Article

Supplemental Information

Supplemental Methods Geographic Data for Birth and Residence Location Hospital were <30 km apart and were ’ grouped together as #6007; because Inclusion and Exclusion Criteria Fredericia Municipality s population Until December 31, 2006, Denmark density was approximately twice that was divided into 270 districts. On of Kolding Municipality, we assigned This cohort study included all live January 1, 2007, its government #6007 to Fredericia Municipality. births in Denmark from 2004 to consolidated those districts into 98 2012, identified by using the MBR. municipalities, and allocated each Specifying Dates for We included children in the study municipality to one of 5 regions. To Experiencing February ’ “ ” cohort even if their MBR record did compare geographic data over the

not list a father s 10-digit personal entire study period, we harmonized registration number. Out of 568397 data according to the 98-municipality To allocate proper age intervals “ ” total birth records in the MBR, we data structure. We then used national for birth season cohorts as they excluded 6,​668 children (1.2%) from census data taken on January 1, experienced February as depicted the final study cohort who met at 2012 (available from Statistics in Fig 2 B and C in the main article, least one of the following criteria: Denmark, http://​www.​StatBank.​dk/​ we set boundaries for age intervals ’ bev22), to classify each municipality by birth season cohort on the 15th of 1. the 10-digit personal registration ’ number in the MBR for the child or with regard to population density the season s first month to the 15th mother could not be linked to the (number of residents per square of the season s last month (Fig 2). For Danish Civil Registration System, kilometer). example, children born in the spring (green, March to May) experienced which contains information29 on We assigned geographic location ’ February from 8.5 to 11.5 months, vital status’ and migration ; for municipality and region for the because children born on May 15 child s birth (by using data from 2. the child s sex or date of birth was were 8.5 months old on February 1, the MBR) and their residence after inconsistent across registries; and children born on March 15 were birth (by using the Danish Civil 3. a record for a redeemed ’ 11.5 months old on February 28. ’ Registration System). Home births prescription drug preceded a were classified by the mother s Supplemental Methods for ’ child s date of birth; or residence (by using the Danish Civil Interrupted Time Series Analysis 4. the place of childbirth or Registration System) on the child s residence in Denmark could not be date of birth. For hospital births, we ⚬⚬ ascertained, as follows: obtained –a historical list of hospitals The near-coincident IRF bulletin from the Health Care Classification the child had no record of being 51 53 and 7-valent pneumococcal born in a Danish hospital or at System ‍ ‍ (http://​www.​medinfo.​ conjugate vaccination (PCV7) ⚬⚬home in Denmark; dk/​sks/​brows.​php and ftp://​filer.​sst.​ catch-up program were assigned dk/​filer/​sks/​data/​skscomplete/​) and ’ to the same interruption date, May the child had no residence conducted online searches to identify 1, 2006, to allow a 1-month lag for recorded in the Danish Civil each hospital s municipality and bulletin dissemination. Thus, the Registration System by at least region and classified each hospital as 4 interruption points in our final ⚬⚬ ’ their second day of life; university-affiliated or not. analysis occurred at weeks 122, 182, 315, and 352 of the 468-week study the mother s residence was not There were 5 hospital codes in recorded in the Danish Civil period. ’ the historical list that pertained to Registration System on the groups of neighboring hospitals, Risk measurements corresponded ⚬⚬ ’ child s date of birth; or and we assigned each of those codes to distinct cohorts of infants so that ’ the mother s residence on the to the most densely populated there was no risk carryover from ’ ’ child s date of birth did not municipality included in that the same infants being counted in match the child s residence on code s coverage area. For example, multiple birth weeks. Therefore, their second day of life. Fredericia Hospital and Kolding because error terms for each birth PEDIATRICS Volume 140, number 3, September 2017 1

Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF ” w week cohort33 are theoretically after an interruption date were of the IRF bulletin and the PCV7 unrelated,​ our primary analysis did coded as 0 if the birth week catch-up program and (2) the not account for serial autocorrelation occurred before the interruption constancy over time of their effects of error terms. and as time (in weeks) since on antibiotic use. In particular, the the interruption for birth weeks IRF bulletin was less current for Overall annual risks for each year ≤ occurring afterward. The coefficients children born after January 2007 were obtained by taking the mean ofα primary interest were: because they were 3 months old in each year of week-level predicted when the bulletin was published. risks (Fig 3). To group children , mean risk for births occurring β β This sensitivity analysis introduced into birth week cohorts for the immediately before January 2004; a new coefficient ( 1a), which interrupted time series analysis, we 0, baseline linear trend for risk – represented the change in trend defined 52 weeks in the year on the before interruptions (January 1, after January 1, 2007. After this basis of 7-day increments. Exceptions β ’ 2004 April 30, 2006); new interruption, we hypothesized to the 7-day definition for the week 1, change in trend for risk after the that (1) the bulletin s effect on the of birth variable were as follows: (1) β interruption on May 1, 2006; trend would be attenuated because February 29 was always grouped into 2 children born after January 2007 week 9 so that every 4 years there , change in trend for risk after the β would have been no more than 3 were 8 days in week #9; and (2) interruption on July 1, 2007; – months old when the bulletin was week #52 always contained 8 days 3 , change in trend for risk after the published, before the vast majority (24 31 December). interruption on January 19, 2010; of infants require consideration for β ’ We hypothesized that each and their first antibiotic treatment, and interruption would have a gradual 4, change in trend for risk after the (2) the catch-up program s effect on effect over time on the trend of interruption on October 1, 2010. the trend would be amplified because β^ β^ antibiotic prescribing among infants. Trend estimates were equal to increasing numbers of children were Therefore, we did not include baseline trend estimate (​​ 0​​ ) plus ​​ ​​ enrolled over time. Given that we can parameters in our model that would estimates for all trend changes at only observe the mixture of these 2 measure discontinuity (ie, changes33, in54​ interruptions preceding the segment effects, parsing the original second level) between adjacent segments. ‍ of interest; eg, for the third^ segment^ ^ segment into 2 separate segments β β β was intended to illuminate how their To control confounding by (July 1, 2007, until January 19, 2010) 0 1 2 co-occurrence drove time-varying seasonality in our segmented the estimate was equal to ​​ ​​ +​​ ​​ +​​ ​​ . changes in antibiotic use. linear regression model, we usedπi Supplemental Interrupted a transformed35 cosineπi periodic Time Series Sensitivity Sensitivity Analyses 2, 3, and 4 function i with terms for sin(2 /52 Analyses radians) and cos(2i /52 radians), in which denotes the week of birth 36,​37 In the second and third sensitivity during the year, = {1, 2, ..., 52}. We conducted 4 sensitivity analyses analyses, we controlled for Given the full segmented regression of the time series study to assess the seasonality by using a vector of 51 model,Rw α ​ β time after Jan w effects of the number of interruptions birth week indicator variables, by β time after May w we enumerated (analysis 1), how we using the first week of the year as = + 0 ( 1 2004) β time after Jul w controlled for seasonality (analyses the referent (sensitivity analysis + 1 ( 1 2006) β time after Jan w 2 and 3), and how we accounted 2) and by using the cosine function + 2 ( 1 2007) β time after Oct w for potential serial autocorrelation in a 2-stage weighted maximum + 3 ( 19 2010) β πi of error terms (analysis 4). Each likelihood estimation approach + 4 ( 1 2010) β πi sensitivity analysis is described in analogous to a weighted least squares + 5 (sin (2 /52)) 36 detail below, and results from these approach (sensitivity analysis 3). + 6 (cos(2 /52)) analyses are shown in Supplemental Rw in which the dependent variable, Fig 4 and Supplemental Tables 8 and 9. In the fourth sensitivity analysis, we , was the 1-year risk of at least 1 Sensitivity Analysis 1 conducted the primary analysis and redeemedw antibiotic prescriptionw previous 3 sensitivity analyses by during infancyi for children born in using autoregressive parameters to week of the study period, = {1, In the first sensitivity analysis, we evaluate our assumption that there 2, ..., 468}, and denotes the (seasonal) added an interruption on January 1, was no serial autocorrelation of error i “ week of birth during the year, 2007, to relax previous assumptions terms across birth week cohorts. We = {1, 2, ..., 52}. Variables for time about (1) the timing of the effects assessed serial error autocorrelation 2 Kinlaw et al

Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF Article

between birth week cohorts by55 using model controlling for seasonalityα by Models used in the primary analysis Durbin-Watson test statistics. To using a transformed cosine function are shaded in gray, and graphical account for error autocorrelation in (Approachβ A). The referent for results for these models are shown sensitivity analyses, our model for represents the risk (%), the referent in Fig 3 in the main article. The first 0 the maximum likelihood estimator for represents βtheβ trendβ in riskβ sensitivity analysis can be reviewed of the birth week-specific risk (%) per month of calendar time, and in tabular form by comparing included the vector of autoregressive the referents for 1, 2, 3, and 4 Supplemental Table 8 (by using parameters that allowed up to a coefficients represent the change in 4 interruptions) to Supplemental 60-week lag; we usedt backward trend at each interruption. Table 9 (which adds interruption elimination to remove autoregressive 1a) as a comparison between model parameters with a statistic that was The next 2 rows in each series show #1 and model #19. The second

not significant on the basis of an56 a the difference in each parameter for sensitivity analysis can be reviewed priori type I error level of 0.05. models by using Approach B or C by comparing Approach B to Summary of Supplemental Tables compared with the referent model Approach A for any specific setting − 8 and 9 for the series. Plus (+) and minus (eg, model #2 versus model #1). ( ) notation is used to show how The third sensitivity analysis can be estimates differ from the referent reviewed by comparing Approach For each group of models, the estimate forα each series. For example, C to Approach A for any specific Akaike Information Criterion and model #1 estimated a referent risk setting (eg, model #3 versus model log likelihood are shown. The Akaike of 40.1% ( ), with an increase in #1). The fourth sensitivity analysis Information Criterion provides theβ risk of 0.09% per month from can be reviewed by comparing the information on model performance January 1, 2004 to April 30, 2006 results from models that assume − 0 relative to its efficiency, with more ( ), and a changeβ in the trend of independent error terms to results negative values indicating relative 0.41% per month from May 1, 2006 from autoregressive models for any superiority, and the log likelihood to July 1, 2007 ( 1). For that series, specific setting (eg, model #10 versus − provides information on the goodness Approach B (model #2) differed from model #1). Results in Supplemental α − of fit of the model. For each series Approach Aβ (model #1) by 1.15% Tables 8 and 9 show that trend of 3 models, the first row shows with respect to , 0.003%β with changes were robust to multiple each parameter estimate based respect to 0, and +0.004% (shown as specifications that we considered for on a segmented linear regression 0.00) with respect to 1. the linear model.

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF SUPPLEMENTAL FIGURE 4 Graphical results from the sensitivity analysis, which added a fifth interruption to the time series (denoted as 1a) to allow a 7-month lag of the first interruption. The graph shows segmented trend lines for the interrupted time series analysis of the risk of at least 1 redeemed prescription during the first year of life for any antibiotic (black), for amoxicillin (red), or for penicillin V (blue), by birth week cohort among children born in Denmark during 2004–2012. Interruptions are denoted by downward arrows: (1) the near-coincident IRF bulletin and 7-valent pneumococcal conjugate vaccination (PCV7) catch-up enrollment schedule; (1a) the 7-month lag for the first interruption; (2) the standard program for PCV7 enrollment; (3) the nationwide transition from PCV7 to 13-valent pneumococcal conjugate vaccination (PCV13); and (4) the standard program for PCV13 enrollment. Solid vertical lines crossing a segment indicate interruptions in the time series when potential changes in the trend for risk were assessed; dotted vertical lines indicate interruption 1a, which allowed a 7-month lag for the first interruption. Segmented trend lines are adjusted for seasonality by using a transformed cosine periodic function. For each segment, trend estimates are shown as the change in risk (%) per month.

