We previously reported a clinical prediction rule to estimate the probability of rebound hyperbilirubinemia using gestational age (GA), age at phototherapy initiation, and total serum bilirubin (TSB) relative to the treatment threshold at phototherapy termination. We investigated (1) how a simpler 2-variable model would perform and (2) the absolute rebound risk if phototherapy were stopped at 2 mg/dL below the threshold for treatment initiation.

Subjects for this retrospective cohort study were infants born 2012–2014 at ≥35 weeks’ gestation at 1 of 17 Kaiser Permanente hospitals who underwent inpatient phototherapy before age 14 days. TSB reaching the phototherapy threshold within 72 hours of phototherapy termination was considered rebound. We simplified by using the difference between the TSB level at the time of phototherapy termination and the treatment threshold at the time of phototherapy initiation as 1 predictor, and kept GA as the other predictor.

Of the 7048 infants treated with phototherapy, 4.6% had rebound hyperbilirubinemia. The area under the receiver operating characteristic curve was 0.876 (95% confidence interval, 0.854 to 0.899) for the 2-variable model versus 0.881 (95% confidence interval, 0.859 to 0.903) for the 3-variable model. The rebound probability after stopping phototherapy at 2 mg/dL below the starting threshold was 2.5% for infants ≥38 weeks’ GA and 10.2% for infants <38 weeks’ GA.

Rebound hyperbilirubinemia can be predicted by a simpler 2-variable model consisting of GA and the starting threshold–ending TSB difference. Infants <38 weeks’ gestation may need longer phototherapy because of their higher rebound risk.

We previously reported a 3-variable clinical prediction rule that quantifies the risk of the bilirubin level rebounding to phototherapy levels after inpatient phototherapy.

We simplified the rule while maintaining excellent discrimination using as predictors only gestational age and the difference between the current bilirubin level and the treatment threshold at the time phototherapy was started.

Predicting rebound hyperbilirubinemia can help clinicians decide when to discontinue phototherapy for infants undergoing treatment of neonatal jaundice. We recently devised a 3-variable clinical prediction rule that quantifies the rebound risk after the first inpatient phototherapy according to an infant’s gestational age (GA), age at phototherapy initiation, and total serum bilirubin (TSB) level relative to the American Academy of Pediatrics (AAP) phototherapy threshold at treatment termination.^{1} An alternative approach is to discontinue phototherapy when the TSB is at least 2 mg/dL below the treatment threshold at the age of phototherapy initiation (M.J. Maisels, MB, BCh, DSc, personal communication, 2018). We sought to determine (1) if a 2-variable model, with just GA and the TSB relative to the threshold at phototherapy initiation, would perform as well as our previous 3-variable model and (2) the absolute risk of rebound if phototherapy were stopped as suggested.

## Methods

### Study Cohort

Our retrospective cohort consisted of 7048 newborns born in Kaiser Permanente Northern California hospitals between 2012 and 2014 at ≥35 weeks’ GA who underwent their first inpatient phototherapy before age 14 days. We excluded infants who did not have at least 2 TSB levels before phototherapy termination and infants with a conjugated bilirubin level of ≥2 mg/dL before or during their first phototherapy admission. Details of the cohort have been previously described.^{1} In brief, 39.6% of the infants were <38 weeks’ GA, and 14.5% had positive direct antiglobulin test (DAT) results. Phototherapy was initiated at a mean age of 2.3 (SD 1.3) days and terminated at a mean age of 3.6 (SD 1.3) days. The mean TSB level at phototherapy termination was 9.8 (SD 2.7) mg/dL. Approximately 90% of infants had a TSB measurement after inpatient phototherapy termination. There was an order for home phototherapy equipment during the hospitalization for 4.4% of infants, who were thus assumed to have continued on home phototherapy after inpatient treatment. An additional 6.6% of infants had an order for home equipment after hospitalization and were thus assumed to have restarted on home phototherapy after discharge.

