METHOD AND COMPUTER PROGRAM FOR PREDICTING BILIRUBIN LEVELS IN NEONATES

Abstract

The invention relates to a method and a computer program for estimating a bilirubin level of a neonate, comprising the steps of: Acquiring a series of bilirubin levels estimated at different time points from a sample obtained from a neonate, Acquiring a plurality of covariates from the neonate, each comprising an information about a neonatal property, Providing a pre-defined bilirubin model function, wherein the bilirubin model function is configured to describe a time course of a bilirubin level of a neonate, —Determining a plurality of model parameters of the bilirubin model function, wherein each model parameter is estimated from at least one covariate of the plurality of covariates and an associated population model parameter, Determining from the series of acquired bilirubin levels and the bilirubin model function with the determined model parameters an expected bilirubin level of the neonate for a time particularly later than a lastly acquired bilirubin level of the series of bilirubin levels.

Claims

1. A method of treating physiological jaundice in a neonate, comprising the steps of: a. detecting and identifying physiological jaundice in a neonate; and b. exposing the neonate having physiological jaundice to phototherapy to treat the physiological jaundice; wherein said detecting and identifying comprises calculating a bilirubin level and determining that the calculated bilirubin level is higher than a provided maximum bilirubin level, by performing the steps of: 1) acquiring a series of bilirubin levels estimated at different time points from a neonate, 2) acquiring a plurality of covariates from the neonate, each covariate comprising an information about a neonatal property, 3) providing a predefined bilirubin model function, wherein the bilirubin model function is configured to describe a time course of the bilirubin level of the neonate, 4) determining a plurality of model parameters of the bilirubin model function, wherein each model parameter is estimated from at least one covariate of the plurality of covariates and an associated population model parameter, and 5) determining from the acquired series of bilirubin levels and the bilirubin model function with the determined model parameters an expected bilirubin level of the neonate for a time later than a lastly acquired bilirubin level of the series of bilirubin levels, wherein the bilirubin model function is a rate equation relating a time-varying bilirubin production rate Kprod, with a time-varying bilirubin elimination rate Kelim, and particularly a time-varying phototherapy exposure function PT, wherein the bilirubin production rate Kprod, the bilirubin elimination rate Kelim and particularly the phototherapy exposure function PT comprise the plurality of model parameters.

2. The method according to claim 1, wherein the model function is expressed as $\frac{d}{dt}\mathrm{Bilirubin}\left(t\right)=\mathrm{Kpro}d\left(t\right)-\left(Kelim\left(t\right)+PT\left(t\right)\right).Math.\mathrm{Bilirubin}\left(t\right)$ wherein $\frac{d}{\mathrm{dt}}$ is a time-derivative operator, wherein Bilirubin(t) is the bilirubin level at a time t.

3. The method according to claim 1, wherein the bilirubin production rate Kprod(t) is expressed as Kprod(t)=Kin.sub.Base.Math.exp(−K.sub.PNA.Math.t)+KAD, wherein Kin.sub.Base and K.sub.PNA are model parameters comprised by the plurality of model parameters, wherein Kin.sub.Base is an excess neonatal bilirubin production rate at time zero, wherein KAD is a normal bilirubin production rate, and wherein K.sub.PNA is a decay rate of the bilirubin production rate Kprod(t).

4. The method according to claim 1, wherein the bilirubin elimination rate Kelim(t) is expressed as $\mathrm{Keli}m\left(t\right)=\frac{\mathrm{KEMAX}.Math.t^H}{T50^H+t^H},$ wherein KEMAX is a model parameter comprised by the plurality of model parameters, wherein KEMAX is a maximum stimulation rate of bilirubin, T50 is a time when the time-varying bilirubin elimination rate has increased to 50% of its value at t=0, wherein H is a Hill coefficient.

5. The method according to claim 1, wherein PT(t) is expressed as PT(t)=KP.Math.S(t), wherein KP is a model parameter comprised by the plurality of model parameters and particularly wherein S(t) is a time-varying step function indicating the times when phototherapy has been received by the neonate, particularly wherein S(t) assumes only two values, particularly values of 0 or 1.

6. The method according to claim 1, wherein the at least one covariate, particularly at least two covariates, comprises one of the following information: A birth weight, particularly as a continuous covariate, A gestational age, particularly as a continuous covariate, A delivery mode, particularly as a categorical covariate, comprising the information whether the neonate was delivered by Caesarean section or by vaginal delivery; A type of feeding, particularly as a categorical covariate, comprising the information whether the neonate is fed by mother milk or by formula milk; A received phototherapy, particularly as a categorical covariate, comprising the information whether the neonate has received phototherapy or not in the past and/or will receive phototherapy in the future, A weight loss compared to the birth weight, particularly as a continuous covariate, A low birth weight, as a categorical covariate, comprising the information whether the birth weight was below or above a predefined birth weight, wherein the predefined weight is particularly 2500 g; A respiratory support, particularly as a categorical covariate, comprising the information whether the neonate has received respiratory support after delivery or not.

