Bounded Integer approach to model time-varying SOFA scores from patients with carbapenem resistant infections
Viktor Rognås (1), Mats O Karlsson (1), Leonard Leibovici (2), Yehuda Carmeli (3), George L Daikos (4), Emanuele Durante-Mangoni (5), Mical Paul (6,7), Lena E Friberg (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden, (2) Department of Medicine, Rabin Medical Center, Beilinson Hospital, Petah Tikva, Israel, (3) Sackler Faculty of Medicine, Tel Aviv University, Ramat-Aviv, Israel, (4) First Department of Medicine, Laikon General Hospital, Athens, Greece, (5) Internal Medicine, University of Campania ‘L Vanvitelli’, and AORN dei Colli-Monaldi Hospital, Napoli, Italy, (6) Institute of Infectious Diseases, Rambam Health Care Campus, Haifa, Israel, (7) The Ruth and Bruce Rappaport Faculty of Medicine, Techion – Israel Institute of Technology, Haifa, Israel
Objectives: A Bounded Integer [1,2] modeling approach can be used to model ordered categorical data when the number of categories becomes too cumbersome for a classical ordered categorical modeling approach. The aim was to explore the ability of the Bounded Integer modeling approach to elucidate if colistin exposure had any influence on how SOFA [3] (sequential organ failure assessment) score changed over time. The SOFA score is a composite score used to evaluate organ dysfunction. The score is structured as ordered categorical data with 25 categories, range 0–24, where 0 is considered normal organ function. Previous time-to-event analysis of the AIDA study data [4] indicates that higher SOFA scores correlate with a higher hazard of death.
Methods: The AIDA study contributed clinical data from 406 critically ill patients, ages 17–95 years (median 68 years). Recruited patients had bacterial infections that were carbapenem-resistant (MIC ≥ 2 mg/L), and colistin susceptible (MIC ≤ 2 mg/L). The study evaluated treatment with colistin + meropenem versus colistin alone. Colistin concentration measurements were available from 350 of the patients. SOFA scores were assessed by the study investigators at 4 time-points: onset of disease (before randomization), randomization (day 1), day 7 and day 14.
A Bounded Integer modeling approach was applied: The mean and standard deviation (SD) of a normally distributed latent variable was modeled as a function of predictors of interest, including interindividual random effects (additive for the mean, exponential for the SD). The fractional areas of the estimated distribution within each of 25 intervals given by the 24 quantile function values (1/25 to 24/25) of a standard normal distribution are taken to be the probability of the SOFA score.
Model development was performed using the software NONMEM 7.43 and PsN 4.8.8. For model evaluation and selection, improvements in the objective function value, goodness-of-fit (visual predictive checks, VPC) and reduction in the Pearson residual were used. Parameter estimation was done using a three-step method: A short iterative two-stage step to improve the initial estimates for the random effects, followed by a maximum likelihood estimation through a stochastic-approximation expectation-maximization step and finally an importance sampling step to achieve the likelihood value.
Covariates were explored on the mean parameter using stepwise covariate modeling (forward addition, p<0.05; backward deletion, p<0.01). The tested covariates included average colistin concentration up to 24 and 120 hours (after the first dose after randomization), treatment arm, age, time-varying serum albumin concentration, log-MIC values for meropenem/colistin, as well as time itself to describe disease progression.
Results: The typical estimated [MP1] [LF2] SOFA score at baseline was 6 (median observed was also 6), with a relative standard error (RSE) of 5%. The SD (z-scale) was estimated as 0.18 (RSE 5%). The mean and SD parameters had an interindividual standard deviation of 0.21 (RSE 6%) and 0.28 (RSE 46%), respectively. Significant covariates, after inclusion of disease progression (decreasing SOFA score with time), were average colistin concentration 24 hours after first dose after randomization (Hazard ratio (HR) in relation to a median patient: 1.05 [1.01 1.08] per mg/L increase), and log-MIC values for meropenem (HR: 1.08 [1.02 1.14] per log increase in MIC). Pearson residuals followed a N(0, 1) distribution for all time points. The VPC showed that the model adequately described the data.
Conclusions: The Bounded Integer modeling approach was successfully applied to SOFA score data. The model could characterize the reduction in SOFA score over 14 days for the typical patient, as well as the variability between patients. The model indicated that high colistin exposure was associated with a high SOFA score. This finding might be confounded by kidney function since both colistin concentration and SOFA score increase with reduced kidney function.
References:
[1] Hu C, Yielding N, Davis HM, et al. Bounded outcome score modeling: application to treating psoriasis with ustekinumab. J Pharmacokinet Pharmacodyn (2011) 38:497-517.
[2] Wellhagen GJ, Kjellsson M, Karlsson MO, A bounded integer model for rating and composite scale data, PAGE 27 (2018) Abstr 8743 [www.page-meeting.org/?abstract=8743] (Accessed February 2019)
[3] Singer M, Deutschman CS, Seymour CW, et al. The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3). JAMA. 2016;315(8):801–810. doi:10.1001/jama.2016.0287
[4] Dickstein Y, Leibovici L, Yahav D, et al. Multicentre open-label randomised controlled trial to compare colistin alone with colistin plus meropenem for the treatment of severe infections caused by carbapenem-resistant gram-negative infections (AIDA): A study protocol. BMJ Open 2016; 6:1–10.