### Predictor and Outcome Variables

All of the variables were derived from electronic data sources.^{1} We used the time of the first order for phototherapy as the time of phototherapy initiation. We estimated the time of phototherapy termination by using (1) nursing flowsheet documentation of discontinuation of phototherapy (25% of cohort); (2) if no such documentation was available, we used the time stamp of the discontinuation order (41%); and (3) if there was neither a nursing flowsheet nor order, we used the 1 hour before discharge time (34%). To estimate the TSB level at the time of phototherapy termination, we used the TSB level closest to the time of phototherapy discontinuation if 1 was measured between 3 hours before and 1 hour after treatment termination (24.6% of the cohort). If no TSB level was measured in this time window, we estimated a TSB at 3 hours before phototherapy termination by linear extrapolation using the last 2 TSB levels before termination. As previously reported, the average difference between an infant’s extrapolated TSB value and his or her last measured TSB was 0.4 (SD 1.1) mg/dL. For this analysis, we subtracted the estimated TSB at phototherapy termination (ending TSB) from the AAP treatment threshold at phototherapy initiation (starting threshold) and used this difference and the GA (dichotomized at <38 weeks) to form a 2-variable model. Rebound hyperbilirubinemia was defined as the TSB reaching or exceeding the hour-specific AAP phototherapy threshold within 72 hours of discontinuing phototherapy, as in our previous report. In our study cohort, 4.6% of infants had rebound hyperbilirubinemia.

### Statistical Analyses

To derive and validate this 2-variable prediction rule, we used the same random-split samples previously used to derive the 3-variable prediction rule. As before,^{1} we summed the variables multiplied by 10 times their logistic regression coefficients to formulate a prediction score. Because the logistic coefficients are equal to the logarithm of the odds ratios, summing them is equivalent to multiplying their odds ratios. We assessed model fit in the validation data set with a calibration plot and the Hosmer-Lemeshow test (10 groups), and we assessed discrimination with the area under the receiver operating characteristic (AUROC) curve. We performed analyses using Stata 14.2 (Stata Corp, College Station, TX).

## Results

Of the 7048 infants, the mean difference between the starting threshold and ending TSB was 4.4 (SD 3.5) mg/dL. The logistic coefficients from the derivation data set were 1.55 (95% confidence interval [CI], 1.02 to 2.08) for GA <38 weeks and −0.43 per mg/dL (95% CI, −0.52 to −0.34) for the starting threshold–ending TSB difference. The equation for the score is thus:

The Hosmer-Lemeshow χ^{2} (8 degrees of freedom) was 9.21 (*P* = .33) in the validation data set (*n* = 3530). Figure 1 shows the calibration curve on the validation data set. The discrimination of this 2-variable model was similar to that of the 3-variable model. In the derivation data set (*n* = 3518), the AUROC of the 2-variable model was 0.877 (95% CI, 0.856 to 0.899) compared with 0.887 (95% CI, 0.864 to 0.910) in the 3-variable model. In the validation data set, the AUROC was 0.876 (95% CI, 0.854 to 0.899) compared with 0.881 (95% CI, 0.859 to 0.903). In the subset of infants with a measured TSB at phototherapy termination (*n* = 1737), the AUROC was slightly higher at 0.901 (95% CI, 0.874 to 0.927).

The score can be translated into a predicted probability of rebound hyperbilirubinemia by consulting Fig 2. Alternatively, the following equation can be programmed into a spreadsheet, mobile application, or Web site. The mean difference of an infant’s predicted probability of rebound hyperbilirubinemia using the 2 different models was 0% (SD 4.6%). Stopping phototherapy at 2 mg/dL below the starting threshold gave a rebound probability of 2.5% for infants ≥38 weeks’ gestation and 10.2% for infants <38 weeks’ gestation. For infants <38 weeks’ gestation, phototherapy would need to be stopped at 5.5 mg/dL below the starting threshold to have a rebound probability (2.6%) similar to that of infants ≥38 weeks’ GA who stopped phototherapy at 2 mg/dL below the starting threshold.

## Discussion

We originally evaluated 10 variables (including race and ethnicity, DAT status, and formula and home phototherapy use) and by backward logistic regression devised a 3-variable clinical prediction rule that estimates the probability of rebound hyperbilirubinemia for an individual infant. That rule was based on (1) GA, (2) age at phototherapy initiation, and (3) TSB relative to the treatment threshold at phototherapy termination.^{1}

Here, using the same large infant cohort, we turned the previous 3-variable model into a 2-variable model by using the difference between the starting threshold and ending TSB as 1 predictor, effectively combining the age at initiation with the relative TSB at termination. We kept GA as the other predictor. The AUROC of this simpler model was excellent and only minimally lower than that of the 3-variable model. Similarly, the calibration is excellent. The worst point on the calibration plot is when the predicted risk of rebound is ∼5% and the observed risk was 7%, a small absolute difference (Fig 1). However, calibration should be assessed in additional populations.