7. The method according to claim 1, wherein the at least one covariate comprises an information about a blood incompatibility, particularly as a categorical covariate, comprising the information whether the neonate had an ABO blood type incompatibility or a rhesus incompatibility or both.

8. The method according to claim 6, wherein the model parameter Kin.sub.Base is estimated from the covariate comprising the information on the delivery mode, particularly wherein Kin.sub.Base is lower, if the neonate was born by Caesarean section as compared to a neonate that was born by vaginal delivery; K.sub.PNA is estimated from the covariates comprising the information about weight loss, the low birth weight, type of feeding, and a received phototherapy, particularly wherein K.sub.PNA is lower, if the neonate received phototherapy as compared to a neonate that has not received phototherapy; KEMAX is estimated from the covariate comprising information about the type of feeding, particularly wherein particularly KEMAX is lower if the neonate is fed with mother milk as compared to a neonate that has been fed by formula milk; and/or KP is estimated from the covariate comprising information about the respiratory support, particularly wherein KP is higher, if the neonate did not receive respiratory support as compared to a neonate having received respiratory support.

9. The method according to claim 1, wherein each model parameter P is estimated from the at least one covariate COV.sub.i by weighting the associated population model parameter P.sub.0 of the model parameter P with the at least one covariate COV.sub.i, particularly wherein each model parameter P is determined by P=P.sub.0.Math.(1+θ .Math.(COV.sub.i−median(COV))), if the covariate is a continuous covariate and by P=P.sub.0.Math.(1+θ .Math.COV.sub.i), if the covariate is a categorical covariate, wherein θ is a weighting factor for adjusting the weight of the covariate on the respective model parameter.

10. The method according to claim 1, wherein the expected bilirubin level of the neonate is determined by use of a maximum a posteriori probability estimate method (MAP), processing the acquired bilirubin levels and the bilirubin model function with the determined model parameters.

11. The method according to claim 1, wherein the bilirubin levels of the acquired series of bilirubin levels are acquired during a course of at least 24 hours, and wherein at least two bilirubin levels are estimated.

12. The method according to claim 1, wherein the bilirubin levels are determined from a sample, particularly a blood sample, obtained from the neonate.

13. (canceled)

14. The method according to claim 1, wherein the time interval for phototherapy exposure is estimated by the method according to the invention, when determining the expected bilirubin level.

15. A computer program for determining a bilirubin concentration of a neonate, wherein the computer program comprises computer program code, wherein when the computer program is executed on a computer, the computer executes the method according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0129] In FIG. 1 a concept of the model-function describing postnatal bilirubin levels and phototherapy effect in preterm neonates is shown. The neonatal hyperbilirubinemia can be seen as an imbalance between increased production and decreased elimination. Based on neonatal physiology, Kprod and Kelim change over time. Bilirubin production rate is maximal at birth because of the initial high red blood cells hemolysis, and then decreases to normal elimination rates as can be observed in heathy adult. Bilirubin elimination rate increases with age corresponding to the maturity/ontogeny of hepatic function. Transcutaneous phototherapy can increase the elimination rate of bilirubin.

[0130] In FIG. 2 simulations of postnatal bilirubin changes for two scenarios are shown. The dashed curves correspond to a “best case” scenario with 10.sup.th and 90.sup.th percentiles (outer lines) of the simulations and the 50.sup.th percentile (middle line). The best case scenario is defined by the following covariates: neonate with a birth weight of 1880 g delivered by Caesarean section, who lost 6% of his birth weight, fed with formula milk, without respiratory support and who did not receive phototherapy. The solid curves correspond to a “worst case” scenario with 10.sup.th and 90.sup.th percentiles of the simulations (outer lines) and the 50.sup.th percentile line (in the middle). The worst case scenario is defined by the following covariates: neonate with a birth weight of 1100 g, vaginally delivered, who lost 15% of his birth weight, fed with mother milk, with respiratory support and who received phototherapy at 80 hours.

