Confounding by Conception Seasonality in Studies of Temperature and Preterm Birth

Abstract

Background:

Seasonal patterns of conception may confound acute associations between birth outcomes and seasonally varying exposures. We aim to evaluate four epidemiologic designs (time-stratified case-crossover, time-series, pair-matched case-control, and time-to-event) commonly used to study acute associations between ambient temperature and preterm births.

Methods:

We conducted simulations assuming no effect of temperature on preterm birth. We generated pseudo-birth data from the observed seasonal patterns of birth in the United States and analyzed them in relation to observed temperatures using design-specific seasonality adjustments.

Results:

Using the case-crossover approach (time-stratified by calendar month), we observed a bias (among 1,000 replicates) = 0.016 (Monte-Carlo standard error 95% CI: 0.015–0.018) in the regression coefficient for every 10°C increase in mean temperature in the warm season (May–September). Unbiased estimates obtained using the time-series approach required accounting for both the pregnancies-at-risk and their weighted probability of birth. Notably, adding the daily weighted probability of birth from the time-series models to the case-crossover models corrected the bias in the case-crossover approach. In the pair-matched case-control design, where the exposure period was matched on gestational window, we observed no bias. The time-to-event approach was also unbiased but was more computationally intensive than others.

Conclusions:

Most designs can be implemented in a way that yields estimates unbiased by conception seasonality. The time-stratified case-crossover design exhibited a small positive bias, which could contribute to, but not fully explain, previously reported associations.

Seasonal patterns of birth have long been observed in human populations.^1,2 In the United States, the pattern is generally characterized by a trough of births in spring and peak in late summer.³ This seasonal birth pattern is thought to be primarily driven by seasonally varying conception rates, which could be due to biologic factors affecting fecundability (e.g., vitamin D, temperature effects on sperm, day length) and cultural and behavioral factors such as seasonal behaviors in pregnancy planning or coital frequency,^1,4–6 factors that could differ across space, time, and population subgroups (e.g., age, race, socioeconomic status).⁷ Seasonal patterns of pregnancy loss could also potentially contribute to observed seasonal patterns of live births.⁸ These seasonal patterns could introduce bias for studies of preterm birth based on temporal contrasts of a short-term change in an exposure if peaks or troughs in exposure (e.g., ambient temperature) align with clusters of ongoing pregnancies in late gestation.

Researchers have used different study designs such as time-stratified case-crossover,^9–13 time-series,^12,14–16 case-control,^17–20 and time-to-event^21–25 to study acute associations between seasonally varying exposures, such as air pollution and ambient temperature, and preterm birth. Conventionally, these designs have different study population definitions, effect measures, and approaches for adjusting for seasonally varying confounders.

In the time-stratified case-crossover design, cases serve as their own controls, with control periods selected on the same day of week within the study month, to adjust for time-invariant and slowly varying confounders.^26,27 An underlying assumption for this design is that either the exposure or all other risk factors for disease do not change over the time window in question,^28–30 an assumption that could be violated by seasonal patterns of conceptions.

The time-series design is commonly used to study short-term changes in environmental exposures and health outcomes. It can accommodate overdispersion and auto-correlation.^29,31 To adjust for seasonal confounding, researchers commonly use a spline function on time (e.g., the day of study) as covariates to control for unmeasured seasonally varying confounders. Unfortunately, effect estimates can be sensitive to the specification of the spline function (e.g., placement and number of knots). To directly control for seasonal patterns of conception, counts of fetuses at risk can be introduced as a weighted offset³² with the conditional probability of birth at a given gestational age used to generate weights.^15,16

Although the case-control design is less commonly used to study time-varying exposures and preterm births, some studies^17–20 have used this approach to estimate the acute association of environmental exposures (e.g., air pollution and temperature) instead of a full-cohort analysis because of the computational difficulties in fitting models with a large sample size. For example, a pair-matched case-control approach allows the gestational exposure window in the control to be matched to the gestational window when the case delivered. This approach should inherently control for seasonality of conception since cases and controls are matched on gestational timing of the exposure window.