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF Article

SUPPLEMENTAL TABLE 4 One Year Risk of Overall and Selected Medication-Specific Redeemed Antibiotic Prescriptions by Year of Birth in Denmark, 2004–2012 Overall Amoxicillin Penicillin V Erythromycin Year of Birth Risk 99% CI Risk (%)a 99% CI Risk (%)a 99% CI Risk 99% CI (%)a (%)a 2004 41.1 40.6 to 41.6 24.9 24.5 to 25.4 21.1 20.6 to 21.5 4.1 3.9 to 4.4 2005 41.4 40.9 to 41.9 26.0 25.6 to 26.5 21.0 20.6 to 21.5 3.5 3.3 to 3.7 2006 42.6 42.1 to 43.1 28.3 27.9 to 28.8 20.6 20.2 to 21.0 3.6 3.4 to 3.7 2007 38.7 38.2 to 39.2 25.5 25.1 to 26.0 17.9 17.5 to 18.3 2.8 2.7 to 3.0 2008 38.9 38.4 to 39.4 26.0 25.5 to 26.4 18.0 17.6 to 18.4 2.8 2.6 to 2.9 2009 40.1 39.6 to 40.6 27.5 27.0 to 27.9 18.2 17.8 to 18.6 2.6 2.4 to 2.7 2010 39.9 39.4 to 40.4 27.0 26.6 to 27.5 17.3 16.9 to 17.8 2.7 2.5 to 2.9 2011 36.9 36.4 to 37.4 23.7 23.2 to 24.1 17.3 16.9 to 17.8 1.1 1.0 to 1.3 2012 34.8 34.3 to 35.4 22.5 22.1 to 23.0 16.0 15.6 to 16.4 0.2 0.2 to 0.3 a Risk estimates for at least 1 redeemed antibiotic prescription for during infancy by using the complement of the Kaplan-Meier survival function, which accounted for censoring at death or emigration. The sum of medication-specific risks exceeds overall risk because infants could be prescribed >1 medication in their first year.

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF b 6.7 5.7 5.5 5.0 4.8 4.3 4.5 2.0 0.4 Share (%) 5 to 4 to 5 4 to 5 3 to 4 3 to 4 3 to 3 to 1 to 0 to 99% CI Erythromycin a 5 4 4 4 3 3 3 1 0 Rate b 36.0 35.9 33.3 32.5 32.3 31.0 30.5 32.8 32.8 Share (%) Penicillin V 99% CI 27 to 28 27 to 28 26 to 27 22 to 23 22 to 23 22 to 23 22 to 23 21 to 22 19 to 20 a 28 28 27 23 23 23 22 22 20 Rate b 50.0 52.9 55.8 56.6 56.7 58.7 57.5 55.2 56.6 Share (%) Amoxicillin 99% CI 38 to 39 40 to 42 44 to 46 39 to 40 39 to 41 42 to 44 41 to 43 36 to 37 33 tp 35 a 39 41 45 40 40 43 42 36 34 Rate b 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Share (%) ÷ (total no. of redeemed prescriptions for all antibiotics). Overall 99% CI 77 to 79 77 to 78 80 to 82 69 to 71 70 to 71 72 to 74 72 to 74 65 to 67 59 to 61 a Rates of Overall and Selected Medication-Specific Redeemed Antibiotic Prescriptions by Year Birth in Denmark, 2004 – 2012  78 77 81 70 70 73 73 66 60 Rate 2004 Year of birth 2005 2006 2007 2008 2009 2010 2011 2012 Share of antibiotic rate = (no. redeemed prescriptions) Rate = no. of redeemed prescriptions per 100 infant years follow-up. SU PP LE M ENTAL TABLE 5 a b