[0131] In FIG. 3A individual predictions of time-dependent bilirubin production rates for two populations of neonates are shown. In FIG. 3B individual predictions of time-dependent bilirubin elimination rates for two populations of neonates are shown. The individual predictions of FIG. 3A: bilirubin production rates, Kprod, and FIG. 3B: bilirubin elimination rates, Kelim, for neonates who received phototherapy treatment (black crosses) and neonates who did not receive phototherapy (black circles) are plotted against time. Each point (cross or circle) corresponds to Kprod or Kelim for a given neonate at a given time. The dashed and solid curves correspond to a smooth curve of all data in neonates with and without phototherapy, respectively.

[0132] In FIG. 4A and FIG. 4B a visual Predictive Check to evaluate the predictive performance of the method according to the invention is shown. Bilirubin levels are plotted against time for FIG. 4A: neonates who did not receive phototherapy treatment, and FIG. 4B: neonates who received phototherapy. Dashed curves correspond to the simulated confidence interval (95%) of the median and the 10.sup.th and 90.sup.th percentiles. The solid curves are the observed median and 10.sup.th and 90.sup.th percentiles.

[0133] In FIG. 5 observed individual bilirubin profiles (series of bilirubin levels) versus time are shown. Each curve corresponds to one neonate. The x-axis is the time (in hours) since birth and the y-axis is the measured bilirubin concentration (in μmol/L).

[0134] FIG. 6A to FIG. 6F show the influence of a specific covariate on the associated model parameter.

[0135] FIG. 6A shows the influence of the covariate comprising the information about the delivery mode on the model parameter Kin.sub.Base. The solid curve corresponds to a simulated neonate born by Caesarean section and the dashed curve to a neonate vaginally delivered.

[0136] FIG. 6B shows the influence of the covariate comprising the information about the weight loss on the model parameter K.sub.PNA. The solid, long dashed, dashed and dotted curves correspond to simulated neonates with a maximum weight loss from baseline of −15%, −10%, −5% and 0%, respectively.

[0137] FIG. 6C shows the influence of the covariate comprising the information about the type of feeding on the model parameter K.sub.PNA and KEMAX. The solid curve corresponds to simulated data for neonates fed by formula milk and the dashed curve to a breastfed neonate.

[0138] FIG. 6D shows the influence of the covariate comprising the information about the low birth weight on the model parameter BILI0. The dashed curve corresponds to a simulated neonate with a low birth weight (<2500 g), and the solid curve to a neonate with a birth weight >2500 g.

[0139] FIG. 6E shows the influence of the covariate comprising the information about the birth weight on the model parameter K.sub.PNA. The dotted, dashed, long dashed and solid curves correspond to simulated neonates with a birth weight of 3100 g, 2600 g, 1600 g and 1100 g respectively.

[0140] FIG. 6F shows the influence of the covariate comprising the information about the respiratory support on the model parameter KP. The solid curve corresponds to a simulated neonate without respiratory support and the dashed cure to a neonate with respiratory support. They both received one phototherapy cycle at 80 hours.

[0141] FIG. 7A shows goodness-of-fit plots, namely measured bilirubin levels plotted against individual predictions. FIG. 7B shows goodness-of-fit plots, namely measured bilirubin levels plotted against population predictions. The black line corresponds to the identity line. On the x-axis the predicted bilirubin levels are plotted, and on the y-axis the measured bilirubin levels are plotted. The method according to the invention exhibits a narrow distribution.

[0142] FIG. 7C shows goodness-of-fit plots, namely conditional weighted residuals (CWRES) plotted against population predictions. FIG. 7D shows goodness-of-fit plots, namely conditional weighted residuals (CWRES) plotted against time. The horizontal line corresponds to y=0.

[0143] FIG. 7E shows the predicted and measured bilirubin levels of individual neonates (ID: 1 to ID: 16). Bilirubin levels are plotted against time for the specific neonate. Dots correspond to observed (measured) bilirubin values. Solid curves are the individual predicted bilirubin levels estimated with the method according to the invention and dashed curves correspond to the population predicted profiles.

[0144] FIG. 8A shows the observed (measured) bilirubin levels plotted against forecasted bilirubin levels after 2 days of life. The solid line corresponds to the identity line. On the x-axis the forecasted bilirubin level is plotted, and on the y-axis the measured bilirubin level is shown.

[0145] FIG. 8B shows bilirubin observations plotted against the first forecasted value after the first phototherapy cycle. The solid line corresponds to the identity line.

[0146] Objectives of this invention are to [0147] (i) provide a method and a model function describing the physiological patterns of bilirubin level during the first weeks of life in preterm neonates particularly with hyperbilirubinemia; [0148] (ii) characterize and quantify the effect of phototherapy on bilirubin kinetics and levels; [0149] (iii) identify and quantify relevant covariates that influence the bilirubin level in a neonate, and [0150] (iv) utilize the existing model to develop a bedside decision support tool that help caregivers to further individualize and enhance management of preterm neonates with jaundice.

