Safety Pharmacology Society Webinar:

Pharmacokinetics and Statistics

Pharmacokinetics Characterization of drug properties

– Cmax, Tmax, half-life, AUC, etc. – Responsible groups may be known as PKDM,

ADME, or simply PK – Exposure can be expressed in terms of weight/vol

(ng/mL), or molarity (µM) – Plasma protein binding will impact the free

concentration In vitro assays are often devoid of protein and therefore

considered 100% free

Toxicokinetics ICH definition: ‘...the generation of

pharmacokinetic data, either as an integral component in the conduct of non-clinical toxicity studies or in specially designed supportive studies, to assess systemic exposure’

Required for determination of how exposure is related to treatment effects: PK/PD

Some definitions Oral bioavailability (F) = the fraction of the

administered oral dose which reaches the systemic circulation. – Modifiers: absorption and first-pass extraction. – Absorption depends on solubility and permeability

may be reduced by the action of efflux transporters, such as P glycoprotein,

– First-pass extraction altered by metabolism in the gut wall and/or liver as well as elimination in the bile

Definitions II Plasma half-life (t1/2)

– Influenced largely by two factors: volume of distribution (V) and clearance (CL) Distribution is the reversible movement of drug between

plasma and tissues. – Dependent on ionization and lipophilicity

Clearance is the sum of all mechanisms – hepatic metabolism, biliary secretion, renal filtration, renal

metabolism, etc.

Distribution and Elimination

Hysteresis – Timing is Everything Loops indicate a disconnect

between exposure and effect.

– tolerance, distributional delay, feedback regulation, input and output rate changes, agonistic or antagonistic active metabolites, uptake into active site, slow receptor kinetics, delayed or modified activity, etc.

330

340

350

360

370

380

390

400

410

250255260265270275280285290295300

0 5000 10000 15000 20000

QTc

B (N

HP) (

mSe

c)

QTc

F (d

og) (

mse

c)

Exposure (ng/mL)

Moxifloxacin Hysteresis

Dog (100 mg/kg)

NHP (175 mg/kg)

Louizos, Christopher, et al. "Understanding the Hysteresis Loop Conundrum in Pharmacokinetic/Pharmacodynamic Relationships." Journal of Pharmacy & Pharmaceutical Sciences 17.1 (2014): 34-91.

Toxicokinetic variables Species, gender, age, inter-animal variability,

presence of other drugs, duration of dosing, food effects, etc. – Rats clear nicardipine faster than other species – Females sometimes have higher exposures than

males – Exposures can be extrapolated from other

studies, but beware of assumptions

TK sampling Options I Collect samples from animals during study

– Most relevant: Target animal at target time – Most disruptive: collection will likely disturb functional

parameters – Automated sampling (now) or analysis (future) may support

Collect from animals used after study complete – Uses same animals (but at a different time) – Requires additional time (can limit to single dose)

TK sampling Options II Collect from parallel group

– Different animals, but in the same environment/facility (could be same formulation)

– Can save time, requires additional compound Rely on PK from separate study

– Requires faith in consistent behavior of the drug

TK dilemmas SP studies typically are single dose. What if

exposure increases with repeated dosing? Should you target the expected higher exposure, or stick with day one?

What is the impact of emesis on exposure in the preferred Latin-square crossover design? Should animals be grouped by dose or exposure?

Statistics Like a drunk with a lamp post, statistics

should be used for support, not illumination – Vin Scully

Facts are stubborn, but statistics are more pliable – Mark Twain

Statistical considerations Safety pharmacology traditionally targets single dose effects

which permits some useful study designs Cross over design allows testing all animals with multiple

doses, including vehicle. Treatment group differences are minimized to improve the sensitivity to detect treatment effects.

By measuring all treatments on the same day, the impact of minor procedure or process changes is minimized.

Study power tradeoffs Power: The likelihood that a study will detect a

statistically significant change in a specific variable More animals on study will improve statistical

sensitivity, with clear monetary costs – How much sensitivity are you willing to pay for?

Robust design will ameliorate the risk of incidental loss of animals or data

– A big study is expensive, but less so than 2 studies – Development timing is rarely blessed with extra time

Ramifications of ‘Low Power’ or ‘Underpowered’

Underpowered studies waste resources as they lack the power needed to reject the null hypothesis.

If the aim is to test a null-hypothesis, conducting an underpowered study will almost certainly be a waste of time in the sense that the outcome will likely be statistically nonsignificant and therefore inconclusive.

As nonsignificant results are sometimes wrongly interpreted as evidence of no effect, low-powered studies can also misdirect further research on a topic.

Ramifications of ‘High Power’ or ‘Overpowered’ studies In an overpowered study everything is statistically

significant. For example, any study with more than 1,000 observations will be more than capable of detecting essentially trivial effects.

Being highly powered, such studies are apt to yield statistically significant results that may be essentially meaningless.

Unnecessary waste of resources (animals, materials, money, etc).