In the time-to-event design with discrete follow-up time (e.g., by week),^21,22,25,33 gestational age is viewed as time-to-event data by defining an at-risk window (weeks 20–36 of gestation) in which preterm birth can occur. The use of time-varying exposures allows for the estimation of associations with short-term environmental exposures, while incorporating different probability of delivery at different gestational ages. However, with each birth having multiple rows of time-varying exposures, it can be computationally intensive for a large sample size.

It is possible that several previous studies that have reported higher risks of preterm birth with increasing temperatures could be partially or fully spuriously driven by conception seasonality. To our knowledge, no quantitative simulation study has been conducted to investigate how effectively the aforementioned designs and adjustment approaches for confounding by conception seasonality. We used a simulation study to quantify possible bias caused by seasonal patterns of conceptions assuming the null is true using birth records from 50 US Metropolitan Statistical Areas (MSA), and we examined whether bias remained after implementing specific approaches to adjustment for seasonality in each design.

METHODS

Illustrative Birth Data

We used empirical birth data to inform the simulation parameters (e.g., seasonal patterns of conceptions and gestational age distribution at birth). We obtained empirical US birth data from the National Center for Health Statistics (NCHS, https://www.cdc.gov/nchs/data_access/vitalstatsonline.htm) during 1982–1988, years for which geographic information and birth date are publicly available. We selected singleton births with complete information on gestational age and DOB, from the fifty most populous MSA (2010 Census). The study protocol was approved by the University of Nevada, Reno Institutional Review Board (IRB no.: 1164285–8).

Pseudo-birth Data

We used birth records from the 50 most populous MSAs to estimate the empirical US seasonal pattern of conceptions from which we generated pseudo-births with seasonality.

We simulated last menstrual period (LMP) dates for each pregnancy, which are by convention used as the starting point for calculating gestational age and occur on average 2 weeks before conception. We generated 1,000 datasets (LMP dates from 1 January 1985 to 14 February 1988; we generated for a longer time period than ultimately included in each analysis, which varied by design, to ensure the risk set of fetuses would be fully enumerated) following the conception patterns estimated from the LMP dates in the empirical birth records (the line in Figure 1A). We drew daily LMP counts from a normal distribution (Eq 1), where the mean varies by LMP date (Eq 1, Figure 1A), and the standard deviation varies by LMP month. We calculated daily mean and standard deviation at LMP month from the empirical births. Specifically, we simulated daily counts as

$$C_i~N(\stackrel{-}{C_i},S{D}_{m\left(i\right)})$$ (1)

where $C_i$ represent LMP counts on day $i$ of month $m\left(i\right)$ (i.e., $m(.)$ a function that maps calendar day to calendar month), $\stackrel{-}{C_i}$ is the mean number of LMP counts on day $i$, and ${\mathrm{S}\mathrm{D}}_{m\left(i\right)}$ is the standard deviation during study month $m\left(i\right)$ across 50 MSAs.

FIGURE 1.

One realization of simulated daily conception counts (dots) and expected mean of daily counts (line) with (A) and without (B) seasonality of conceptions aggregated across 50 Metropolitan Statistical Areas. LMP, last menstrual period.

We generated another 1,000 datasets where no seasonality of conceptions was present (i.e., daily LMP counts were drawn from a normal distribution with the overall constant mean of 5,300 and standard deviation of 680, both derived from the empirical birth data). Estimates generated from this scenario are expected to be unbiased and could indicate errors in the simulation or biases attributable to factors other than conception seasonality. We implemented all models with and without adjustment for seasonality, to assess whether the adjustment affected bias.

To assign birth date, we randomly assigned each pregnancy a gestational age in weeks (20–48 weeks old) and an MSA based on the overall distributions (gestational age mean ± SD: 39.3 ± 2.7 weeks, eFigure 1; http://links.lww.com/EDE/C5) in the empirical birth data. As a result, the outcome (i.e., preterm birth rate) does not vary across MSA. We note that all designs disregard gestational time after 37 weeks. We calculated date of birth (DOB) from LMP date and assigned gestational age (Eq 2). By randomly assigning gestational age and subsequent birth date, gestational age assignment is independent of ambient temperature (i.e., assuming a null association between acute temperature and preterm birth).

$$DOB=LMP+Gestational\_Age\times 7+ϵ,$$ (2)

where $ϵ~\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}(0,6)$ represents random assignment of number of extra days (integer) between 0 and 6 (because birth at 36 weeks would include those born at 36 and 0 days up to 36 and 6 days). We also conducted a sensitivity analysis drawing from a continuous distribution of gestational age, which did not affect conclusions (eFigure 2; http://links.lww.com/EDE/C5).