[0151] A total of 95 late preterm neonates with physiological jaundice receiving phototherapy or not has been used to test the method according to the invention. From the reviewed 95 neonates, 5 patients with insufficient number of bilirubin observations (less than 3 acquired bilirubin levels in the series) and 2 neonates with aberrant bilirubin levels (profiles) have been excluded. Thus, a total of 88 neonates are used for the evaluation and testing of the method according to the invention.

[0152] The method according to the invention is designed to predict longitudinal bilirubin data, i.e. expected bilirubin levels, from preterm neonates with hyperbilirubinemia during their first weeks of life.

[0153] Postnatal bilirubin levels can be described with a turnover model, considering the bilirubin level as a function of the time-dependent rates of a bilirubin production, Kprod and a first-order bilirubin elimination, Kelim, as described in FIG. 1.

[0154] As can be seen in FIG. 1, Kprod and Kelim change over time, i.e. they change with increasing postnatal age (PNA). The bilirubin production rate Kprod is maximal at birth, particularly because of the initial high red blood cell's (RBC) hemolysis, due to the higher RBCs turnover and shorter lifespan in neonates. It decreases to a normal production rate for a healthy adult within 10 days.

[0155] The bilirubin elimination rate Kelim increases with time corresponding to the maturity/ontogeny of hepatic function in the neonate. Different time-dependent functions have been tested such as linear, exponential or saturable Emax for Kelim. It turns out that the saturable Emax function describes the bilirubin elimination most accurate.

[0156] In FIG. 1 the effect of phototherapy on the bilirubin level has not been taken into account.

[0157] If a transcutaneous phototherapy effect is taken into account, the model function comprises an additional term PT(t) that is associated to the bilirubin elimination.

[0158] In the model function, the bilirubin production rate, Kprod, is modelled as a decreasing age-dependent exponential function (c.f. FIG. 1, left panel). An additional constant bilirubin production rate KAD is added to the exponential function to reflect the adult production of bilirubin. The elimination rate, Kelim, is modelled with an increasing age-dependent Emax function to describe the ontogeny of hepatic function (c.f. FIG. 1, right panel). Transcutaneous phototherapy is assumed to increase the elimination of bilirubin.

[0159] The model function can be described with the following equation:

[00003]$\frac{d}{dt}\mathrm{Bilirubin}=\mathrm{Kpro}d\left(t\right)-\left(\mathrm{Kelim}\left(t\right)+PT\left(t\right)\right).Math.\mathrm{Bilirubin}\left(t\right)$$\text{with:}$$\mathrm{Kprod}\left(t\right)={\mathrm{Kin}}_{Base}.Math.\exp \left(-K_{PNA}.Math.t\right)+\mathrm{KAD}$$\mathrm{Kelim}\left(t\right)=\frac{\mathrm{KEMAX}.Math.t^H}{T50^H+t^H}$$\mathrm{Bilirubin}\left(0\right)=\mathrm{BILI}0$$PT\left(t\right)=\mathrm{KP}.Math.S\left(t\right)$

[0160] Kprod (t) in units of (μmol.Math.L.sup.−1.Math.hour.sup.−1) and Kelim(t) in units of (hour.sup.−1) are the time-dependent bilirubin production rate and bilirubin elimination rate, respectively. t is the time, corresponding to the postnatal age (PNA) measured in the units of (hour). Bilirubin(t) represents the bilirubin concentration (μmol.Math.L.sup.−1) at the time t. KP (hour.sup.−1) is the additional bilirubin elimination rate constant accounting for the effect of phototherapy on Kelim(t). S(t) represents a binary function equal to 0, when the neonate is not under phototherapy at the time t, and equal to 1 if the neonate receives phototherapy at the time t. Kin.sub.Base (μmol.Math.L.sup.−1.Math.hour.sup.−1) is the basal neonatal bilirubin production rate in addition to the adult bilirubin production rate KAD (μmol.Math.L.sup.−1.Math.hour.sup.−1). K.sub.PNA defines the shape of the time-dependent bilirubin production rate. KEMAX (hour.sup.−1) is the maximum stimulation of bilirubin elimination rate, T50 (hour) the time at which Kelim(t) equals 50% of KEMAX and H (dimensionless) is the Hill coefficient determining the steepness of the time-dependent rate of bilirubin elimination. The initial condition of bilirubin at time 0 h is estimated with the parameter BILI0 (μmol.Math.L.sup.−1), as commonly done in pharmacometric modelling [2]. Inter-individual variability (IIV) is estimated on Kin.sub.Base, BILI0, KEMAX, T50, K.sub.PNA and KP. The data does not support estimation of IIV on H and thus is fixed to 0 for H. For the population approach, log-normal parameter distributions are assumed, and a mixed error model, combining additive and proportional components, is used to reflect residual variability, including measurement errors in acquired bilirubin levels.