Dilemma: BOTH Over and Under Powered Some parameters are pretty tight (QRS)

while other are notoriously variable (HR) The same study may be powered to detect

very small (arguably trivial) changes in one variable and at the same time not be able to determine if large changes in another variable are treatment related

Prospective Statistical Power Prospective statistical power is the desired/anticipated power for a

future study and is typically used to estimate the sample size required for a future study

Prior to conducting an experiment: - Establish a desired threshold for statistical significance (e.g., α = 0.05) - Identify the power desired for the experiment (e.g., 80%) - Identify the effect size that is scientifically meaningful - Obtain an estimate of the variability for measured parameter - Identify the statistical methods that will be employed to analyze the data - Compute the sample size required

Retrospective Statistical Power Retrospective statistical power is the power of the

actual study based on the observed data – What was the power of this SPECIFIC study?

After conducting the experiment compute the actual power using:

– the observed effect size – the observed variability – the observed sample size – the statistical methods employed on the data

Example of Retrospective Statistical Power Analysis

From: Ewart, L., Milne, A., Adkins, D., Benjamin, A., Bialecki, R., Chen, Y., ... & Valentin, J. P. (2013). A multi-site comparison of in vivo safety pharmacology studies conducted to support ICH S7A & B regulatory submissions. Journal of pharmacological and toxicological methods, 68(1), 30-43.

This table shows the change from vehicle that can be detected using group sizes shown, for each parameter with 80% power, assuming the statistical analysis approaches described [a cross site comparison].

Study Design Impact on Statistical Power

21

Group Size

Values PR QRS QT QTc HR

msec msec msec msec Beats/min 4DCO N= 8 Baseline 79 34 258 336 113 Absolute ∆ 2.1 0.5 12.3 10.8 9.3 %∆ 2.3 1.6 5.3 3.9 8.4 Parallel N=3 Baseline 78 31 265 347 105 Absolute ∆ 29 16 157 111 67 %∆ 37.2 52.1 59.3 31.9 63.7 N=5 Absolute ∆ 19 11 104 74 44 %∆ 24.6 34.3 39.1 21.3 41.9 N=10 Absolute ∆ 13 9 71 56 29 %∆ 17.0 27.9 26.9 16.0 27.8

Absolute: Minimum detectable change, %Δ: Detectable % change at 0.8 power

Power Analysis: Contractility

22

Rats Dogs Compound Parameter Units Baseline Absolute Percent Baseline Absolute Percent Itraconazole LVEDP mmHg 7 1 19 15 2 12

dP/dtmax mmHg/sec 8862 781 9 3478 281 8 dP/dtmin mmHg/sec 7125 709 10 3417 173 5 Tau mSec 9 2 24 30 2 9

Atenolol LVEDP mmHg 10 3 27 15 2 16

dP/dtmax mmHg/sec 8320 924 11 3331 566 17 dP/dtmin mmHg/sec 6555 520 8 3336 221 7 Tau mSec 11 3 30 30 4 8

Amrinone LVEDP mmHg 13 4 21 14 2 7

dP/dtmax mmHg/sec 8324 1434 15 3372 225 14 dP/dtmin mmHg/sec 6508 944 11 3247 115 8 Tau mSec 14 3 17 30 2 5

Pimobendan LVEDP mmHg 19 4 19 16 2 13

dP/dtmax mmHg/sec 7682 1103 11 3486 263 8 dP/dtmin mmHg/sec 5756 512 7 3438 229 7 Tau mSec 20 2 11 31 2 7

Absolute: Minimum detectable change, Percent: Detectable % change at 0.8 power

Select Valid Statistical Method to Improve Sensitivity of a Statistical Analysis

There are statistical analysis techniques to be considered to improve the sensitivity of the analysis

Including a baseline covariate Parametric analysis instead of nonparametric analysis Use quantitative response rather than qualitative response

A more sensitive method means more efficient use of N!

Statistical method for data analysis needs to be specified in the design

Last-time-point measurement Repeated Measurement

Analysis of Variance

Analysis of Covariance

Analysis of Variance at each

time point

Analysis of Covariance at

each time point

Repeated Measure

analysis of Covariance

Worse power

Better Power

Worse power

Better Power

Better Power

Dr. Lei Zhou, Amgen

Comparing to Baseline or Comparing to Control

Comparing to placebo control is preferable, – Baseline can be used as a covariate in the statistical model to improve the

sensitivity of the analysis – Group comparison can be performed on change from baseline – Treatment effect being evaluated is as purely as possible

When comparing to baseline is necessary to assess treatment effect given practicality concerns

– Effect being evaluated may be confounded by factors other than treatment – Often not enough pre-dose measurements are available – Sensitivity for tests of treatment effect could be increased if such comparison is

valid – Crossover designs could be considered to remove potential bias when

applicable

24

References Non-clinical models: Validation, study design and statistical

consideration in safety pharmacology. M.K. Pugsley, R. Towart, S. Authier, D.J. Gallacher, M.J. Curtis. Journal of Pharmacological and Toxicological Methods 62, 2010, 1–3.

Cardiovascular safety assessments in the conscious telemetered dog; utilisation of super-intervals to enhance statistical power. Sivarajah, A., Collins, S., Sutton, M. R., Regan, N., West, H., Holbrook, M., et al. Journal of Pharmacological and Toxicological Methods 62(1), 2010,12–19.