We analyzed simulated birth data using four designs, restricting analysis to a subset of the simulated births based on best practices of the design. Namely, case-crossover and time-series define the study population based on birth dates, whereas the case-control and time-to-event approaches are defined from an underlying cohort defined by conception dates. Table 1 summarizes dates of inclusion (by birth or conception) for each design. Because a range of conception dates does not correspond perfectly to a subsequent range of birth dates, the births included in the designs differed somewhat. Thus, we conducted analyses expanding the study population subsets for each design by 6 months to ensure that conclusions regarding bias were not affected by the range of LMP dates or birth dates included (eFigure 3; http://links.lww.com/EDE/C5). All regression coefficients are presented per 10°C increase in 7-day average of mean temperature (acute effects).

TABLE 1.

Definitions of Study Population by Design Within the Hypothetical Study Period Between 1 January 1986 and 31 December 1987

Study Design	Inclusion Criteria		Average Sample Size Per Replicate
	Full Year	Season-specific
Time-stratified case-crossover	Preterm births born between 1 January 1986 and 31 December 1987	Preterm births were stratified by seasona	354,884 preterm
Time-series	Time-series data were limited to the period 1 January 1986 and 31 December 1987 with fetus-at-risk (20–36 weeks) sets fully enumerated,	Time-series data were stratified by seasona after the weights and offset were created.	4,432,328 pregnancies were at-risk and 354,884 preterm births occurred during 1 January 1986 and 31 December 1987
Pair-matched case-control	Births whose LMP dates were between 14 August 1985 and 29 Janaury 1987b	Cases and controls whose at-risk window (20 weeks-36 weeks 6 days) overlaps with warma and cold seasona	261,348 cases and 261,348 matched controls selected from underlying cohort of 2,809,426 conceptions
Time-to-event	Births whose LMP dates were between 14 August 1985 and 29 Janaury 1987b	Follow-up week stratified by seasona	261,348 preterm births and 522,696 of full-term births randomly selected from underlying cohort of 2,809,426 conceptions

^aWarm season was defined as May–September; cold season was defined as October–April.

^bPregnancies with LMP dates between 14 August 1985 and 29 Janaury 1987 will all be born between 1 January 1986 and 31 December 1987.

Time-stratified Case-crossover Design

The time-stratified case-crossover design^9,10,12,34 included preterm births (births during gestational age 20–36 weeks) born between 1 January 1986 and 31 December 1987 in the study (on average 354,884 preterm births per dataset, Table 1). Control dates were the same day of week as the event date within the same calendar month (i.e., 3–4 control periods per case). We conducted conditional logistic regression to estimate the association bewteen 7-day average mean temperature and preterm birth across all simulated datasets with or without seasonality. Since time-stratified case-crossover adjusts time-invariant factors by design, there is no unadjusted model for this method (Table 2).

TABLE 2.

Model Specification for the Four Designs (Time-stratified Case-crossover, Time-series, Pair-matched Case-control, and Time-to-event) for the Unadjusted and Adjusted Models