[0161] Covariates

[0162] The influence of a covariate, i.e. factors that influence bilirubin changes on a specific model parameter can be tested utilizing a standard stepwise forward selection—backward deletion approach as known from the state of the art.

[0163] The covariate—model parameter relationships/dependencies for a categorical covariate COV.sub.cat with two possible conditions (0 or 1) is P=P.sub.0.Math.(1+θ .Math.COV.sub.cat), and for a continuous covariate COV.sub.cont the covariate—model parameter relationships/dependencies is P=P.sub.0.Math.(1+θ.Math.(COV.sub.cont−median(COV.sub.cont))) with P.sub.0 the typical value of the model parameter P, i.e. P.sub.0 is the population model parameter, for a neonate with a covariate equal to the reference value (COV.sub.cat=0 or COV.sub.cont=median(COV.sub.cont) and θ the estimated parameter describing the magnitude of the covariate-model parameter relationships.

[0164] The covariates can also be used to account for a so-called population effect (neonates who received phototherapy versus neonates who did not receive phototherapy).

[0165] For this purpose a mixture model can be evaluated. The mixture model allows the use of multimodal distribution of model parameters in case of different subpopulations, and thus assumes that one fraction of the population has one set of population model parameters while the remaining fraction has another set of population model parameters, depending on the value of the associated covariate.

[0166] Such a population effect (neonates who received phototherapy versus those who did not receive phototherapy) can be found on K.sub.PNA.

[0167] Therefore, the model parameter K.sub.PNA has two associated population model parameters depending on the value of the associated covariate (here the categorical covariate comprising the information whether the neonate has received phototherapy).

[0168] None of the available covariates is able to replace or compensate for the population effect on K.sub.PNA. A mixture model on K.sub.PNA can therefore be used in the model function, assuming that 50% of neonates have the typical value of K.sub.PNA equal to K.sub.PNA0, while the other 50% has the typical value K.sub.PNA1. The fraction of individuals belonging to each subpopulation is fixed to 50%. K.sub.PNA0 and K.sub.PNA1 can be estimated. The major part of the inter-individual variability (IIV) on K.sub.PNA is explained by covariates and the mixture model and is thus fixed to a low value of 5%.

[0169] Individual predictions of time-dependent bilirubin production rates, Kprod, and bilirubin elimination rates, Kelim, for both neonates who received phototherapy treatment and those who did not receive phototherapy are plotted in FIG. 3. A separation between the two populations for the time-dependent bilirubin production rate Kprod can be clearly distinguished (c.f. FIG. 3A), while there is no difference for the time-dependent bilirubin elimination rate Kelim (c.f. FIG. 3B). Indeed, K.sub.PNA is higher in the group without phototherapy leading to a steeper decrease in Kprod compared to the group with phototherapy.

[0170] The other covariates do not require taking into account the population effect.

[0171] The model parameter Kin.sub.Base is higher in neonates born by vaginal delivery leading to higher bilirubin values compared to those born by Caesarean sections (FIG. 6A). Neonates with low birth weight having a higher baseline bilirubin (BILI0) (FIG. 6D). Increased weight loss and birth weight and mother milk feeding are associated with lower values of K.sub.PNA (FIG. 6E), so longer time for Kprod to reach adult values and thus higher bilirubin levels. Mother milk feeding is associated with lower maximum stimulation of bilirubin elimination rate (KEMAX) (FIG. 6C), and thus slower bilirubin elimination. Finally, the effect of phototherapy on bilirubin elimination (KP) is reduced in neonates with respiratory support (FIG. 6F). All these covariate-model parameter effects on the weight changes of a typical neonate are illustrated in FIGS. 6A to 6F.

[0172] In FIG. 2 postnatal bilirubin levels of two scenarios of neonates exhibiting specific covariates are illustrated. As can be seen from the results of 1000 simulations, a first scenario leads (i) to lower bilirubin levels compared to a second scenario (ii). [0173] (i) “best case” scenario of a newborn with a birth weight of 1880 g delivered by Caesarean section, who lost 6% of his birth weight, fed with formula milk, without respiratory support and who did not receive phototherapy; [0174] (ii) (ii) “worst case” scenario of a newborn with a birth weight of 1100 g vaginally delivered, who lost 15% of his birth weight, fed with mother milk, with respiratory support and who received phototherapy at 80 hours.

