Individualized sample timing for PK studies using accessible PD data - PowerPoint PPT Presentation

Individualized sample timing for PK studies using accessible PD data Matthew S. Shotwell, Ph.D. Department of Biostatistics Vanderbilt University School of Medicine Nashville, TN, USA August 29, 2017

Introduction PK Studies ◮ serial blood sampling in individual after dose ◮ goal: estimate change in concentration in body over time ◮ timing of samples affects statistical precision ◮ efficient timing depends on uncertain parameters ◮ can use other information to reduce uncertainty

Muscle relaxants ◮ muscle relaxants (paralytics) often part of general anesthesia ◮ facilitates intubation by relaxing muscles around larynx ◮ prevents involuntary movement during surgery ◮ large initial intubating dose (0.1mg/kg) ◮ small maintenance dose every 30min (0.01mg/kg) ◮ significant PK/PD heterogeneity ◮ requires monitoring

Why study PK? Better understanding of PK heterogeneity may: ◮ facilitate individualized dosing ◮ reduce adverse events (residual paralysis; aspiration) ◮ reduce time in OR and cost

Why optimize PK study design? ◮ maximize information in sample ◮ reduce number of subjects or samples ◮ design task is relatively cheap

Generic optimal design 1. identify optimal sample times a priori 2. sample all subjects at same times

Individualized optimal design ◮ optimize sample times for each subject ◮ need additional information about subject

Monitoring paralysis Muscle paralysis monitored by: ◮ electrical stimulation of ulnar nerve ◮ train of four stimuli (TOF) stimuli ◮ count twitches (TOF count)

Monitoring paralysis

Monitoring paralysis

Generic vs. individualized Generic: 1. identify optimal sample times a priori 2. sample all subjects at same times Individualized: 1. monitor and record twitch counts 2. use twitch counts to individualize sample times 3. sample subject at optimal times

PK/PD model Three compartment “biophase” model: dm 1 = − k 10 m 1 − k 12 m 1 + k 21 m 2 − k 13 m 1 + k 31 m 3 dt dm 2 = k 12 m 1 − k 21 m 2 dt dm 3 = k 13 m 1 − k 31 m 3 dt ◮ m 1 - amount of drug in blood ( c 1 = m 1 /v 1 ) ◮ m 2 - amount of drug in tissues ◮ m 3 - amount of drug in “biophase” or “effect” compartment ◮ aim: estimate kinetic parameters θ = { k 10 , k 12 , k 21 , k 13 , k 31 }

Stat. model: twitch count Proportional odds logistic regression (POLR) model: logit [ Pr ( z il ≤ ν )] = α νi + m 3 ( t il , θ i ) β i ◮ ν = 0 . . . 3 ◮ i - subject index 1 . . . n ◮ l - measurement index 1 . . . q ◮ t il - measurement time ◮ z il - measured twitch count ◮ α νi - intercept ◮ β i - log odds ratio

Examples ◮ TOF counts ◮ Example general vs. individualized strategies

Stat. model: blood concentration Additive normal error model: y ij = γ i m 1 ( t ij , θ i ) + ǫ ij ◮ i - subject index 1 . . . n ◮ j - measurement index 1 . . . m ◮ t ij - measurement time ◮ y ij - measured drug concentration ◮ γ i = 1 /v i ◮ ǫ ij error

Priors π ( θ ) for kinetic parameters ◮ 272 surgical cases from EHR: ◮ fitted to PK/PD and POLR model described above ◮ collection of θ estimates treated as prior for θ This type of prior: ◮ simulates a practical PK study ◮ heterogeneous patients undergoing surgery ◮ variability in dosing (amount and timing) based on clinical need

Sample time optimization Design sample times: ξ = { t 1 , · · · , t m } Information matrix m ∂m 1 ( t j , θ ) ∂m 1 ( t j , θ ) � M ( ξ, θ ) = ∂θ T ∂θ j =1 D-optimality (local) criterion: D ( ξ, θ ) = | M ( ξ, θ ) | ED-optimality (robust) criteria: � ED ( ξ ) = D ( ξ, θ ) π ( θ ) � ED ( ξ | z ) = D ( ξ, θ ) π ( θ | z ) ◮ generic optimal design: ξ g en maximizes ED ( ξ ) ◮ individualized optimal design: ξ i maximizes ED ( ξ | z i )

D-relative efficiency D-relative efficiency: � D ( ξ i , θ i ) � 1 /p R i = D ( ξ g en , θ i ) “How much efficiency is gained in estimating θ i by using individualized optimal design relative to generic optimal design”

Simulation study Simulation steps: 1. simulate subject from prior 2. simulate twitch counts (POLR) 3. compute D-relative efficiency: generic vs. individualized optimal sampling

Results (strategy 1/2) Generic: 1. identify optimal sample times during first dose 2. sample all subjects at same times Individualized: 1. monitor and record twitch counts during first dose 2. use twitch counts to select subject-specific sample times 3. sample subject at optimal times during second dose D-relative efficiency (25th/50th/75th): 0.36/0.49/0.68

Sample times (strategy 1/2)

Results (strategy 2/2) Generic: 1. identify optimal sample times during first dose 2. sample all subjects at same times Individualized: 1. simultaneously sample and monitor during first dose 2. use twitch counts to continuously update/individualize times D-relative efficiency (25th/50th/75th): 1.01/1.02/1.05

Conclusions With regard to a fast-acting paralytic (vecuronium bromide): ◮ first dose most informative ◮ paralytics distribute and eliminate quickly ◮ uncertainty in concentration prior to second dose ◮ individualized optimal designs may be less efficient ◮ efficiency very sensitive to dosing history ◮ gains in D-efficiency for individual PK is < 10%

Future directions ◮ consider ‘local’ (vs. ‘robust’) individualization ◮ ξ i maximizes D ( ξ, ˆ θ i ) ◮ ˆ θ i is estimate using twitch counts ◮ consider efficiency in estimating mixed-effects models

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