We conducted a cohort study utilizing data from the Danish Medical Birth Registry [14] to identify all live singleton births with a gestational age of ≥ 35 weeks at Aarhus University Hospital between January 1, 2002, and November 30, 2016. The study population comprised infants with available data on birth weight, who survived the neonatal period, and remained resident in Denmark on day 29 post-birth (N = 65,365; see Supplementary Fig. 1). In Denmark, each resident is assigned a unique identification number in the Danish Civil Registration System, facilitating accurate data linkage across national registers [15, 16]. Only children born at Aarhus University Hospital were included in this study due to incomplete information on neonatal phototherapy in other regions of Denmark [17]. We used data from the Danish registries and no consent forms are needed according to Danish data protection regulation. Our research adhered to the ethical principles outlined in the Declaration of Helsinki and the study was approved by the Danish Data Protection Agency (reference number: 2016–051-000001, serial number 1515, approval date: 11. June 2019). We utilized ChatGPT to assist in revising the language of our manuscript, but we carefully reviewed and incorporated the revisions.

Data on bilirubin measurements, including total serum bilirubin and unconjugated bilirubin, were extracted from the clinical laboratory information system (LABKA). Implemented in 2000 within the Central Denmark Region, LABKA offers comprehensive coverage within this region, encompassing Aarhus University Hospital [18]. The system aggregates test results from samples collected in both public and private hospitals, as well as those collected by general practitioners and submitted to clinical biochemistry departments.

Key test items during the neonatal period included total serum bilirubin (TsB) of neonates (NPU04145), total serum bilirubin (NPU01370), unconjugated bilirubin (NPU01366), and conjugated bilirubin (NPU17194), with the NPU terminology employed for result identification and communication across clinical laboratories [18].

The dataset contains details such as sampling date and time, results, and units of tests conducted. For this study, bilirubin measurement primarily pertains to total serum bilirubin and/or unconjugated bilirubin, given the negligible presence of conjugated bilirubin during the neonatal period. Multiple bilirubin measurements could be recorded for a child during this period, with the highest value selected for analysis.

Data on neonatal phototherapy treatment were extracted from the Danish National Patient Register (DNPR) [19]. Children receiving neonatal phototherapy were identified if they were coded with procedure codes BNGC (Phototherapy) or BNGC0 (Phototherapy to neonates) in the DNPR, with treatment dates falling within the neonatal period (up to 28 days of age). Clinical practices adhere to phototherapy guidelines for neonatal hyperbilirubinemia adapted by the Danish Pediatric Society in 1992 and 2012 from guidelines established by the American Academy of Pediatrics (see Supplementary Table 1a) [2, 20]. The information about the devices, light spectrum, intensity used for neonatal phototherapy at Aarhus University Hospital could be found in the Supplementary Table 1b. Since 2011, the Danish recommendation of intensity for neonatal phototherapy is a minimum 30 microwatts/cm2/nm, measured at initiation. Phototherapy usually last for 24 h before taking a bilirubin measurement to judge if the treatment should continue or not (personal communication with coauthor JPP).

Diagnoses of epilepsy were retrieved from the DNPR [21]. Children were classified as having epilepsy if they were registered with ICD-10 codes G40-G41 as either a primary or secondary diagnosis after the neonatal period. The date of epilepsy onset was defined as the date of hospital contact that led to the diagnosis.

Data on date and time of birth, sex of the child, gestational age at birth, birth weight, Apgar score at five minutes, maternal age at the time of birth, and parity were obtained from the Danish Medical Birth Registry. The age of the child in hours at the time of blood sample collection for bilirubin tests was determined by utilizing both the date and time of birth and blood sample collection.

Children were classified based on gestational age and birth weight percentile: those with a birth weight below the 10th percentile for their gestational age were categorized as small for gestational age (SGA), those with a birth weight above the 10th percentile were classified as large for gestational age (LGA), and those with a birth weight between the 10th and 90th percentile were deemed appropriate for gestational age (AGA). Information on family disposable income was obtained from Statistics Denmark [22].

Diagnoses of major congenital malformations in the neonatal period (within 28 days after birth) were extracted from the DNPR. Information on major congenital malformations (see Supplementary Table 2), other neonatal factors (see Supplementary Table 3) during the neonatal period, as well as maternal factors during pregnancy (see Supplementary Table 4), were also obtained from the DNPR.

Characteristics of children were summarized for children with neonatal phototherapy and children without neonatal phototherapy among the total population and among children with available measurement of bilirubin. For children with measurement of bilirubin, we estimated mean and standard deviation of the maximum of bilirubin measured in the neonatal period and the age of neonates at time of bilirubin measurement.

Crude and adjusted hazard ratios (HRs) of epilepsy for children with neonatal phototherapy compared to those without neonatal phototherapy were estimated using Cox proportional regression models. Children were followed from day 29 after birth until the onset of epilepsy, death, emigration, or the end of follow-up on December 31, 2016. Age served as the time scale in the Cox proportional regression models.

Adjusted HRs of epilepsy were calculated in two ways, the traditional multivariable model and propensity score matching model, since the propensity score matching model enable us to take more covariates into account than the traditional one. In the analyses using the multivariable model [23], each factor (including sex, gestational age, intrauterine growth [SGA, AGA, LGA], congenital malformation, Apgar score, neonatal and maternal risk factors, birth year, family income, maternal age, and parity) was included as an independent variable. In the analyses using propensity score matching, propensity scores of neonatal phototherapy were computed based on child and maternal risk factors (27 in total, see Table 1). We employed a 1:3 ratio using nearest neighbor matching with a caliper of 0.1 of the standard deviation of the logit of the propensity score and ensured common support of propensity score (overlap in the propensity score distribution between the treatment and control groups) [24]. We did balancing test of neonatal and maternal factors between children with neonatal phototherapy and children without neonatal phototherapy before and after propensity score matching.

We conducted similar analyses in the subgroup of children who had at least one bilirubin measurement in the neonatal period enabling us to further adjust for bilirubin related factors and estimate the influence of phototherapy itself on epilepsy risk. In the multivariable model, we further adjusted for gestational age- and age-specific quartiles of bilirubin level (1st, 2nd, 3rd, 4th quartile) and age at the time of bilirubin measurement (1st, 2nd,3rd, 4th, 5–7, 8–14, 15–21, and 22–28 days after birth). For propensity score matching, we included gestational age- and age-specific quartiles of bilirubin level and age at the time of bilirubin measurement in the calculation of the propensity score of neonatal phototherapy (see Table 1). To obtain gestational age- and age-specific quartiles of bilirubin, children were categorized into quartiles within each stratum based on gestational age (35, 36, 37, 38, or ≥ 39 gestational weeks) and age at the time of bilirubin measurement (< 48 h, 48–71 h, 72–95 h, 4–14 days, and 15–28 days).

All analyses were performed with STATA, version 16 (StataCorp LLC, College Station, TX, USA).