Supplementary methods

Case diagnosesThe following best-estimate autism spectrum disorder (ASD) diagnoses were assigned based on Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision (DSM-IV-TR)1 criteria: Autistic Disorder (299.00), Asperger’s Disorder (299.80), Pervasive Developmental Disorder Not Otherwise Specified (PDD-NOS, 299.80). ASD cases among NPR-identified children who were not evaluated at the ABC Study Clinic were those assigned the following International Classification of Diseases, Tenth Revision (ICD-10) F84 diagnoses: childhood autism (F84.0), atypical autism (F84.1), Asperger’s syndrome (F84.5), other PDD (F84.8) or PDD, unspecified (F84.9).2

Cases were classified as ASD with or ASD without mental retardation/intellectual disability (ID) in an effort to determine whether fever was specifically associated with certain ASD subgroups. Comorbidity with ID was based on intelligence quotient (IQ) data from ABC clinic assessments, as available (IQ<70) or NPR data consistent with a diagnosis of an ID (ICD-10 codes F70, F71, F72, F73, F78 or F79). ASD cases with ABC clinic IQ score <70 and/or who were found to have any ICD-10 code in the range of F70-F79 in NPR linkage data were assigned to the ASD with ID group. ASD cases without an ABC clinic IQ score <70 and who also had not received an NPR ID ICD-10 code were assigned to the ASD without ID group.

Exposure data (fever and fever-associated antipyretics)Exposure timing: assignment of questionnaire data on timing of fever exposure to trimesters Two time periods for maternal reporting of fever and medication use overlapped across questionnaires: 1) the “13+ weeks” period on the 17-week questionnaire and the “13-16 week” period on the 30-week questionnaire; and 2) the “29+ week” period on the 30-week questionnaire and the “last part of (during) pregnancy” period on the questionnaire administered to mothers at child age 6 months postnatal. To address this overlap, we collapsed the 13+ (17-week questionnaire) and 13–16 week (30-week questionnaire) reporting intervals into one category, and assigned data from 29+ weeks (30-week questionnaire) to the third trimester along with 30+ week data from the 6-month postnatal questionnaire (original questionnaire items, Supplementary Table S1). As noted elsewhere, trimesters were defined as follows: first trimester, 0–12 weeks; second trimester, 13–28 weeks and third trimester, 29 weeks to end of pregnancy.

For dose-response analyses we retained the timing of events within 4-week intervals, assigning a maximum of one fever event to any 4-week interval. Discrete fever events were then summed across all of pregnancy (“any time during pregnancy”) and also calculated separately for the period after 12 weeks’ gestation.

Antipyretic data Fever-associated acetaminophen (paracetamol) exposure was defined as use of any medications for the reported indication of fever with Anatomical Therapeutic Chemical Classification System codes that reflect inclusion of paracetamol (acetaminophen): N02BE01 (paracetamol), N02BE51 (paracetamol, combinations excluding psycholeptics), or N02BE71 (paracetamol, combinations with psycholeptics). When mothers reported taking multiple medications in multiple time intervals, all medications were considered as taken in each time interval. Endorsement of use of an acetaminophen-containing medication for fever in an individual time interval was considered as medication use throughout that entire time interval.

Exposure to other fever-associated antipyretics (ibuprofen). To examine the degree to which the ASD risk associated with fever might be modified by classes of antipyretic drugs other than acetaminophen, relative to the degree of modification of fever-associated risk observed with acetaminophen, we assessed the risk modification associated with the nonsteroidal anti-inflammatory drug (NSAID), ibuprofen. Given smaller numbers, modification of ASD risk in association with fever exposure by ibuprofen was only examined in secondary analyses. Women reporting use of ibuprofen (ATC codes M01AE01 [ibuprofen], M01AE51 [ibuprofen, combinations]) specifically for treatment of fever were defined as exposed throughout the time period reported. When mothers reported more than one medication and selected multiple time intervals within an individual questionnaire, all reported medications were considered to have been taken in all of the time intervals that the mother had designated for medication use.

Potential confoundersWe evaluated parental and child variables that might influence associations between the primary maternal exposure (fever) and ASD risk: maternal age, smoking, parity; parental education; birth month, and birth year. Confounding variables were functionally defined as those that were significantly associated with both the outcome and the primary exposure, and were not hypothesized to be a mediator (Supplementary Table S3). Missingness was treated using the

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pairwise deletion method. Because three primary exposures were being examined (fever exposure in three trimesters), the significance levels of the associations between a potential confounder and the primary exposures were adjusted for multiple comparisons using the Bonferroni procedure.

