05 - Handling Limit of Detection Values for Sepsis Biomarkers in Neonates

Background:
C-reactive protein (CRP) and procalcitonin (PCT) are commonly used sepsis biomarkers, though few studies have shown comparisons of these biomarkers in very-low birthweight (VLBW) infants. It is essential to compare these to determine what may be a better biomarker for sepsis diagnosis. Our study includes infant data from two neonatal intensive care units in Tennessee. One study site did not report measures of CRP and PCT below a limit of detection (LOD), or clinical cut-off. Concentrations below the LOD, deemed left-censored observations, can have large effects on the distribution of the data. We examined the data for neonates at their first sample date, day 0, and discovered roughly 24% of the day 0 CRP values were at or below the LOD of 5.0 mg/L , and 3% of the day 0 PCT values were at or below the LOD of 0.10 ng/mL.

Methods:
Multiple approaches were considered for handling left-censored values. Simple substitution methods such as replacing values at or below the LOD with LOD/2 and LOD/√2 were examined. Regression on order statistics (ROS), maximum likelihood estimation (MLE), and Kaplan-Meier estimation (KM), are computational methods investigated to estimate the mean and standard deviation (SD) of the CRP and PCT values. The ROS method was used for further analyses in determining the effect of LOD on summary statistics, correlation, and regression. ROS functionality was utilized from the NADA package in R and was conducted for the site that had censored values, further splitting by study year to adjust for any potential measurement differences. Censored values were imputed with ROS estimates and combined with the detected values to get a set of observations with no censoring. Linear regression model performance was measured with Akaike's information criteria (AIC) and deviance. AIC evaluates how well the model fits the data by estimating the information lost by the complexity of the model. Deviance is another goodness of fit estimate that determines how much variation in the data the model accounts for. Lower AIC and deviance indicates a better fit. All analyses were conducted with R, version 4.1.1.

Results:
The effect of imputation using the ROS method was compared with using the LOD and LOD/√2 to replace left-censored values. Before performing ROS on the censored data, the overall mean (SD) for pairwise complete observations of CRP and PCT values were 16.7 (27.9) and 8.5 (16.4), respectively. After performing ROS, the overall mean (SD) for CRP and PCT were 15.4 (26.9) and 8.5 (16.4), respectively. As expected, shrinkage of the mean was observed. Linear regression was used to model the association between CRP and PCT. Values of CRP and PCT were log transformed and a restricted cubic spline with 3 knots was used on CRP to model the non-linear relationship. An interaction term was included between CRP and Site. The ROS model had a smaller AIC and deviance than the LOD/√2 model; 784.2 and 430.0 compared to 788.3 and 438.1, respectively. Furthermore, diagnostic plots of ROS imputation regression model compared to LOD and LOD/√2 regression models indicated the ROS model more closely followed the Normality assumption and showed there are no longer patterns of residuals due to the LOD. The attenuation of the mean and SD of CRP and PCT and improved fit of the linear regression model with ROS compared to LOD/√2 indicates that imputation by ROS for left-censored observations provides information we are missing due to the LOD.

Conclusion :
Left censoring is common in biomarker data, as values below a threshold may be deemed negligible. Nonetheless, to understand how these biomarkers can be used to predict sepsis diagnosis, we need to estimate these values and their distribution. Furthermore, ignoring censoring leads to biased estimates. ROS has provided insight to gauge the true distributions of CRP and PCT values. Similar results will be presented for KM, MLE, and multiple imputation methods.

Limits of detection

Sepsis biomarkers

Neonatology

Regression on order statistics

Left-censoring 

Mid-Level

Knowledge

Women in Statistics and Data Science 2022