A simultaneous PK/PD model for muscle relaxant using muscle twitch counts Elizabeth A. Sigworth, Matthew S. Shotwell, PhD Department of Biostatistics, Vanderbilt University Medical Center

Background: neuromuscular blockade Vecuronium paralyzes skeletal muscles during surgical procedures Residual muscle blockade can lead to post-surgical complications The ”train-of-four” count monitors patient paralysis through surgery Predictions of future TOF counts can help physicians choose additional doses and safely time the extubation of their patients

Approach: two linked model components A three-compartment pharmacokinetic/ pharmacodynamic (PK/PD) model for changes in drug concentration after bolus administration Diffuse multivariate normal prior defined on each parameter Maximum a posteriori estimates of m3(t) found using numerical gradient descent method m1,m2, and m3: amount of drug (g) in each compartment k10: rate of elimination of drug from the first compartment k12, k21, k13, and k31: rates of drug transfer among compartments

Approach: two linked model components A proportional odds logistic regression model to predict TOF count, conditional on m3(t) Predicted count chosen to minimize an asymmetric loss function Predicted values above the actual count are penalized twice as heavily as errors of the same magnitude below c(t): predicted TOF count at time t m3(t): amount of drug (g) in the third compartment 𝝰k: intercept for category k 𝝱: log odds ratio associated with a one g increase in m3(t)

Validation methods Observational data Simulated data Fit model for each patient on all data prior to the last dose Use parameters to predict TOF counts after last dose Validate by comparing predicted and actual values in terms of magnitude, direction, and distribution of errors Simulate new patient profiles with counts drawn from the multivariate normal distribution defined by observed patient parameters Validate and compare accuracy of different timings for TOF counts (every minute, every ten, every twenty)

Results # Patients # Predicted Accuracy Within one Real data 140 335 40.3% 75.1% One minute 200 489 48.1% 87.8% 10 minutes 477 45.3% 81.8% 20 minutes 460 45.2% 80.9%