[0175] Estimates for population model parameters and their IIV from the model function are provided in Table 2. RSE of population model parameters and corresponding IIV values demonstrate acceptable precision of said parameters.

TABLE-US-00001 TABLE 2 Parameter estimates of the final model. RSE RSE estimate IIV IIV Parameter (unit) Estimate (%) (% CV) (%) Kin.sub.Base (μmol/L/hour) 2.8 7 13 20 BILI0 (μmol/L) 15.4 19 34 11 KEMAX (hour.sup.−1) 0.009 18 47 18 T50 (hour) 110 6 24 16 H 8.98 30 0 FIX — K.sub.PNA0 (hour.sup.−1) 0.0099 19 5 FIX — K.sub.PNA1 (hour.sup.−1) 0.022 13 5 FIX — KP (hour.sup.−1) 0.022 13 47 17 KAD (μmol/L/hour) 0.43 30 0 FIX — Vaginal delivery effect on KinBase 0.29 23 — — Weight loss effect on KPNA 0.028 44 — — Birth weight effect on KPNA −0.0002 55 — — Mother milk effect on KPNA −0.26 34 — — Low birth weight effect on BILI0 1.16 35 — — Mother milk effect on KEMAX −0.28 45 — — Respiratory support effect on KP −0.42 24 — — Probability for mixture model 0.5 FIX — — — Residual error: additive 0.099 11 — — Residual error: proportional 3.68 21 — — CV: coefficient of variation; FIX: fixed parameter; IIV: inter-individual variability; RSE: relative standard error.

[0176] The typical baseline bilirubin (BILI0) is estimated at 15.4 μmol.Math.L.sup.−1 in a neonate with a birth weight>2500 g and at 33.26 μmol.Math.L.sup.−1 in a neonate with a birth weight<2500 g. The typical (i.e. the average population parameter) total basal production rate of bilirubin Kin.sub.Base+KAD is estimated at 3.23 μmol.Math.L.sup.−1.Math.hour.sup.−1 in a typical neonate delivered by Caesarean section and at 4.05 μmol.Math.L.sup.−1.Math.hour.sup.−1 in a typical neonate vaginally delivered. The maximum stimulation of bilirubin elimination rate (KEMAX) is estimated to be slowed by one-half (T50) at a typical age of 110 hours. K.sub.PNA0 is estimated to be equal to 2.2 times K.sub.PNA1 (0.022 hour.sup.−1 versus 0.0099 hour.sup.−1). The time-dependent bilirubin elimination rate is increased by 0.022 hour.sup.−1 in neonates without respiratory support and by 0.013 hour.sup.−1 in neonates with respiratory support.

[0177] Prediction and Estimation of Individual Bilirubin Levels According to the Method of Invention

[0178] Two different predictions or estimations can be made with the method according to the invention: [0179] (i) A forecast/projection of individual bilirubin time courses (or profiles) after few days of life, and [0180] (ii) An early prediction of the risk for receiving phototherapy.

[0181] The model function with covariates and associated model parameters is applied to the series of acquired bilirubin levels (particularly acquired from a sample of the neonate within the first two days of life) in order to forecast individual bilirubin levels up to two weeks of life. A maximum a posteriori Bayesian method (MAP) is used to predict or forecast bilirubin levels for a individual neonate with hyperbilirubinemia. The same MAP method can be applied to forecast the bilirubin level after a first phototherapy cycle.

[0182] The maximum a posteriori (MAP) Bayesian method uses a point estimate of the mode of model parameters' posterior density, corresponding to the product of a prior (model function and population parameters' log-normal distributions) and a likelihood (residual error model).

[0183] Individual bilirubin predictions can be graphically compared with an observed bilirubin level. The predictive performance can numerically be evaluated by calculating mean percentage error (MPE) to assess prediction bias and mean absolute percentage error (MAPE) and root mean squared error (RMSE) to estimate prediction accuracy [1].

[0184] The mean percentage error (MPE), mean absolute percentage error (MAPE) and root mean squared error (RMSE) can be calculated to evaluate bias and accuracy of the predictions:

[00004]$\mathrm{MPE}\left(\%\right):\mathrm{MPE}=\frac{1}{n}.Math.\frac{\left(Obs-Pred\right)}{\mathrm{Obs}}\times 100$$\mathrm{MAPE}\left(\%\right):\mathrm{MAPE}=\frac{1}{n}.Math.\frac{.Math.\mathrm{Obs}-P\mathrm{red}.Math.}{Obs}\times 100$$\mathrm{RMSE}\left(g\right):\mathrm{RMSE}=\sqrt{\frac{1}{n}.Math.{\left(\mathrm{Obs}-\mathrm{Pred}\right)}^2}$

[0185] Wherein, n is the number of observations.

