.6, 69.1) −0.005
At 12 months 83.4 (82.6, 84.1) 0.003
Pregnancy-based
At 3 months 49.0 (48.9, 49.2) 0.009
At 6 months 69.8 (69.6, 69.9) 0.014
At 12 months 85.4 (85.3, 85.5) 0.023
Pregnancy-based, excluding treated couples
At 3 months 52.1 (51.9, 52.3) 0.040
At 6 months 74.1 (73.9, 74.2) 0.058
At 12 months 90.4 (90.3, 90.5) 0.073
aDifference between the design-specific estimate and the reference value, as
estimated by the incident cohort for the same duration of follow-up.
b95% CI for the current duration design were estimated by bootstrapping.
cPrevalent cohort approach restricted to recent initiators, i.e., to couples who have
started the period of unprotected intercourse for less than 6 months at the time of
inclusion.
FIGURE 1. Cumulative pregnancy chances by four sampling
approaches, on simulated data, in the simulation run including
heterogeneity in fecundability, age dependency, and sterility.
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Epidemiology • Volume 30, Number 1, January 2019 Comparison of Four Designs to Assess Fecundity
© 2018 Wolters Kluwer Health, Inc. All rights reserved. www.epidem.com | 125
(HR, 0.78). The current duration estimate was the least biased
(HR, 0.72), but had by far the widest confidence interval (0.57,
0.92, compared, e.g., with 0.75, 0.80 for the incident cohort).
DISCUSSION
This study is to our knowledge the first systematic compar-
ison of most available models for the analysis of human fecund-
ability in the general population. Within a realistically simulated
population, we have applied four main different study designs
to describe the fecundity level of the population and the impact
of a risk factor on fecundity. In terms of ability to describe the
fecundity level of the population, the pregnancy-based design
tended, as expected, to over-estimate the fecundity level of the
population, which was particularly obvious if couples with infe-
cundity treatment were excluded or, equivalently, in populations
where efficient infecundity treatments are not widely available.
Regarding the ability to highlight the impact of a risk factor on
fecundity, all four designs analyzed by proportional hazards
regression suffered from attenuation bias. The attenuation was
reduced by censoring analyses at 6 months follow-up.
Population
Our approach was based on a carefully simulated popu-
lation that had many of the features of a real population.7,34,42
The model assumed that it is possible to identify and
recruit a random subsample of women before they start a
period of unprotected intercourse (in the incident cohort
design), which is something that not all couples plan long in
advance.43 We also assumed that one was able to identify and
recruit all couples starting a period of unprotected intercourse
within a 1-year period, which may also be practically very
challenging. For these reasons, the eligibility rate of the inci-
dent cohort approach is probably strongly overestimated. As
an illustration, in Denmark, screening among 52,255 women
members of a trade union, living as a couple, and 20–35 years
of age allowed to recruit and follow-up 430 women, a rate
of 0.8% encompassing ineligibility and refusals. This rate is
much lower than the rate of 4% of women assumed to be eli-
gible in the incident cohort design in our simulation.