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF Article b 9.8 8.1 7.4 6.4 6.1 5.4 5.5 2.3 0.5 Share (%) 6 to 5 to 5 to 6 4 to 4 to 4 to 4 to 1 to 2 0 to 99% CI Erythromycin a 6 5 6 4 4 4 4 2 0 Burden b 27.4 27.1 25.7 25.4 25.4 23.9 22.7 23.5 23.4 Share (%) Penicillin V 99% CI 17 to 18 17 to 18 19 to 16 to 17 16 to 17 16 to 17 16 to 16 to 14 to 15 a 17 18 19 16 17 16 16 16 14 Burden b 56.1 59.1 61.6 62.1 61.3 63.6 63.2 63.2 65.4 Share (%) Amoxicillin 99% CI 35 to 36 38 to 39 46 to 40 to 41 40 to 44 to 45 to 46 42 to 43 40 to 41 a 36 38 46 40 40 44 45 43 40 Burden b 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 000 infant days of follow-up. Share (%)

Overall 99% CI 63 to 64 65 to 74 to 75 64 to 65 65 to 66 68 to 69 71 to 72 67 to 68 61 to 62 a Burdens of Overall and Selected Medication-Specific Redeemed Antibiotic Prescribing Patterns by Year Birth in Denmark, 2004 – 2012, Continued  63 65 75 65 65 69 71 67 61 Burden 2004 Year of birth 2005 2006 2007 2008 2009 2010 2011 2012 Share of antibiotic burden = (days supplied) ÷ (total days supplied for all antibiotics). Population-level antibiotic drug burden = days supply per 10 SU PP LE M ENTAL TABLE 6 a b

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF SUPPLEMENTAL TABLE 7 Segmented Linear Regression Model Results for 1-y Risk of Having at Least 1 Redeemed Antibiotic Prescription During Infancy Among Children Born in Denmark, 2004–2012 Parameter Any Antibiotic (J01) Amoxicillin (J01CA04) Penicillin V (J01CE02) Estimatea (%) 99% CI Estimatea (%) 99% CI Estimatea (%) 99% CI Intercept 40.135 39.310 to 41.960 23.490 22.766 to 24.214 21.047 20.465 to 21.630 b Trend01Jan2004_30Apr2006 0.090 0.045 to 0.135 0.170 0.131 to 0.210 −0.006 −0.038 to 0.026 b Trend01May2006_30Jun2007 −0.316 −0.390 to −0.241 −0.224 −0.289 to −0.159 −0.226 −0.278 to −0.173 b Trend01July2007_18Jan2010 0.066 0.030 to 0.102 0.089 0.057 to 0.121 0.007 −0.019 to 0.032 b Trend19Jan2010_30Sep2010 −0.198 −0.324 to −0.071 −0.317 −0.428 to −0.206 −0.021 −0.110 to 0.068 b Trend01Oct2010_31Dec2012 −0.193 −0.243 to −0.142 −0.138 −0.182 to −0.094 −0.084 −0.120 to −0.049 sin(2πi/52) 5.521 5.209 to 5.833 4.172 3.898 to 4.445 2.899 2.679 to 3.119 cos(2πi/52) −1.690 −2.000 to −1.380 −1.339 −1.610 to −1.067 −1.066 −1.284 to −0.847 i, week of birth during the year, i = {1, 2, ..., 52}. a Estimates correspond to the risk (intercept) or change in risk (other parameters) per 100 children. b Trend estimates are scaled to month intervals, corresponding to change in linear risk per month of calendar time for births occurring between boundary dates.