Design	Statistical Model	Model Specification	Notation
Time-stratified case-crossover	Conditional logistic regression	$Logit\left[P\left(PTB\right)\right]={\beta }_1\times T_{mean}+\sum _{p=1}^{N}MatchingStratu{m}_p$ $Log\left(\frac{\mu \left(PTB\right)}{Z}\right)={\beta }_1\times T_{mean}+{\beta }_3\times Log\left(W_i\right)$	${\beta }_1$ is the coefficient per 10°C increase in mean temperature (denoted as Tmean); $\sum _{p=1}^{N}MatchingStratu{m}_p$ indicates the model is conditioned on matching strata (calendar month and day-of-week).
Time-series	Poisson regression	$Log\left(\frac{\mu \left(PTB\right)}{Z}\right)={\beta }_1\times T_{mean}+{\beta }_3\times Log\left(W_i\right)$	$\mu \left(PTB\right)$ is the daily preterm birth counts; offset Z represents ongoing fetuses-at-risk of preterm birth; $log\left(W_i\right)$ represent the logarithms of gestational week-weighted probability of giving preterm birth across study period.
Pair-matched case-control	Conditional logistic regression	$Logit[P(PTB)]={\beta }_1\times T_{mean}+\sum _{p=1}^{N}MatchingStratu{m}_p+\sum _{j=1}^n{\beta }_{2j}\times LM{P}_{m{y}_j}$	$\sum _{p=1}^{N}MatchingStratu{m}_p$ indicates logistic regression conditioning on matching pairs, where regression coefficients were not estimated; $\sum _{j=1}^n{\beta }_{2j}LM{P}_{-}m{y}_j$ represents the dummy variables for study month (e.g., January, 1986, Feburary,1986…, December, 1987) of last menstrual period date.
Time-to-event	Cox proportional hazard model	$\lambda (t)={\lambda }_0(t)\exp ({\beta }_1\times T_{mean}+\sum _{j=1}^n{\beta }_{2j}\times LM{P}_{m{y}_j})$	$\sum _{j=1}^n{\beta }_{2j}LM{P}_{-}m{y}_j$ the dummy variables for study month (e.g., January, 1986, Feburary,1986…, December, 1987) of last menstrual period date.

The bold term represents the design-specific adjustment for seasonality of conception in each design except for time-stratified case-crossover.

Time-series Design

In the time-series approach, we used the seasonality adjustment method proposed by Vicedo-Cabrera et al.,¹⁶ which is given as (Eq 3)

$$Y_i\mid {\mu }_i~\mathrm{Poisson}\left({\mu }_i\right),$$

$$\log \left(\frac{{\mu }_i}{z_i^{\left(w\right)}}\right)={\beta }_0+{\beta }_1\times T_{meani},$$ (3)

where $Y_i$ is the outcome count on study day $i,{\mu }_i$ is the expected outcome count on day $i$, and the corresponding weighted offset $z_i^{\left(w\right)}$ study day $i$ is given as (Eq 4)

$$z_i^{\left(w\right)}=\sum _{j=20}^{36}\left(Z_{ij}\times W_j\right),$$ (4)

where $Z_{ij}$ is the fetuses-at-risk study day $i$ and gestational age $j(j=20,21,\dots ,36\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s})$ and ${\mathrm{W}}_{\mathrm{j}}$ is the probability of giving birth conditional on the gestational age $j$. Older gestational ages have greater probability of birth, and therefore greater contribution to $z_i^{\left(w\right)}$. We note that, per the original method, the offset of fetuses-at-risk are enumerated on a weekly basis during the study period.

We can rewrite Eq 4 as

$$z_i^{\left(w\right)}=Z_i\times W_i$$

where $W_i$ is the weighted probability of giving birth on day $i$ across gestational ages given as (Eq 5):

$$W_i=\frac{\sum _{j=20}^{36}\left(Z_{ij}\times W_j\right)}{Z_i}$$ (5)

and $Z_i={\sum }_{j=20}^{36}{Z}_{ij}$ is the overall fetuses-at-risk, summed across gestational age 20 to 36 weeks.

We then replaced $z_i^{\left(w\right)}$ in Eq 3 with $Z_i\times W_i$ (as shown in Eq 4) such that

$$\mathrm{l}\mathrm{o}\mathrm{g}\left(\frac{{\mu }_i}{z_i^{\left(w\right)}}\right)=\mathrm{l}\mathrm{o}\mathrm{g}\left(\frac{{\mu }_i/Z_i}{W_i}\right)=\mathrm{l}\mathrm{o}\mathrm{g}\left(\frac{{\mu }_i}{Z_i}\right)-\mathrm{l}\mathrm{o}\mathrm{g}\left(W_i\right).$$ (6)