More generally, we assumed a lack of selection bias,
with the exception of the fact that the pregnancy-based design
excluded infertile couples. This is optimistic; indeed, couples
with long TTP might be more prone to participate in fecundity
studies with collection of biological samples, compared with
couples with shorter TTP.44,45
We did not consider a retrospective design in which one
would attempt to collect the TTP of unsuccessful attempts at
pregnancy, in addition to that of periods of unprotected inter-
course leading to a pregnancy. Identification of such unsuc-
cessful attempts at pregnancy has been advocated16 and
attempted.46,47 This corresponds to the so-called historically
prospective cohort, which we expect to be less biased than the
pregnancy-biased design implemented here. To efficiently con-
sider the historically prospective cohort design in our simula-
tion study, one would have needed realistic information on the
structure of recall error of unsuccessful attempts at pregnancy
and their duration. In practice, it seems relevant to try collect-
ing information on these unsuccessful attempts in retrospective
studies, if only to use them in sensitivity analyses.16,46,47
TABLE 4. Estimates of the Effect of a Risk Factor A on the Probability of Pregnancy
Study Design
Sample
Size
Number of
Eventsa
Prevalence of Risk
Factor A (%)
Hazard Ratio (95% CI)b
Not Adjusted Adjusted
Censoring at 12 months
Incident cohort 43,523 25,345 20.2 0.79 (0.76, 0.81) 0.79 (0.76, 0.81)
Current durationc21,431 - 23.1 0.78 (0.73, 0.84) 0.78 (0.73, 0.84)
Current duration, excluding treatmentsc20,825 - 23.0 0.78 (0.73, 0.84) 0.78 (0.73, 0.84)
Prevalent cohort 20,825 11,593 23.0 0.86 (0.82, 0.90) 0.85 (0.81, 0.89)
Prevalent cohort, entry<6 monthsd14,725 10,037 22.1 0.85 (0.81, 0.89) 0.85 (0.81, 0.89)
Pregnancy-based 348,268 292,564 20.5 0.82 (0.81, 0.82) 0.82 (0.81, 0.83)
Censoring at 6 months
Incident cohort 43,523 23,394 20.2 0.77 (0.75, 0.80) 0.78 (0.75, 0.80)
Current durationc15,048 - 22.0 0.77 (0.68, 0.89) 0.72 (0.57, 0.92)
Current duration, excluding treatmentsc14,725 - 22.1 0.75 (0.65, 0.86) 0.73 (0.58, 0.91)
Prevalent cohort 14,725 6,248 22.1 0.77 (0.73, 0.82) 0.77 (0.73, 0.82)
Prevalent cohort, entry<6 monthsd14,725 6,248 22.1 0.77 (0.73, 0.82) 0.77 (0.73, 0.82)
Pregnancy-based 348,268 236,556 20.5 0.79 (0.78, 0.80) 0.79 (0.78, 0.80)
A hazard ratio of pregnancy below one indicates reduced fecundability. Simulation of 1,000,000 women, assuming that factor A reduced fecundability by a multiplicative factor 0.7.
aEvents correspond to pregnancies. The “-” for the current duration approach indicates no pregnancies as in this design women are recruited during the period of unprotected
intercourse without follow-up.
bHazard ratio of pregnancy, as estimated from Cox proportional hazards model. Adjusted hazard ratios have been adjusted for woman’s age at the start of the period at risk and parity.
cThe hazard ratio in the current duration approach is derived from McLain’s method.41 Observations with current duration above 12 (or 6) months are excluded instead of censored.
dPrevalent cohort in which only couples who have been trying for less than 6 months at inclusion are recruited.
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Eijkemans et al. Epidemiology • Volume 30, Number 1, January 2019
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Measurement Error and Confounding
We assumed that time to pregnancy was assessed with-
out error, which is clearly optimistic for the pregnancy-based
approach. Indeed, although the distribution of retrospectively
assessed TTP has been shown to be relevant at the population
level,48 recall error exists at the individual level.49 Such errors
are likely to lead to decreased power in studies aiming at char-
acterizing the effect of exposures on fecundity.50 A simula-
tion study characterized measurement error on TTP from the
differences in TTP reported using a simple questionnaire and
a more refined one taken as a gold standard (thus probably
underestimating measurement error compared with a perfect
measure of TTP). Measurement error entailed a decrease in
power by about 0.2 for a given population size and a bias in
the estimated fecundability ratio by one fifth in the estimated
fecundability reduction associated with exposure.50 If applied
to our data, this bias would increase the HR associated with
factor A in the pregnancy-based design from 0.79 to 0.84,
starting from a theoretical value of 0.70. In other words, with
these assumptions, the pregnancy-based design would only
see half of the real effect of the risk factor (a 16% instead of
a 30% decrease).
Furthermore, we assumed a lack of misclassification
for the exposure factor considered. Measurement error will
generally be higher for the designs in which there is some ret-
rospective component in the assessment of the exposure, such
as the pregnancy-based and the current duration designs. This
will, for example, be the case if exposure is assessed from a
biospecimen, which can be collected at the start of the fol-
low-up period in incident and prevalent cohorts designs but
is collected retrospectively for the pregnancy-based and cur-
rent duration designs. Biomarkers of many currently produced
chemicals have short-term variations,51 which would preclude
reliance on the pregnancy-based and current duration designs.