The rebound probability predicted by the 2-variable model may differ from that of the 3-variable model by up to ∼5%, more noticeably for infants <38 weeks' GA. Possible scenarios include the 2-variable model’s estimates being lower for those who start phototherapy younger and have relatively short treatment durations and higher for those who stay on phototherapy longer. For example, if a DAT-negative infant of 37 weeks’ gestation starts phototherapy at 24 hours of age and stops at 48 hours of age at an ending TSB of 7.9 (2 mg/dL below the starting threshold), then the predicted rebound probability would be ∼10.2% on the basis of the new model compared with 15% on the basis of the previous model.

If phototherapy were discontinued at 2 mg/dL below the threshold for treatment initiation, the predicted probability of rebound is 2.5% for infants ≥38 weeks’ gestation but 10.2% for infants <38 weeks’ gestation. Lower GA has been well established as a risk factor for both hyperbilirubinemia and rebound hyperbilirubinemia.^{2}^{,}^{–}^{4} In most previous studies of rebound hyperbilirubinemia, phototherapy was stopped when the TSB decreased below a fixed threshold or at the physicians’ discretion.^{2}^{,}^{3}^{,}^{5}^{,}^{6}

A randomized controlled trial from Israel compared discontinuing phototherapy at 3 vs 1 mg/dL below the threshold for phototherapy initiation. They reported no significant difference in the occurrence of rebound hyperbilirubinemia within ∼24 hours.^{7} However, 19% of infants in that study had rebound, which is higher than estimated by our prediction rule. The trial, however, had a small sample size (*n* = 52), and 15% of the infants had glucose-6-phosphate dehydrogenase (G6PD) deficiency.^{7} The prevalence of G6PD deficiency in our population is unknown but likely lower.^{8}^{,}^{9} G6PD deficiency is a known cause of hemolysis and severe hyperbilirubinemia^{10}^{,}^{11} but has not been well characterized in rebound hyperbilirubinemia.

As before, this 2-variable prediction rule has several limitations.^{1}^{,}^{12} Notably, it does not capture the rebound risk after the second episode of inpatient phototherapy, and because almost 97% of the cohort started treatment before age 5 days, it does not capture the rebound probability of older infants. The prediction rule also has not yet been externally validated.

## Conclusions

Rebound hyperbilirubinemia after inpatient phototherapy can be predicted by a simple 2-variable model consisting of GA and the difference between the starting treatment threshold and the ending TSB level. For infants <38 weeks’ GA, it may be prudent to continue phototherapy longer because of their higher risk of rebound hyperbilirubinemia.

Dr Chang conducted the statistical analysis and interpretation of data and drafted the initial manuscript; Dr Newman conceptualized and designed the study and guided the statistical analysis and interpretation of data; and both authors revised and reviewed the manuscript and approved the final manuscript as submitted.

**FUNDING:** No external funding.

## References

## Competing Interests

**POTENTIAL CONFLICT OF INTEREST:** The authors have indicated they have no potential conflicts of interest to disclose.

**FINANCIAL DISCLOSURE:** The authors have indicated they have no financial relationships relevant to this article to disclose.

## Comments

## RE: Predicted Rebound probability at ending TSB of zero mg/dL

I would like to thank Dr. Pearl Chang and her group for this work. I would like to make one point. I observed the following when I calculated the PRP from birth to 96 hours of age at ending TSB of zero mg/dL:

1. Lower risk phototherapy threshold: PPR: 0.34% (birth)–0.01% (64 hrs) and zero from 64 to 96 hrs of age.

2. Medium risk: 3.2% (birth)–0.02% (96 hrs)

3. High Risk: 5.1% (birth)–0.06% (96 hrs)

This calculation shows that as expected the PRP at zero ending TSB (baseline PRP) is high among those who are known to be at risk for hyperbilirubinemia. Figure 1 (calibration curve) shows that the predicted rebound probability (PRP) reached zero. So, this high baseline PRP suggests that It might be more informative if the authors presented a calibration curve for each risk group separately. More importantly, perhaps we need if adding the baseline PRP to the PRP will improve the PRP performance. This adjustment may also help to explain why PRP of 5 % was the worst point on the calibration curve.