Hence,

$$\mathrm{l}\mathrm{o}\mathrm{g}\left(\frac{{\mu }_i}{Z_i}\right)={\beta }_0+{\beta }_1\times T_{mean}+{\beta }_w\times log\left(W_i\right)$$ (7)

where the overall risk set $\left(Z_i\right)$, remained as the offset and the logarithms of the weighted probability of giving birth $\left(W_i\right)$ was introduced into the equation as an explanatory variable. Poisson regression was conducted to estimate the regression coefficient for the exposure variables. A model adjusted for seasonality was implemented by introducing $log\left(W_i\right)$ in Eq 7 as a covariate (Table 2). Time-series were limited to the period 1 January 1986–31 December 1987 with fetus-at-risk sets fully enumerated. We also conducted sensitivity analysis allowing the scaling of standard error to account for overdispersion.

Pair-matched Case-control Design

We also examined a pair-matched case-control design (matching on MSA).^17–20 Fixed cohort bias can occur in retrospective birth cohort studies that define inclusion based on birth dates within a fixed start and end date because shorter pregnancies are missed at the start of the study, and longer pregnancies are missed at the end.²⁴ To avoid this bias, we defined the underlying cohort as births with LMP dates between 14 August 1985 (20 weeks before the beginning of the study) and 29 January 1987 (48 weeks before the end of the study, on average 261,348 preterm births per dataset, Table 1). Cases (20–36 weeks) and randomly sampled (within MSA) controls (≥37 weeks) were matched in a 1:1 ratio. The exposure period for each case was the 7 days before birth, and we used the same 7-day gestational period as the exposure period for each matched control (e.g., if the case was born in week 36, the control’s exposure was at week 36).^17,19 We analyzed data using conditional logistic regression, with indicator variables for LMP month and year combined added for seasonality adjustment (Table 2).

Time-to-event design

To eliminate the fixed cohort bias, we defined a cohort as births whose LMP dates were between 14 August 1985 and 29 January 1987. To reduce the computational burden introduced by reduction of the sample size, we included a random sample of full-term births twice the size as that of the preterm births (on average 261,348 preterm births per dataset, Table 1). Each individual is followed during pregnancy with the counting process starting at 20 weeks to either the week that the preterm birth happened (outcome=1), or to 36 weeks (censored as the pregnancy no longer contributes to the risk set).^21,25,33,35 We used Cox proportional hazard models to estimate the association between mean 7-day temperature and preterm birth. We added indicator variables for LMP month and year combined for seasonality adjustment (Table 2).

Once the data were set up according to each design, we linked the birth data to observed meteorologic data with MSA-level 7-day average mean temperature calculated from Daymet.^17,36

For each design, we ran analyses across 1,000 simulated datasets with seasonality and another 1,000 without seasonality. We then calculated bias (the difference between the mean of regression coefficients of the 1,000 replicates and 0), Monte-Carlo standard error (MCSE), 95% confidence interval (CI) for the bias, and type 1 error proportion (i.e., proportion of coefficient 95% CIs excluding 0). Definitions for the metrics are shown in Table 3. We conducted the simulation using R, version 4.0.4.

TABLE 3.

Definition of Bias, Monte-Carlo Standard Error, 95% Confidence Interval, and the Type 1 Error Proportion (%)

Metric	Formula	Description
Bias	$\frac{1}{1000}\sum _{j=1}^{1000}({\widehat{\beta }}_j-0)$	The average difference between the null (ß=0) and its estimate across 1,000 replicates.
Monte-Carlo standard error (MCSE)	$\frac{S{D}_{\widehat{\beta }}}{\sqrt{1000}}$	An estimate of the standard deviation of the sampling distribution of the bias estimator.
95% CI	[bias±1.96 × MCSE]	95% confidence interval for the true bias.
Type 1 error proportion (%)	$\frac{\mathrm{Number}\mathrm{of}95\%\mathrm{CIs}\mathrm{exclude}0}{1000}\times 100\%$	Proportion of coefficient 95% CIs excluding 0