The influence on crude odds ratios (OR) when introducing selected confounders was examined in two ways (Supplementary Table S4). First, each selected confounder was added into the crude logistic regression model individually to examine its influence on the OR. Second, we built logistic regression models by adding selected confounders sequentially; at each step, the confounder that changed the absolute value of the coefficient of the main exposure by the smallest magnitude in comparison to any changes found in the previous step was introduced next into the model. The procedure continued until all selected confounders were included in the model.

Missing or discrepant dataThere were two main types of missing data to be addressed: 1) missing values within confounders; 2) missing timings of fever episodes for mothers indicating that they had experienced more than three fevers on the 30-week questionnaire (376 of 401 mothers endorsing the item indicating three or more fever episodes; 73 of these women failed to provide any fever timing). Complete data for timings of fever events within trimesters was required to impute missing values within the confounding variables; at the same time, we also needed complete confounding variable data to generate timings for fever events for mothers who reported three or more fever episodes on the 30-week questionnaire but failed to fully specify when these episodes occurred. To resolve this dilemma, an iterative imputation algorithm, illustrated below, was applied.

Discordance in data regarding presence and/or timing of fever and antipyretic exposures were resolved as summarized in Supplementary Table S2. Procedures for resolving the primary types of data discordance are provided in the “ Fever and antipyretic exposures” section in Methods in the main text. These methods were pertinent to the 17-week and 6-month questionnaires and primarily involved applying the maternally-provided timing for fever exposure to define the timing for antipyretic exposure when no timing was provided for medication use, and applying the maternally-provided timing for fever-associated antipyretic exposure to define the timing for fever exposure when no timing was provided for the fever episodes.

For instances where mothers failed to complete the timing for fever episodes and also failed to report the timing of antipyretic use (17-week and 6-month questionnaires), and only provided an ATC code, subjects were excluded from the analysis (n=12). Subjects with highly discordant data on the 6-month questionnaire, wherein they endorsed both the box indicating the absence of fever in the 30+ week period in addition to the box indicating the presence of fever or fever-associated medications in the same 30+ week period, were also excluded (n=178).

Women who did not endorse the “fever greater than 3 times” item on the 30-week questionnaire and who also failed to provide any fever timing were designated as nonexposed to fever and to antipyretic medication (n=32). For women with imputed fever timing (as detailed above and in the iterative imputation algorithm below) who also indicated taking one of the selected antipyretics (acetaminophen or ibuprofen), medication timing was defined by the imputed fever timing.

Iterative Imputation Algorithm

Step 1: Impute missing values for the confounding variables using an expectation-maximization (EM)-based iterative regression method.3

Step 2: Applying the temporarily complete confounding variables, generate fever event timings for the 376 mothers with incomplete or missing data by the imputation method described below.

Step 3: Go back to Step 1, and iterate until no change is observed from the previous loop.

A primary advantage of this iterative imputation algorithm is that, instead of requiring construction of a joint model for both fever exposure and confounders, here only a rational, conditional model is required for one variable, given the others at a fixed level, at each iteration step. Liu et al.4 has demonstrated the consistency of the proposed imputation estimators of this algorithm, showing that the imputation distribution converges to the posterior distribution of a Bayesian model, under certain regularity conditions.

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Imputation scheme to address missingness of fever timings. To generate timings for the missing fever episodes for the 30-week questionnaire, we applied an imputation scheme5 based on a semiparametric rate function model.5 We rejected alternate methods that would have partially or completely eliminated the majority of women with the greatest exposure to multiple fever episodes (such as listwise or pairwise deletion) as these methods were likely to introduce substantial bias (underascertainment) into our results; we hypothesized that exposure to an increased number of fever episodes is associated with an increased risk of ASD. Assuming missingness occurred at random, the fever timings for each of the 376 mothers were generated with the recurrent fever event process with a semiparametric rate function5 defined as:

E [dN ( t )|ASD , X ]=exp {β0 · I [ASD=1 ]+X ' β }· d μ0 ( t ) Model (1)

where {N (t )} is the counting process of prenatal fever events and dN (t )=N ( t )−N ¿ represents the number of prenatal fever episodes that occur at time t (assuming that only one fever can occur at a time). Therefore, E [dN (t )|ASD , X ]=Pr (dN (t )=1∨ASD, X ); X represents the confounders; β0 and β are parameter coefficients and μ0(t ) is an unspecified baseline mean function which can take any functional form. We used the overall study population, excluding the 376 mothers with missing data, as the training set to estimate β0, β and μ0(t ). Following the consistent estimation procedure of Model (1), we generated additional event timings for fever episodes with the estimated coefficients β̂0, β̂ and μ̂0(t ) given the condition that the total number of fever episodes was greater than three. Because the proportion of missingness is extremely low compared to the overall sample size, the risk of underestimated standard errors was negligible. Thus, single imputation was applied instead of multiple imputation.