Depending on the structure of the error, bias in the dose–
response function can be expected as a result of exposure mis-
classification (e.g., in the case of classical-type error52) and
loss in statistical power (e.g., in the case of classical-type and
Berkson-type errors).
Bias due to reverse causality can also be expected in
these retrospective settings if one does not make efforts to
assess exposure at the start of the period of unprotected inter-
course; for example, couples may modify behaviors associated
with exposure to factors suspected to alter fecundity after a
long period of unprotected intercourse.37 Bias may also exist
in the case when there are time trends in exposure,53 as may
happen for behaviors recently identified as possibly harmful or
beneficial or for contaminants with changing regulatory levels,
such as atmospheric pollutants. This bias is of particular con-
cern for designs in which the date of the start of the period of
follow-up varies with time to pregnancy, which is the case for
the pregnancy-based and current duration designs, but it can be
avoided in incident and prevalent cohort designs. Our simula-
tion assumed a lack of such temporal trends in exposure.
We adjusted for age and parity. The estimated effect of
the risk factor was unaffected by controlling for effect of age,
which is explained by the fact that we assumed independence
of age and risk factor in the simulation. In real life, there
will be more confounders. Again, designs in which confound-
ers need to be assessed retrospectively may be more prone to
residual confounding than designs in which confounders can
be assessed prospectively such as the incident and prevalent
cohort designs. This is all the more a concern since, in the set-
ting of survival analyses, bias in the dose–response function
FIGURE 2. Comparison of the incident and prevalent cohort
designs. (A) Hazard of pregnancy and (B) Number of women
at risk of pregnancy among subjects exposed (dots) and not
exposed (continuous curves) to factor A for the incident (thin
lines) and prevalent (thick lines) cohorts designs. Exposure
prevalence was assumed to be 20% in the source population.
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Epidemiology • Volume 30, Number 1, January 2019 Comparison of Four Designs to Assess Fecundity
© 2018 Wolters Kluwer Health, Inc. All rights reserved. www.epidem.com | 127
is expected not only if factors simultaneously associated with
exposure and outcome are not adjusted for, but also if fac-
tors only associated with the outcome but not with exposure
at the start of follow-up are not considered, or are measured
with error.54
Handling of Infertility Treatments and Other
Censoring Events
The main censoring events considered were fecundity
treatments and couples stopping the period of unprotected
intercourse before the occurrence of pregnancy. One can
adhere strictly to the original “fecundity” purpose of TTP
studies—to obtain estimates of human (biological) fecundity
in the absence of medical intervention—or take a pragmatic
“fertility” view of just estimating ability to conceive in today’s
society where fertility treatment is a reality. In this article,
we presented results relating to both of these views. In the
“fecundity” view, fertility treatment would be considered an
endpoint competing with giving up and with becoming preg-
nant and they would need to be taken into account (by censor-
ing as we did or using competing risk models).
Ability to Describe the Frequency of
Involuntary Infertility
The comparison of the various designs should be done
keeping in mind that there are differences in the outcomes
assessed by each design (the targets of inference, Table 1). The
incident and prevalent cohort designs focus on the occurrence
of pregnancy; in the pregnancy-based design, the outcome
is the occurrence of pregnancy in couples who eventually
become pregnant. The current duration approach estimates
the minimum of TTP and time to give up. This is shorter than
TTP; a similar phenomenon is present in the pregnancy-based
design.36,55
For the pregnancy-based design, the estimated probabil-
ity of involuntary infertility was, as expected, biased toward
lower values; indeed, the conditional distribution of TTP, given
that it is shorter than the time of giving up, is stochastically
smaller than the marginal distribution of TTP. For the current
duration design, our expectation was to see shorter estimates
of the distribution of “length of trying” than those of TTP
from the prospective designs, because of the couples giving
up the pregnancy attempt. This is not apparent from Figure 1
and Table 3, where the differences are small so that this issue
does not seem to entail consequences with the hypotheses on
which our simulation relied.
