1. 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

2. 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

3. 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

4. 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)

5. 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)

6. 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%