The field of medicine is undergoing a fundamental change in which artificial intelligence is connecting with diagnostic instruments, patient information systems and therapy management enabling unforeseen opportunities in transforming the health system towards a modern data-driven patient-oriented approach (Rajkomar et al., 2019). This paradigm shift also affects perinatal medicine as predictive algorithms and artificial intelligence are applied to enhance and individualize maternal, neonatal and perinatal care, with the goal not only to predict mortality (Mangold et al., 2021) but also to facilitate therapeutic decisions for our most vulnerable patients, fetuses and newborns, and their mothers.

In this work, we discuss a predictive algorithm in neonatology, with initial focus on hyperbilirubinemia, a medical condition affecting half of all newborns. Hyperbilirubinemia is a condition defined as elevated serum or plasma bilirubin levels above the reference range of the laboratory, and it is due to disorders or immaturity of bilirubin metabolism. In neonates, transient jaundice is a normal part of postnatal transition (Dennery et al., 2001). Bilirubin has strong antioxidant properties but when reaching too high levels, bilirubin can cross the blood-brain barrier and might cause bilirubin-induced neurotoxicity, of which kernicterus is the most dangerous form (Watchko and Tiribelli, 2013). Thus, medical screening of all neonates for hyperbilirubinemia is recommended to commence prompt therapy, namely phototherapy, once certain thresholds are crossed to prevent neurological complications (Watchko and Tiribelli, 2013). Up to 10% of neonates experience rebound hyperbilirubinemia, requiring re-initiation of treatment (So and Khurshid, 2021), and making hyperbilirubinemia the major reason for re-hospitalization in the first year of life (Schiltz et al., 2014).

Currently, static population-based nomograms for the assessment of neonatal hyperbilirubinemia are applied in daily clinical practice (Dennery et al., 2001). These nomograms are based on percentiles of bilirubin values at a given age in hours and classify neonates into risk groups. More recent risk stratification approaches include additional clinical factors for the prediction of neonatal hyperbilirubinemia shortly after birth (Castillo et al., 2018) or before discharge (Han et al., 2015). Even though approaches for risk stratification provide clinicians with a guideline for their assessment, adherence is only 50% due to cumbersome documentation (Tartaglia et al., 2013; Sampurna et al., 2018). Moreover, it has been found that health care professional noncompliance with best practices is the main reason for kernicterus in countries with highest health care standards (Alkén et al., 2019). Nomogram-based methods are overly general and do not provide an individual prediction of what will happen. Therefore, we aim for personalized prediction by identifying neonates at risk for clinically relevant hyperbilirubinemia more accurately, thus preventing the development of severe neonatal jaundice as well as overtreatment and unnecessary hospital stays.

Machine learning (ML) methods are computationally powerful tools for the analysis of large and heterogeneous datasets almost in real time (Koch et al., 2020a). Such methods can be applied for discriminating between classes or patient populations (e.g. high vs. low risk patient; treatment required yes or no) by identifying relevant variables (features) of interest. As such we recently developed a ML-based tool to predict the probability of whether a neonate will need a phototherapy treatment or not within the next 48 h (Daunhawer et al., 2019). Although this ML tool provides an innovative risk assessment regarding phototherapy requirement, this algorithm does not predict the dynamics of bilirubin kinetics, i.e., this ML algorithm is not able to predict bilirubin levels up to 24 h or 48 h.

Complementary to our previously published ML-based algorithm, we present a predictive PMX-based algorithm (Koch et al., 2020b) that computes individual bilirubin kinetics up to 48 h. The PMX-based algorithm is intended for non-intensive care units to facilitate and optimize management of neonates with jaundice supporting clinical decisions such as 1) is an additional bilirubin measurement necessary? 2) can the neonate be discharged home? 3) can a neonate at risk for clinically relevant hyperbilirubinemia be identified early?

This manuscript has five objectives. First, we describe the development of the PMX-based algorithm. Second, we define clinically relevant scenarios, i.e., prediction up to 24 h based on one bilirubin measurement, and prediction up to 48 h based on two or more bilirubin measurements, and validate the prediction of developed PMX-based algorithm, which is the main goal of this manuscript. An appropriate external validation is a crucial step to perform predictions at the individual patient level. Third, we carry out stress test of this algorithm with increased prediction horizons up to 60 h. Fourth, we assess the sensitivity and specificity of the developed algorithm to evaluate performance relevant to clinical practice in neonatology. Further, we discuss opportunities and challenges of applying “intelligent” ML-, artificial neural networks (ANN)- and PMX-based algorithms in the field of perinatal medicine.

