# Imputation of missing clock times – application to procalcitonin concentration time course after birth

## TL;DR

This paper introduces a method to estimate missing sample times for biomarker data, using procalcitonin levels in neonates as an example.

## Contribution

The novel contribution is a methodology for imputing missing clock times based on standard sampling practices, improving model accuracy.

## Key findings

- Scenario 3, based on standard hospital sampling, showed the best model fit with a ∆OFV of -62.6.
- Scenario 3 estimated a shorter lag time (12.0 hours) for procalcitonin increase after birth compared to other scenarios.
- The proposed methodology can be applied to other cases with missing clock times in biomarker data.

## Abstract

The time course of biomarkers (e.g., acute phase proteins) are typically described using days relative to events of interest, such as surgery or birth, without specifying the sample time. This limits their use as they may change rapidly during a single day. We investigated strategies to impute missing clock times, using procalcitonin for population modelling as the motivating example. 1275 procalcitonin concentrations from 282 neonates were available with dates but not sample times (Scenario 0). Missing clock times were imputed using a random uniform distribution under three scenarios: (1) minimum sampling intervals (8–12 h); (2) procalcitonin concentrations increase for postnatal days 0–1 then decrease; (3) standard sampling practice at the study hospital. Unique datasets (n = 100) were created with scenario-specific imputed clock times. Procalcitonin was modelled for each scenario using the same non-linear mixed effects model using NONMEM. Scenarios were evaluated by the NONMEM objective function value compared to Scenario 0 (∆OFV) and with visual predictive checks. Scenario 3, based on standard sampling practice at the study hospital, was the best imputation procedure 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 to 14.3 h) compared to other scenarios (averages: 15.3 to 18.7 h). A methodology for selecting imputation strategies for clock times was developed. This may be applied to other problems where clock times are missing.

The online version contains supplementary material available at 10.1007/s10928-025-09965-8.