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF Article 4 β .00 .00 .00 +.06 +.06 +.01 +.02 − .01 − .01 − .01 − .01 − .03 ref: .16 ref: .01 ref: .18 ref: − .09 ref: − .06 ref: − .06 3 β .00 .00 .00 .00 +.01 +.01 +.01 +.01 +.02 − .06 − .05 − .02 ref: .00 ref: − .20 ref: − .39 ref: − .26 ref: − .41 ref: − .03 2 β .00 .00 .00 .00 .00 .00 .00 +.02 +.02 +.01 +.01 − .01 ref: .36 ref: .31 ref: .22 ref: .38 ref: .31 ref: .23 1a — — — — — — — — — — — — — — — — — — β 1 β .00 .00 .00 .00 .00 +.01 +.01 Differences in Parameter Estimates Across Models − .01 − .01 − .02 − .01 − .01 ref: − .21 ref: − .39 ref: − .39 ref: − .22 ref: − .41 ref: − .39 0 β .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 − .01 ref: .09 ref: .17 ref: .09 ref: .17 ref: − .01 ref: − .01 α .00 − .04 − .04 − .02 − .03 − .02 − .10 − .71 − .03 − .71 − 1.15 − 1.01 ref: 40.16 ref: 23.54 ref: 21.06 ref: 40.13 ref: 23.49 ref: 21.05 LL — — — — — — 1247 1301 1413 1309 1372 1439 1264 1325 1400 1207 1268 1370 — — — — — — AIC Model Fit Criteria − 2378 − 2486 − 2710 − 2498 − 2615 − 2751 − 2507 − 2622 − 2769 − 2396 − 2519 − 2722 729). 2 5 8 1 4 7 3 6 9 12 15 18 11 14 17 10 13 16 Model # — , not assessed.  Model Fit Criteria and Parameter Estimates Across 4-Interruption Segmented Linear Regression Models for the Risk of at Least 1 Redeemed Antibiotic Prescription Among Infants Born in Denmark, 2004 – 2012 ( N = 561

: 1-stage, cosine function : 1-stage, cosine function : 1-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, cosine function : 1-stage, cosine function : 1-stage, cosine function c c c c c c d d d d d d a, ​ b a, ​ b a, ​ b a a a Set 2: using autoregressive parameters Set 1: assuming independent error terms Amoxicillin A Penicillin V A C C C Any antibiotic A Amoxicillin A Penicillin V A Analysis of interruptions 1, 2, 3, 4 Any antibiotic A C C C B B B B B B Models used in the primary analysis. by using a transformed cosine function. Approach C: 2-stage weighted maximum likelihood estimation of the risk, controlled for seasonality Approach A: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using a transformed cosine function. Approach A: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using Approach B: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using a vector of 51 birth Approach B: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using week indicator variables. SU PP LE M ENTAL TABLE 8 AIC, Akaike Information Criterion; LL, log likelihood; a b c d