This section is structured as follows. First, we explain the magnitude of total serum bilirubin (TSB) measurement errors in clinical practice. Second, we present the study patient populations applied for development and validation of the PMX-based algorithm. Third, we describe the development of the PMX-based algorithm to characterize postnatal bilirubin kinetics. Fourth, we present the development of the PMX-based algorithm to predict individual bilirubin kinetics. Fifth, we outline the validation procedure of the developed PMX-based algorithm. Sixth, we provide information on applied software for descriptive statistics, algorithm development and validation.

This section is structured as follows. First, results of the PMX-based algorithm development is presented. Second, results of the external validation are shown.

As perinatal medicine is undergoing a fundamental change transforming towards a modern data-driven patient-oriented approach new tools that will predict the dynamics of biomarkers for an individual fetus or newborn will become increasingly important in maternal, neonatal and perinatal care. We developed PMX-based algorithms to optimize and individualize dosing of therapeutics in the field of perinatal medicine (Wilbaux et al., 2016a; Wilbaux et al., 2016b; Koch et al., 2017; Nekka et al., 2017; van Donge et al., 2018; Dallmann et al., 2019; van Donge et al., 2019; Wilbaux et al., 2019; van Donge et al., 2020a; van Donge et al., 2020b; Koch et al., 2020c; Dao et al., 2020; Samiee-Zafarghandy et al., 2022). It is time to go beyond classical pharmacological applications and develop algorithms condensing the wealth of clinical data and physiology knowledge into predictive tools coping with the dynamics of biomarkers for an individual fetus or neonate.

These tools can be developed based on various methods, such as PMX-based mathematical-statistical computer models, machine learning (ML) or other artificial intelligence (AI) methods such as artificial neural networks (ANNs). In the following, PMX, ML and ANN approaches are discussed with focus on our perinatal case study.

The undisputed major advantage of ML methods is its computational efficiency in handling big data (Koch et al., 2020a). Large amounts of input features can be processed regarding its relationship with a dependent variable, e.g., a labeled (supervised) binary outcome. On one hand this allows large amounts of input features to be screened, e.g., patient characteristics, for their relevance, but on the other hand the ML-based tool is solely data-driven. Recently, we developed a ML-based tool to predict the probability whether a neonate will need a phototherapy treatment or not within the next 48 h (Daunhawer et al., 2019). Almost 50 features were screened resulting in a relevant subset of only four, which suffices for a strong predictive performance (Daunhawer et al., 2019). Although such ML-based tool provides an innovative risk assessment regarding phototherapy requirement, it does not predict the dynamics of bilirubin kinetics. In addition, ML methods are not pre-destined to represent physiological mechanisms. Hence, we consider ML as a powerful tool e.g., in pre-screening large amounts of input features and in developing diagnostic tools where dynamic aspects of the dependent variable are not of primary importance.

AI methods, such as ANNs, have become popular to analyze data from various fields as ANNs can approximate any function up to a certain accuracy (Hornik et al., 1989). At first glance, this sounds like the perfect tool to learn any kind of behavior. Although this is true in theory, an ANN is solely data-driven, i.e., anything the ANN will learn arises from the analysis dataset which can have essential fundamental consequences. An enormous amount of data may be required covering all possible situations. What ANNs do not see, will not be learned, and may not be accurately predicted. Another issue with ANNs is its black-box property, which makes it almost impossible to understand why a trained ANN looks the way it does. This in turn can limit acceptance of ANN-based algorithms by care givers in clinical practice.

The developed PMX-based algorithm presented in this paper includes known physiology-based, biological, and clinical facts (Bonate, 2006; Koch et al., 2013; Gabrielsson, 2017). As an example, neonates undergo strong maturation processes during the first days and even weeks of life. We think it is “intelligent” to incorporate such scientific, medical understanding into our computer models. Our PMX-based algorithm predicts bilirubin kinetics over time up to 48 h. Hence, not only an answer for a specific question is available for the clinician (Koch et al., 2020a), but the entire bilirubin kinetics is revealed and provided. In addition, due to the availability of the predicted bilirubin kinetics, different clinical end points of interest can be defined in an a-posteriori step, e.g., prediction up to 24 h, 48 h or even longer prediction horizons, as presented in this paper. Moreover, clinically relevant binary end points such as prediction above or below a certain threshold, can be defined, as presented in the sensitivity and specificity computations.