RESULTS

Time-stratified Case-crossover Design

In the time-stratified case-crossover design for the 1,000 simulated datasets with the presence of seasonality of conceptions, for every 10°C increase in mean temperature in the last week before delivery, we observed a small positive bias in the full-year analysis (bias [among 1,000 replicates, denoted as “×1000”] =0.0046, 95% CI: 0.0041–0.0051, OR_bias [bias exponentiated] = 1.01, eTable 1; http://links.lww.com/EDE/C5; Figure 2) and that type 1 error proportion was 14% (eTable 1; http://links.lww.com/EDE/C5). The bias was stronger in the warm season (bias [×1000] =0.016, 95% CI: 0.015–0.018, OR_bias =1.02, type 1 error proportion =23%, eTable 1; http://links.lww.com/EDE/C5; Figure 2). Without the presence of seasonality, the bias estimates were centered at the null as expected; however, the type 1 error proportions were somewhat elevated at 7.8%, 7.9%, and 9.2% for full-year, warm- and cold-season analysis, respectively (eTable 1; http://links.lww.com/EDE/C5). The higher type 1 error observed under no seasonality in the absence of coefficient bias motivated additional analyses simulating the pseudo-birth data using a Poisson distribution (instead of Normal); this yielded an expected type 1 error rate under the no-seasonality scenario (4.8% full year, 4.5% warm, 4.8% cold), and lower but still elevated for the seasonality scenario (8.7% full year, 19% warm, 5.1% cold). Coefficient bias was the same using a Poisson distribution (eTable 2; http://links.lww.com/EDE/C5).

FIGURE 2.

Boxplot of coefficients from 1,000 replicates of simulation for preterm birth per 10°C increase in the 7-day average of mean temperature in the time-stratified case-crossover design with or without seasonality of conceptions for full-year and season-specific analyses. Seasonality was adjusted by design (monthly time strata). The diamond point represents the estimated bias (mean of 1,000 coefficients).

Implementation of a bidirectional control sampling approach (control days are exactly 1 week before and 1 week after the event day) yielded much stronger bias in the coefficients regardless of seasonality (eTables 3–4; http://links.lww.com/EDE/C5, see eAppendix http://links.lww.com/EDE/C5 for discussion). However, when we linked the time-stratified case-crossover dataset with the weighted probability of delivery of births (log(Wi)) developed from the time-series approach (Eqs 3–7) and ran conditional logistic regression with log(Wi) as a covariate, the bias was removed (bias [×1000] = 0.0009, 95% CI: −0.0003–0.002, type 1 error proportion = 4.7%, eTable 4; http://links.lww.com/EDE/C5).

Time-series Design

In the time-series design, with no seasonality of conceptions, we observed no bias in the regression coefficients of mean temperature (Figure 3), suggesting there was no bias induced by data setup or seasonality adjustment. In the presence of seasonal patterns of conceptions, in the unadjusted model in which we left out log(Wi), we observed a positive bias in the coefficient for temperature exposure in the week before birth. For example, the estimated biases (×1000) were 0.013 (95% CI: 0.013–0.013, RR_bias = 1.01), 0.024 (95% CI: 0.024–0.025, RR_bias = 1.03), and −0.0006 (95% CI: 0.0004–0.0009, RR_bias = 1.00) for mean temperature (per 10°C) for full-year, warm season, and cold-season analysis, respectively (Figure 3; eTable 5; http://links.lww.com/EDE/C5), whereas bias was not evident in the adjusted model. In addition, the type 1 error proportion was relatively low in the adjusted model (e.g., 4.2%, full-year analysis, eTable 5; http://links.lww.com/EDE/C5), whereas the type 1 error proportion ranged from 20% to 99% in the unadjusted models (eTable 5; http://links.lww.com/EDE/C5). We conducted sensitivity analyses using a quasi-Poisson model which did not impact results and yielded an overdispersion scale parameter close to 1 (eTable 6; http://links.lww.com/EDE/C5).

FIGURE 3.

Boxplot of coefficients from 1,000 replicates of simulation for preterm birth per 10°C increase in the 7-day average of mean temperature in the time-series design with or without seasonality of conceptions for full-year and season-specific analyses. The diamond point represents the estimated bias (mean of 1,000 coefficients). Seasonality was further adjusted by adding a logarithmic term of the weighted probability of delivery across gestational age to the unadjusted model.