[0186] Acquired series of bilirubin levels plotted against forecasted values after the first two days of life show acceptable graphical agreement (FIG. 8A). Precision of forecasted values are acceptable (MAPE [95% CI]: 23.0% [19.8%-26.2%], RMSE=44.4 μmol.Math.L.sup.−1) and bias is limited (MPE [95% CI]: −4.5% [−8.3%-−0.6%]), with an absolute mean error magnitude between observed weights and forecasted weights of only 1.43%, or 33.7 μmol.Math.L.sup.−1 [95% CI: 30.8 μmol.Math.L.sup.−1-36.5 μmol.Math.L.sup.−1]. CI stands for confidence interval.

[0187] The method according to the invention can also be applied to forecast a first bilirubin level measurement just after the first phototherapy cycle. Observed bilirubin level data plotted against the first forecasted bilirubin level after the first phototherapy cycle shows good graphical agreement (see FIG. 8B). Precision of forecasted values are acceptable (MAPE [95% CI]: 18.3% [12.2%-24.5%], RMSE=33.7 μmol.Math.L.sup.−1) and bias is limited (MPE [95% CI]: −8.5% [−16.3%-−0.6%]),

[0188] The second objective of the invention is to early identify aberrant bilirubin levels or trends that may precede treatment with phototherapy. For that, the probability of receiving phototherapy treatment can be linked with predictors using logistic regression.

[0189] Different predictors can be evaluated in univariate and multivariate models: [0190] (i) all the available neonatal and maternal characteristics and [0191] (ii) the predicted bilirubin levels from the method according to the invention based on an individual series of acquired bilirubin levels during the first two days of life.

[0192] The ability of the method according to the invention, including significant predictors, to differentiate neonates who received phototherapy from those who did not receive phototherapy can be evaluated with a ROC (Receiver operating characteristic) curve by calculating the sensitivity and specificity.

[0193] Among all the available individual characteristics, only the binary factor very low birth weight (birth weight<1500 g versus birth weight>1500 g) is significant. Results from the ROC curve show that the logistic regression method is not able to discriminate neonates who received phototherapy from those who did not receive phototherapy (AUC=0.59, sensitivity=23%, specificity=95%).

[0194] Significant predictors in multivariate logistic regression include: K.sub.PNA, Kin.sub.Base, BILI0 and the very low birth weight. Results from the ROC curve (see FIG. 9) show that a cut-off of 0.6 for the results from the logistic regression method is able to discriminate neonates who received phototherapy from those who did not receive phototherapy with a sensitivity of 72% and a specificity of 85% (AUC=0.87).

[0195] Computing Process

[0196] The software NONMEM 7.3 (ICON Development Solutions, Ellicott City, Md., USA) can be used to fit individual bilirubin data to the model function. Estimations can be made by maximizing the likelihood of the data, with the first-order conditional estimation (FOCE) algorithm with interaction. Data handling, graphical representations, numerical criteria calculations, logistic regressions and ROC curves (see FIG. 9) can be performed with an appropriate computer language.

[0197] Longitudinal bilirubin data with a median [minimum-maximum] of 8 [3-15] observations per individual up to a median [minimum-maximum] of 183 hours [29-320] of life are available. Neonates are all moderate to late preterm with a GA of 33.3 weeks [32.0-34.8] and a birth weight of 1880 g [1050-3500]. Among these neonates, 47 received at least one cycle of phototherapy and 41 neonates did not receive any phototherapy. The time of the start of each phototherapy cycle and the duration is known.

[0198] All individuals' series of bilirubin levels are represented in FIG. 5. In the method according to the invention, the time 0 corresponds to the time of birth.

[0199] Individual characteristics of neonates are summarized in Table 1.

