Introduction: The time course of biomarkers (e.g., acute phase proteins and cytokines) is typically described using days relative to events of interest, without specifying the sample clock time or hours post-event. This limits their use as biomarkers may change rapidly during a single day. Procalcitonin is an acute phase protein biomarker which has been suggested to help diagnosis of infection (concentrations increase within 4 hours [1]). However, concentrations are also increased after non-infective events such as birth [2] and surgery [3] making diagnosis a challenge.
Aim: Investigate strategies to impute missing clock times, using procalcitonin as the motivating example.
Methods: Data: 1275 procalcitonin concentrations were available from 282 non-infected pre-term and term neonates collected as part of patient care following birth [4] with dates but not observation clock times (Scenario 0).
Imputation scenarios: Missing clock times were imputed using a random uniform distribution under three scenarios: 1) multiple observations on the same day were assumed to have a minimum interval between observations of 8 h (Scenario 1A) and 12 h (Scenario 1B); 2) assume procalcitonin concentrations increase during postnatal days 0 – 1 then decrease [2]; 3) standard blood sampling times at the study hospital. Unique datasets (n=100) were created with scenario-specific imputed clock times.
Models: Each scenario was modelled using NONMEM with the same non-linear mixed effects model. A turnover model with first order elimination was used to describe the time course of procalcitonin concentration. The procalcitonin volume of distribution was fixed at 15L/70kg. A one compartment model with a nominal bolus input and first order elimination was used to describe a birth effect stimulus on the production of procalcitonin. Postmenstrual age and total body weight were included as covariates.
Parameter estimation: Scenarios were selected using the NONMEM objective function value compared to Scenario 0 (∆OFV) and evaluated with visual predictive checks. The average and 95% confidence interval of ∆OFV and parameter estimates were calculated for each scenario.
Results: Scenario 3, based on standard sampling practice at the study hospital, was the best imputation strategy with an improved objective function value compared to Scenario 0 (∆OFV: -62.6). Scenario 3 showed a shorter lag time between the birth event and the procalcitonin concentration increase (average: 12.0 h, 95% interval: 9.7 – 14.3 h) compared to other scenarios (averages: 15.3 – 18.7 h).
Figure 1: Visual predictive check (VPC) of model predicted and observed procalcitonin concentration (mcg/L). Scenario 0: without imputation; Scenario 3: standard sampling practice at study hospital. For Scenario 0 the VPC is from the run used for the bootstraps and for Scenario 3 the VPC is for a run associated with a ∆OFV closest to the median ∆OFV. Red lines are observed data and black lines are predicted by the simulation. Solid lines are medians of the observed and predicted values, dashed lines are 5th and 95th percentiles. Shaded areas are 95% confidence intervals for each of the prediction percentiles obtained by simulation.
Conclusion: A methodology for selecting imputation strategies for clock times was developed. This may be applied to other problems where clock times are missing.
References:
- Dandona, P., et al., Procalcitonin increase after endotoxin injection in normal subjects. J Clin Endocrinol Metab, 1994. 79(6): p. 1605-8.
- Chiesa, C., et al., C reactive protein and procalcitonin: reference intervals for preterm and term newborns during the early neonatal period. Clin Chim Acta, 2011. 412(11-12): p. 1053-9.
- D’Souza, S., et al., Procalcitonin and Other Common Biomarkers Do Not Reliably Identify Patients at Risk for Bacterial Infection After Congenital Heart Surgery. PCCM, 2019. 20(3): p. 243-251.
- Fukuzumi, N., et al., Age-specific percentile-based reference curve of serum procalcitonin concentrations in Japanese preterm infants. Scientific reports, 2016. 6(1): p. 1-6.