Pair-matched Case-control Design

In the pair-matched case-control design, we did not observe bias in the coefficient under simulations with or without seasonality of conceptions or adjustment for LMP month and year (Figure 4; eTable 7; http://links.lww.com/EDE/C5). The type 1 error proportions were close to 5%. For example, the bias estimate (×1000) was 0.00005 (95% CI: −0.00013, 0.00022, ORbias = 1.00, type 1 error proportions = 4.8%, eTable 7; http://links.lww.com/EDE/C5), for the full-year analysis in the presence of seasonality.

FIGURE 4.

Boxplot of coefficients from 1,000 replicates of simulation for preterm birth per 10°C increase in the 7-day average of mean temperature in the pair-matched case-control design with or without seasonality of conceptions for full-year and season-specific analyses. The diamond point represents the estimated bias (mean of 1,000 coefficients). Seasonality was further adjusted by adding dummy variables for LMP month and year to the unadjusted model.

Time-to-event Design

In the time-to-event design, we did not find bias in the coefficient for temperature and preterm birth under simulations with or without seasonality of conceptions, and with or without further adjustment for LMP month and year (Figure 5; eTable 8; http://links.lww.com/EDE/C5). In addition, the type 1 error proportion across scenarios ranged between 3.6% and 5.9% (eTable 8; http://links.lww.com/EDE/C5).

FIGURE 5.

Boxplot of coefficients from 1,000 replicates of simulation for preterm birth per 10°C increase in the 7-day average of mean temperature in the time-to-event design with or without seasonality of conceptions for full-year and season-specific analyses. The diamond point represents the estimated bias (mean of 1,000 coefficients). Seasonality was further adjusted by adding dummy variables for LMP month and year to the unadjusted model.

DISCUSSION

We used a Monte-Carlo simulation to investigate the validity of adjustment for seasonality of conceptions in four commonly used study designs for the acute relationship between temperature and preterm birth. We found a slight positive residual bias in the time-stratified case-crossover design, and this bias was greater in the warm season analysis. Positive confounding by seasonality was observed in the time-series design; however, the adjustment for seasonality that included daily weighted probabilities of birth for the pregnancy risk set¹⁶ removed this bias. Last, in the case-control and time-to-event designs, we did not find bias in the coefficients from either the unadjusted or adjusted model in the presence of seasonality of conceptions.

The time-stratified case-crossover design has been widely used to examine acute health effects of temporally varying exposures, notably in the fields of air pollution^37–39 and temperature extremes research,^9,10,34 because there is no need to include flexible temporal terms to adjust for seasonality in the model. However, for a case-crossover study to provide unbiased estimates, time-varying factors (e.g., seasonal characteristics of health and exposure, day-of-the-week effects, or other long-term trends in temperature) must have no trends or patterns within the reference window.^27,28,30,40 Our findings presumably are the result of residual seasonal variation in likelihood of birth in the calendar month, which peak (because of the peak conceptions in December) in the times of year when temperature also peaks.⁷ That we were able to remove this bias by controlling for the weighted probability of birth calculated for the time-series analysis supports this conclusion. In previous studies of acute temperature and preterm birth, the reported associations were relatively large compared with the magnitude of bias we observed. For example, Basu et al. and Avalos et al. have estimated the regression coefficients of 0.15 and 0.20, respectively,^9,10 for preterm birth (scaled to every 10°C increase in the mean apparent temperature), which were about 10 to 12-fold higher than the bias we estimated, suggesting confounding by conception seasonality is unlikely to fully explain these previously reported positive associations. Wang et al., who observed bias in a time-stratified case-crossover study of air pollution and myocardial infarctions, proposed a calibration technique to estimate and remove the bias.⁴¹ However, the main attractiveness of the time-stratified case-crossover design in automatic temporal confounder control would be eliminated by introducing additional bootstrapping steps to calibrate the bias. Our correction approach similarly adds an unconventional element to the design, as it requires enumeration of all fetuses-at-risk. A bidirectional control sampling approach was not a solution, yielding more severe bias independent of seasonality of conception.