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF 4 β .00 .00 .00 .00 +.02 +.04 +.02 − .01 − .01 − .01 − .01 − .02 ref: .03 ref: .21 ref: .18 ref: − .06 ref: − .01 ref: − .08 3 β .00 .00 .00 .00 .00 +.01 +.01 +.01 +.01 − .02 − .02 − .01 ref: − .31 ref: − .46 ref: − .04 ref: − .28 ref: − .44 ref: − .01 2 β .00 +.01 +.01 +.03 +.01 +.01 +.01 +.07 +.15 − .01 − .10 − .06 ref: .75 ref: .69 ref: .31 ref: .87 ref: .76 ref: .28 1a β +.01 +.20 +.11 − .02 − .01 − .01 − .03 − .02 − .01 − .01 − .12 − .26 ref: − .60 ref: − .61 ref: − .12 ref: − .82 ref: − .74 ref: − .10 1 β .00 .00 .00 +.01 +.01 +.01 +.01 +.01 +.07 +.14 − .11 − .06 ref: − .13 ref: − .12 ref: − .17 ref: − .01 ref: − .04 ref: − .16 Differences in Parameter Estimates Across Models 0 β .00 .00 .00 .00 .00 .00 .00 .00 +.01 +.01 − .01 − .02 ref: .07 ref: .14 ref: .05 ref: .14 ref: − .01 ref: − 0.01 α +.01 +.01 +.01 − .16 − .02 − .04 − .21 − .73 − .08 − .75 − 1.25 − 1.17 ref: 40.37 ref: 23.73 ref: 21.09 ref: 40.55 ref: 23.79 ref: 21.15 LL — — — — — — 1257 1313 1414 1320 1376 1441 1214 1279 1371 1268 1329 1398 — — — — — — AIC Model Fit Criteria − 2395 − 2508 − 2710 − 2512 − 2622 − 2752 − 2409 − 2537 − 2721 − 2511 − 2627 − 2765 729) 20 23 26 29 32 35 21 24 27 30 33 36 19 22 25 28 31 34 Model # — , not assessed.  Model Fit Criteria and Parameter Estimates Across 5-Interruption Segmented Linear Regression Models for the Risk of at Least 1 Redeemed Antibiotic Prescription Among Infants Born in Denmark, 2004 – 2012 ( N = 561

: 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, week indicators : 1-stage, cosine function : 1-stage, cosine function : 1-stage, cosine function : 1-stage, cosine function : 1-stage, cosine function : 1-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function : 2-stage, cosine function b b b b b b c c c c c c a a a a a a Set 1: assuming independent error terms Set 2: using autoregressive parameters C Analysis of interruptions 1, 1a, 2, 3, 4 Any antibiotic A Amoxicillin A Any antibiotic A Penicillin V A B B B C C C C Amoxicillin A Penicillin V A B B B C Approach B: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using a vector of 51 birth Approach B: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using week indicator variables. Approach A: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using a transformed cosine function. Approach A: 1-stage maximum likelihood estimation of the risk, controlled for seasonality by using Approach C: 2-stage weighted maximum likelihood estimation of the risk, controlled for seasonality by using a transformed cosine function. Approach C: 2-stage weighted maximum likelihood estimation of the risk, controlled for seasonality AIC, Akaike Information Criterion; LL, log likelihood; a b c SU PP LE M ENTAL TABLE 9

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Kinlaw et al https://doi.org/10.1542/peds.2017-0441 September 2017 Trends in Antibiotic Use by Birth Season and Birth Year 3 140 Pediatrics 2017 ROUGH GALLEY PROOF Article

Supplemental References

51. Schmidt M, Schmidt SAJ, Sandegaard Available at: http://www.​ medinfo.​ dk/​ sks/​ ​ eds. Analyzing Environmental Data. 1st JL, Ehrenstein V, Pedersen L, Sørensen brows.​php. Accessed October 20, 2015 ed. Chichester, England: John Wiley & HT. The Danish National Patient Registry: Sons, Ltd; 2005:41 102 53. Sundhedsdatastyrelsen (Danish Health – a review of content, data quality, and Data Protection Agency). Historical 55. Durbin J, Watson GS. Testing for serial research potential. Clin Epidemiol. Sundhedsvæsenets Klassifikations correlation in least squares regression. 2015;7:449–490 System (SKS) codes. Available at: ftp://​ I. Biometrika. 1950;37(3–4):409–428 filer.sst.​ dk/​ filer/​ sks/​ data/​ skscomplete/​ .​ 52. Sundhedsdatastyrelsen (Danish 56. Penfold RB, Zhang F. Use of interrupted Accessed October 20, 2015 Health Data Protection Agency). time series analysis in evaluating Sundhedsvæsenets Klassifikations 54. Piegorsch W, Bailer J. Nonlinear health care quality improvements. Acad System (SKS-browser, version 4.02). regression. In: Piegorsch W, Bailer AJ, Pediatr. 2013;13(suppl 6):S38–S44

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