Supplementary statistical analysesAssessment of effects of individual confounders on ORs in main models. We examined the effects on ORs in main models through adjustment with each potential confounders individually, and by examination of change in ORs through step-wise introduction of each potential confounder.

ASD risk with fever modified by NSAID antipyretic (ibuprofen). Analyses of the risk associated with fever exposure which could be modified by ibuprofen followed the same procedures detailed in our main analyses, with fever-associated ibuprofen replacing fever-associated acetaminophen (see Methods, main text).

Sensitivity analyses – male population. We considered that effects might differ between male and female populations. Because the number of female ASD subjects was small, we approached this as a sensitivity analysis that limited our study population to boys. The main analyses (see Methods, main text) were repeated.

Sensitivity analyses – stratified on birth year. Some children were as young as 5 years of age at the end of follow up for this set of analyses (i.e., children born in 2009, followed through the end of 2014); thus, many ASD cases in our study sample may still be awaiting diagnostic assignment. To address the possibility that diagnostic misclassification (due to underascertainment) among children born in later birth years may have influenced our fever-associated findings, we stratified the cohort into two categories, spanning the first 5 and the last 5 cohort years (1999-2004 and 2005-2009) and repeated the analysis used for our main models.

Sensitivity analyses – gestational ages. In order to address the possibility that early births obviate fever events in later pregnancy, we restricted to women with gestational age >36 weeks in this sensitivity analysis. Here the main analyses (see Methods, main text) were repeated within this restricted study population.

Sensitivity analyses – under-reporting of fever timings. Among the women with high exposure to fevers on the 30-week questionnaire (three or more episodes reported for time intervals within gestational weeks 13–29+), 376 provided incomplete data for the timing of those fevers. Of these 376 high-exposure mothers with incomplete timing, 73 failed to report even a single timing for any of their fever events. We excluded these 73 mothers and repeated the main analyses in a sensitivity analysis (see Methods, main text).

Supplementary results

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Individual and step-wise influence of individual confounders on ORs. Because accounting for confounders slightly increased ORs in main models we examined their effects both individually and when introduced in a step-wise manner. Birth year, introduced individually, had the most marked influence on ORs in the second trimester (a small increase in OR from 1.33 in crude model to 1.37 when adjusting solely for birth year; Supplementary Table S4A). Birth year also led to the greatest increase when introduced sequentially in the second-trimester adjusted model (a modest increase in OR from 1.33 in crude model to 1.42 in Adjusted Model 2; Supplementary Table S4B).

Sensitivity analyses. Results of sensitivity analyses stratified on earlier vs. later birth year periods are found in the Results section of the main text and in Supplementary Tables S7A and S7B.

In sensitivity analyses excluding girls, risk of ASD was increased slightly for second-trimester fever relative to analyses including both boys and girls (aOR3boys, 1.45; 95% CI, 1.10–1.90). Trends in the first trimester for boys alone were similar to the risk found for first-trimester fever with boys and girls combined (aOR3boys, 1.26; 95% CI, 0.76–2.09). Third-trimester fever showed a trend toward increased risk in boys, similar to the risk found in boys exposed to first-trimester fever (aOR3boys, 1.30; 95% CI, 0.80–2.14), but substantially higher than the risk associated with third-trimester fever for boys and girls combined.

In sensitivity analyses excluding preterm births (32–36 weeks), risk was slightly higher for all trimesters (data not shown).

Additional sensitivity analyses excluded mothers who reported high exposure on the 30-week questionnaire (>3 fever episodes) but required imputation of fever timings due to failure to provide specific timing for any of these episodes. Exclusion of these women did not substantively influence the association of second-trimester fever with ASD risk (aOR3, 1.37; 95% CI, 1.07–1.77).

References

1 APA. Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision (DSM-IV-TR). Fourth Edition, Text Revision edn. American Psychiatric Association: Arlington, 2000.

2 World Health Organization. Mental Disorders: A Glossary and Guide to Their Classification in Accordance With the 10th Revision of the International Classification of Diseases: Research Diagnostic Criteria (ICD-10). World Health Organization: Geneva, Switzerland, 1993.

3 Raghunathan TE, Lepkowski JM, Hoewyk JV. A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodol 2001; 27: 85–95.

4 Liu JC, Gelman A, Hill J, Su YS, Kropko J. On the stationary distribution of iterative imputations. Biometrika 2014; 101: 155–173.

5 Little RJA, Rubin DB. Statistical Analysis with Missing Data. John Wiley & Sons, Inc.: New York, New York, 1986.

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