TABLE-US-00002 TABLE 1 Summary of individual characteristics. Median [Minimum-Maximum] Characteristics Number of individuals (%) Number of neonates 88 Time of follow up (hours) 183 [29-320] Time of follow up (days) 7.6 [1.2-13.3] Number of bilirubin observations per individual 8 [3-15] Baseline bilirubin (μmol/L) 42 [13-92] Number of cycle of phototherapy: 0 41 (47%) 1 28 (32%) 2 15 (17%) 3  4 (4%) Duration of phototherapy (hours) 24 [8-59] Birth weight (g) 1880 [1050-3500] Low birth weight: birth weight <2500 g: yes 84 (95%) no  4 (5%) Very low birth weight: birth weight <1500 g: yes 13 (15%) no 75 (85%) Maximum weight loss (%) −5.38 [−16.51-0] Gestational age (weeks) 33.3 [32-34.8] Gender: girl 51 (58%) boy 37 (42%) Arterial pH 7.31 [6.88-7.50] Baseline hemoglobin (g/L) 188 [134-255] APGAR at 5 minutes: ≤8 55 (63%) >8 33 (37%) Delivery mode: Caesarean section 57 (64%) Vaginal delivery 31 (36%) Prolonged preterm rupture of membrane: yes 22 (25%) no 66 (75%) Multiple pregnancy: single 55 (63%) twins or triplets 33 (37%) Treatment with amoxicillin or amikacin: yes 20 (23%) no 68 (77%) Type of feeding: exclusively formula milk  9 (10%) mother milk (exclusively or 79 (90%) supplementary) Infection: suspected or proven 21 (24%) none 67 (76%) Infant respiratory distress: yes 44 (50%) no 44 (50%) Respiratory support: yes 40 (45%) no 48 (55%) O2 support: yes 19 (22%) no 68 (78%) Mother's age (years) 31 [20-40] Mother diseases: none 58 (66%) yes (infection, gestational hypertension, 30 (34%) PE, HELLP, DM, GDM) Coombs test: Positive  2 (2%) Negative 77 (88%)

[0200] Data are presented as median [minimum-maximum] or number of subjects (%).

[0201] APGAR 5: Apgar score at 5 minutes; PE: pre-eclampsia; HELLP syndrome: complication of pre-eclampsia; DM: diabetes mellitus; GDM: gestational diabetes mellitus.

[0202] Neonatal jaundice occurs in literally all newborns and, although in the majority of cases this condition is self-limited, a fraction of neonates need to be treated with phototherapy or other medical interventions are required. Failure to promptly identify newborns at risk for developing severe jaundice can lead to life-long neurologic sequelae, including potential reduction in IQ score.

[0203] The method according to the invention is capable of predicting the physiological patterns of bilirubin levels during the first weeks of life in preterm neonates with hyperbilirubinemia. Further, neonatal physiology in the model development with time-dependent decrease in input rate (Kprod) and ontogenic effect on the output rate (Kelim) is taken into account.

[0204] The method according to the invention is not only able to identify late preterm neonates that are at risk for hyperbilirubinemia but can also characterize and project effects of phototherapy sessions on individual bilirubin profiles.

[0205] Bilirubin charts known from the state of the art show clear limits as these are not taking the dynamics of bilirubin changes during the first weeks of life into account and cannot be used to project individual bilirubin profiles.

[0206] In contrast, the method according to the invention accounts for both covariates and time dependent changes of bilirubin level. As such it can be applied to predict not just a reference curve from a neonatal population but also individual bilirubin levels during the first weeks of life of a specific neonate. A decision support tool, particularly a computer program, based on the method according to the invention is expected and designed to [0207] (i) allow for a risk-based approach of neonatal hyperbilirubinemia, thus reducing hospitalization costs, [0208] (ii) support health-care professionals in planning appropriate follow-up strategies for discharged neonates with jaundice, [0209] (iii) facilitate planning of early surgical procedures such as circumcision, and has the potential to [0210] (iv) minimize the risk for the need for readmission and longer term neurological sequelae.

[0211] It is noted that the method according to the invention is particularly limited to late preterm neonates with physiological jaundice receiving (or not receiving) phototherapy. As such the method may particularly not be used to project bilirubin levels or the risk for phototherapy in other neonatal populations.

[0212] The method according to the invention is the first method that describes bilirubin levels and kinetics and phototherapy effects in preterm neonates with physiological jaundice during the first weeks of life. A user-friendly online tool that can be used to forecast individual bilirubin levels and phototherapy effects is disclosed as well. Said tool can optimize treatment strategies for neonates with jaundice. A decision support tool that permits neonatologists to quantitatively individualize management of late preterm neonates with jaundice is provided.

REFERENCES

[0213] [1] Sheiner L B, Beal S L. Some suggestions for measuring predictive performance. J Pharmacokinet Biopharm 1981; 9(4):503-12. [0214] [2] Dansirikul C, Silber H E, Karlsson M O. Approaches to handling pharmacodynamic baseline responses. Journal of pharmacokinetics and pharmacodynamics 2008; 35(3):269-83. doi: 10.1007/s10928-008-9088-2.# [0215] [3] Berk et al., Studies of bilirubin kinetics in normal adults, J Clin Invest. 1969