The case-crossover approach also yielded higher than expected type 1 error even under the no-seasonality scenario. Generating the daily LMP counts under a Poisson distribution rather than a normal distribution did not yield a higher type 1 error rate, highlighting the impact of distributional assumptions made in any analysis. We note that the empirical data of daily LMP counts looked more like those we generated under the Normal distribution. This may suggest a possible limitation of the case-crossover approach and conditional logistic regression dealing with overdispersed data independent from conception seasonality. Others have noted that the ability to scale standard errors is an advantage of the time-series approach.²⁹ Despite the small observed bias and higher than expected type 1 error, the uncorrected time-stratified case-crossover approach may still be the design of choice in certain study settings to avoid other larger problems. For example, when the exposures are highly spatially resolved and thus cannot be collapsed into a time-series of counts or when there is stronger concern about individual-level confounding factors, which could affect the case-control or time-to-event approaches that rely on comparisons between individuals.

To adjust for the confounding by seasonality in a time-series design, Vicedo-Cabrera et al.¹⁶ refined the “pregnancy-at-risk” approach implemented by Darrow et al.³² so that counts do not have to be separated by gestational week. This approach corrects for the varied probability of preterm birth due to different gestational age distribution across days. We found this approach fully adjusted the bias from seasonality of conceptions in our simulation. Nevertheless, time-series requires a large enough population sharing exposures to support aggregated count analysis, which limits its application to contexts that utilize highly spatially resolved air pollution levels or temperatures that prohibit aggregating the counts because individuals are assigned different exposures. Other methods that use individual-level exposure contrasts might be more appropriate in this context.

The pair-matched case-control design, has been used instead of full-cohort analysis for the purpose of improving computational efficiency^17–20 when there are millions of birth records. In addition to conception seasonality, other seasonal confounders, which we did not introduce in this simulation, would also have been accounted for by adjusting conception month and year. We matched cases and controls from the same MSA and compared the exposure of the control at the same gestational age as the case when the case was born. This should account for conception seasonality by design because spikes in conceptions affect both cases and controls; that is, if 36-week-old preterm cases are disproportionately occurring during the hottest time of summer because of conception seasonality, controls will also be disproportionately reaching their 36th week at the same time. As a result, the unadjusted model is expected to be unbiased by conception seasonality. However, use of an unadjusted model in future empirical case-control studies is unrealistic because there are likely other seasonal confounders that could potentially impact the validity of the estimates that need to be adjusted in the analysis.

Our results suggested that the time-to-event design yields unbiased estimates in both adjusted and unadjusted models in the presence of seasonality. This approach accounts for seasonality of conception by comparing all subjects at the same gestational week. However, the time-to-event design with time-varying exposures expands the size of the data by over 100-fold (119 follow-up days between week 20 and 36) requiring more computational resources.

Where we observed bias (time-stratified case-crossover and unadjusted time-series design) in the presence of seasonality of conception, we observed more bias in the warm season than in the cold season. We suspect that this is due to a peak in conceptions in the United States in December and a subsequent peak in late-gestation pregnancies in the mid- to late summer months, which happens to correspond to the highest temperatures of the year. In other geographic locations where temperatures and conception patterns align differently, the bias estimates would be expected to be different. For example, seasonality of birth has historically been more pronounced in China than the United States,⁴² with peaks occurring in October. In addition, we did not examine alternative lag structures for temperature, however bias observed for 7-day average temperatures should indicate some bias on individual lag days due to the correlation between lag days.

In conclusion, estimates for the association between mean 7-day temperature and preterm birth were slightly biased in the time-stratified case-crossover design but were unbiased under specific conditions in the other designs. Although the magnitude of the bias was relatively small, the effects of interest also tend to be small, and a small true effect has public health relevance, given the common exposure and outcome. Our simulation assessed the isolated impact of conception seasonality; there are many other considerations and sources of bias that influence design selection. Nonetheless, our findings provide quantitative evidence that can inform researchers when choosing a design and adjustment method for a specific study.