Discussed PMX-, ML- and ANN-based methods have in common that an external validation, i.e., a dataset from another medical center, is necessary before application in clinical practice. The major goal of this paper was to present an external validation of the PMX-based algorithm based on a dataset that was not available during algorithm development. In addition to typical validation procedures in pharmacometrics (Lavielle, 2014), we applied the statistical concept of sensitivity and specificity for the external validation of the PMX-based algorithm. This is to demonstrate that one can translate PMX-based algorithms that forecast dynamics of biomarker responses or disease progression into simplified algorithms that predict a binary outcome.

The developed, predictive PMX-based algorithm was applied in two different clinically relevant scenarios in neonatology. In the first scenario, bilirubin kinetics is predicted up to 24 h into the future based on a single bilirubin measurement with a median relative (absolute) prediction difference of 8.5% (median absolute prediction difference 17.4 μmol/l), and sensitivity and specificity of 95.7 and 96.3%, respectively. In the second scenario, bilirubin kinetics is predicted up to 48 h into the future based on two bilirubin measurements with a median relative (absolute) prediction difference of 9.2% (median absolute prediction difference 21.5 μmol/l), and sensitivity and specificity of 93.0 and 92.1%, respectively. Moreover, a scenario with two or more bilirubin measurements and various stress tests based on increasing the prediction horizon were also performed. In all these cases, similar values regarding the applied validation metrics were obtained.

Recently, the PMX-based algorithm has even been validated with three additional external, independent datasets: 1) clinical dataset from Greece consisting of neonates with transcutaneous bilirubin (TcB) measurements only, 2) clinical dataset from Germany consisting of neonates with TSB only, TcB only, or combinations of TSB and TcB measurements, and 3) clinical dataset from Kenya, Africa, consisting of neonates with TSB and TcB measurements. Results from these additional external validation studies will be published in the near future.

Until now, best practice has been to plot measured bilirubin values to given nomograms in a paper or electronic-based fashion to identify the current level of patients’ jaundice status. Then, for estimating individual risk of a given neonate and to provide a recommendation for next measures, including further bilirubin controls or specific therapy management steps, various clinical parameters need to been considered by the responsible health care provider. As long as the neonatal patient is hospitalized anyway there is only the medical challenge. In contrast, once there is no other reason for keeping the patient in hospital or the patient is already in the outpatient service, clinical decision making becomes even more demanding as additional organizational, economic and legal challenges may arise (Brown et al., 2021). However, there are no randomized and quasi-randomized studies available specifically addressing bilirubin therapy, namely home-versus hospital-based phototherapy (Malwade and Jardine, 2014).

Our intelligent PMX-based algorithm for prediction of bilirubin kinetics is based on differential equations that characterize maturation processes and other balance properties and are then trained and validated on large datasets. PMX-based algorithms can complement “artificial intelligence” such as ML- and ANN-based approaches in perinatal medicine. PMX-based algorithms leverage and integrate scientific, medical knowledge with intelligent learning from clinical data. Our developed intelligent algorithm for bilirubin level prediction will be incorporated in a clinical decision support tool with the goal to further optimize and individualize treatment of preterm and term neonates, our most vulnerable patients. The presented case of hyperbilirubinemia illustrates the potential of intelligent, predictive ML-, ANN- or PMX-based algorithms in neonatology.

There are numerous opportunities for such clinical decision support tools to further enhance and personalize care of mothers and their unborn and born children. Neonatal jaundice is just one of many medical conditions affecting newborn babies. There are many other diseases in fetuses, neonates and their mothers rooted in the specific dynamics of pregnancy and transition from intra-uterine to extra-uterine life (Evers and Wellmann, 2016). In contrast to adult medicine where health is defined as a continuum and the absence of physical and mental degradation, in perinatal medicine, health is a matter of cycles, growth, development and maturation processes. As such intelligent algorithms and tools designed for predicting medical conditions in perinatal medicine must address these specific properties.