## RE: A Simpler Prediction Rule for Rebound Hyperbilirubinemia

I congratulate the Authors on validation of their previously described model. However, I strongly urge them (and the Journal) to adopt the guidelines suggested by the TRIPOD (Transparent Reporting for a multivariable prediction model for Individual Prognosis or Diagnosis) 1 Specifically, a calibration curve would be enable the reader to see how the model performs as the score increases. As usually occurs in similar models, most patients have low scores, hence there is less information and wider confidence intervals as the score increases. Although the AUC (Fig 1) is a useful statistical measure of model performance, it is a metric of aggregate performance, not how well the model predicts outcomes for specific scores. Similarly, Figure 2 may be misinterpreted by the reader, since it implies a precise probability of rebound hyperbilirubinemia for each score. As can be seen from Table 4, the scores are not uniformly distributed. There are smaller samples and fewer adverse events at higher scores, making those rebound estimates less precise than those at lower scores.

(1) “Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis (TRIPOD): Explanation and Elaboration” by K.G.M. Moons, D.G. Altman, J.B. Reitsma, J.P.A. Ionnidis, P. Macaskill, E.W. Steyerberg, A.J. Vickers, D. F. Ransohoff and G. S. Collins, Annals of Internal Medicine 2015:162:W1-W73.

Thomas Riggs, MD, PhD (Associate Editor, Statistics, American College of Obstetrics and Gynecology and retired pediatric cardiologist).

## RE: Rebound Hyperbilirubinemia – Chang-Score revised

Congratulations to the authors for improving their initial 3-variable clinical prediction rule (1) to quantify the risk of the total bilirubin level (TB) rebounding to phototherapy levels after inpatient phototherapy into a more simple 2-variable model by using only the predictors gestational age (GA) and the difference between the current TB and the treatment threshold at phototherapy initiation (2), both rules with equally excellent calibration.

The revised score and the predicted score-related probability of rebound demonstrate that the AAP hyperbilirubinemia guideline recommendation (3) which indicated that phototherapy may be discontinued when the TB level falls to <14 mg/dL is too restrictive, because this threshold value is said to be associated with a rebound risk of merely less than 0.05% in mature newborns (GA ≥ 38 weeks).

Furthermore the new Chang-Score could be even more simplified for the use in the daily routine. Instead of calculating the rebound probability by the means of a score and an exponential function it is sufficient for the discussion with the caregivers to know, that mature newborns, based on the 3-day TB-threshold of 20 mg/dL, the most often case in a pediatric neonatal ward, have a rebound probability of about 2.5%, 1.5%, resp. 1.0% when they are treated with phototherapy to a TB of 18, 17, resp. 16 mg/dL.

On a side note, it appears to me that the reason to develop that 2-variable model was the identified limitation “age at phototherapy initiation”, the third variable of the 3-variable model, which made the former score only helpful within the first 4 to 5 days of life (4). Thus, it is very satisfying to see that my small comment did in a tiny way contribute to the highly relevant Chang-score. However, it remains a dull aftertaste as in the discussion of the recent article (1) my comment was only mentioned indirectly by merely citing the “Authors’ response” to my comment (5).

1. Chang PW, Kuzniewicz MW, McCulloch CE, Newman TB. A clinical prediction rule for rebound hyperbilirubinemia following inpatient phototherapy. Pediatrics. 2017;139(3): e20162896

2. Chang PW, Newman TB. A Simpler Prediction Rule for Rebound Hyperbilirubinemia. Pediatrics. 2019;144(1):e20183712

3. American Academy of Pediatrics Subcommittee on Hyperbilirubinemia. Management of hyperbilirubinemia in the newborn infant 35 or more weeks of gestation. Pediatrics. 2004;114(1):297–316

4. Korsch E. Chang's Score Is Only Helpful Within the First 4 to 5 Days of Life. Pediatrics. 2017;140(2).e20171694A.

5. Chang PW. Authors’ response. Pediatrics. 2017;140(2):e20171694B