Ability to Highlight an Effect of Risk Factors on
Fecundability
When we simulated the impact of a risk factor influenc-
ing fecundability, the most striking feature of our results was
the attenuation bias, which impacted all four designs. This
was obvious from the fact that the estimated hazard ratios
of pregnancy associated with the risk factor were generally
in the 0.8–0.9 range while the theoretical value was 0.7, an
underestimation by one-third to two-thirds. Attenuation bias is
a serious issue in survival analysis, and a rich literature exists
for what we here describe as incident cohorts27,28 (see refer-
ence 56 for references). After a very long duration, the ratio of
the hazard rates of pregnancy between exposed and unexposed
subjects converges to one (i.e., a lack of observed effect of
exposure), which is a manifestation of attenuation bias. This
situation is obvious from Figure 2A, showing that, with the
hypotheses of our study, this convergence of the hazard ratio
to one is reached after about 10 months of unprotected inter-
course. This suggests that durations longer than 9–10 months
do not provide any information in terms of the possible effect
of the exposure considered. Consequently, authors should see
censoring not as a procedure entailing a loss of information
but rather as an efficient way to limit bias. The fact that the
attenuation was larger in the prevalent cohort than in the inci-
dent cohort can be explained by the fact that the number of
subjects at risk was largest at the start of the period of unpro-
tected intercourse for the incident cohort, when attenuation is
weakest, while for the prevalent cohort, the number of sub-
jects at risk was highest around month six, when attenuation
bias was large (Figure 2B); because the overall estimate is a
weighted average of the estimates based on the numbers at
risk during follow-up, the prevalent cohort will give an esti-
mate that is more biased than that of the incident cohort. Some
studies relying on the prevalent cohort design have restricted
eligibility to couples who have started the period of unpro-
tected intercourse for 3 months or less, thus further limiting
the oversampling of couples with a long duration at inclusion
and the resulting attenuation bias.24
Focusing on the start of the period at risk through cen-
soring is a known28 simple cure for attenuation bias. The con-
vergence of the hazard ratio to one around 10 months led us
to censor observations around month 6, but shorter censor-
ing duration can be considered to further limit bias. For most
designs but the current duration one (for which there were
convergence issues with the estimator57), further censoring
at durations shorter than 6 months tended to slightly further
reduce bias, at the cost of increases in the width of confi-
dence intervals (not detailed). Following this logic, a study of
atmospheric pollution effects on fecundability has focused on
the first month of unprotected intercourse, disregarding later
months.11 Most pregnancy-based studies censor observations
after 12 months, which on the basis of our simulation may not
be enough.
We have used validated statistical approaches to analyze
data. Other approaches are possible, including combining the
data collected by different designs. For example, it may be
possible to make use of the information of the current duration
(elapsed between the start of the period of unprotected inter-
course and the time of inclusion) when analyzing prospective
TTP data from a prevalent cohort. An estimator allowing to
combine prospectively collected and retrospectively collected
time-to-event information, collected in the same subject, has
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Eijkemans et al. Epidemiology • Volume 30, Number 1, January 2019
128 | www.epidem.com © 2018 Wolters Kluwer Health, Inc. All rights reserved.
been proposed and applied in a study of pneumonia occur-
rence in HIV subjects.58 To our knowledge, a similar approach
has not been implemented in the field of fecundity studies yet.
In conclusion, the compared study designs show little
bias in assessing the level of infertility in a population (with
the exception of a pregnancy-based design excluding cou-
ples with infertility treatment), but require special care (e.g.,
through censoring analyses at 6 months or possibly earlier) to
limit attenuation bias when analyzing the effect of an environ-
mental risk factor using standard regression modeling. Dis-
regarding other sources of bias, many previously published
studies not censoring observations at short durations may
have underestimated the effect, if any, of risk factors. Overall,
if issues related to recall error and exposure misclassification
due to a retrospective assessment of exposures are ignored,
there appear to be no strong differences between designs in
terms of bias. The current duration approach was, with our
assumptions, the least biased in terms of estimation of the
effect of a factor influencing fecundability; however, it was
also the one with the largest variance. For factors that are likely
to vary strongly over periods of several months (as would, e.g.,
be the case for many currently produced chemicals or biologic
parameters such as hormonal levels) and in the absence of
modeling approaches that would allow efficiently predict the
level of these factors back in time, incident or prevalent cohort
designs should be preferred; these are to be used with careful
sensitivity or fine-tuning analyses to quantify and if possible
remove attenuation bias.
ACKNOWLEDGMENTS
The authors thank Jean Bouyer (Inserm) for useful
discussions at the initiation of this project.
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