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Sebastian Ueckert1, Elodie L. Plan1, Kaori Ito2, Mats O. Karlsson1, Brian W. Corrigan2, Andrew C. Hooker1
Improving cognitive testing with IRT and optimal design
1. Pharmacometrics Research Group, Uppsala University, Uppsala, Sweden 2. Global Clinical Pharmacology, Pfizer Inc, Groton, CT, USA
PODE 2013 - POPULATION OPTIMUM DESIGN OF EXPERIMENTS
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ALZHEIMER’S DISEASE • Fatal disease • Most common form of dementia • Prevalence is 13% for age > 65
(US) • Increasing problem in aging
societies
• Cause remains vastly unknown • Only symptomatic treatment • No cure
Why no/few treatments?
Diagnosis
3
Clinical Routine
Observations
MMSE
Clinical Trials
ADAS-cog
ADCS-CGIC
CDR-SB
Alzheimer’s Disease
Fasting Plasma Glucose
Clinical Routine
Clinical Trials
Diabetes
ADAS-cog Score
4
• Cognitive subscale of Alzheimer’s Disease Assessment Scale • Cognitive assessment including broad range of sub-tests e.g.,
?Naming Objects
Commands
Construction
Ideational Praxis
7 June2012
?Orientation
Ability to Speak
Ability to Understand
Remembering Words LAKECLOCKFORESTANIMAL
5 7 8
Rosen et al. 1984
ADAS-cog Score
TASK BASED RATER ASSESSED
ADAS-cog Score Model
𝑦𝑖𝑖𝑖 Response of (category assigned to) subject 𝑖 for item 𝑗 at time 𝑖𝑘 𝑀 Number of test items in ADAS-cog assessment 𝑦�𝑖𝑖 ADAS-cog score
𝑦�𝑖𝑖 ≈�𝑦𝑖𝑖𝑖
𝑀
𝑖=1
Commonly used pharmacometric model:
𝑦�𝑖𝑖 = 𝜃0 + 𝜂0𝑖 + 𝜃1 + 𝜂1𝑖 ⋅ 𝑡𝑖𝑖 + 𝜀𝑖𝑖 𝜂0𝑖 , 𝜂1𝑖 ∼ Normal 0,Ω
𝜀𝑖𝑖 ∼ Normal 0,𝜎
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ADAS-cog IRT Model
From now: consider only data from 1 time point (drop 𝑘 index)
𝐷𝑖 Latent variable “cognitive disability” of patient 𝑖 f𝑖 Response function for test 𝑗
P 𝑦𝑖𝑖 = 𝑥 = f 𝑖 𝑥,𝐷𝑖
𝐷𝑖 ∼ Normal 0,1
Instead of summary score, calculate
𝐷�𝑖 = arg max𝐷
� log f 𝑖 𝑦𝑖 ,𝐷𝑀
𝑖=0
+ log p 𝐷; 0,1
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Item Response Theory
ADAS-cog IRT Model
7
?
7 June 2012
?
LAKE CLOCK FOREST ANIMAL
COGNITIVE DISABILITY
?
ADAS-cog IRT Model Latent variable model:
𝐷𝑖 ∼ Normal 0,1 Response Models:
g 𝜿,𝐷 = 𝜅1 + (𝜅2 − 𝜅1)𝑒𝜅3 𝐷−𝜅4
1 + 𝑒𝜅3 𝐷−𝜅4
𝜿 = 𝜅1, 𝜅2, 𝜅3, 𝜅4
P 𝑦𝑖𝑖 = 1 = g 𝜿𝑖 ,𝐷𝑖 P 𝑦𝑖𝑖 = 𝑙 =
𝑛𝑙
g 𝜿𝑖 ,𝐷𝑖𝑙 1 − g 𝜿𝑖 ,𝐷𝑖
𝑛−𝑙
P 𝑦𝑖𝑖 = 𝑙 =g 𝜿𝑖 ,𝐷𝑖 g 𝜿𝑖 ,𝐷𝑖 + 𝛿𝑙 𝑙−1𝑒−g 𝜿𝑗,𝐷𝑖 −𝛿𝑙
𝑙!
P 𝑦𝑖𝑖 ≥ 𝑙 = g 𝜿𝑖 ,𝐷𝑖 P 𝑦𝑖𝑖 = 𝑙 = P 𝑦𝑖𝑖 ≥ 𝑙 − P 𝑦𝑖𝑖 ≥ 𝑙 + 1
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Binary:
Count (binomial):
Count (generalized Poisson):
Ordered categorical:
Parameter Estimation
• Test specific parameters 𝚱 = (𝜿1, … ,𝜿𝑀)(167 in total) estimated from clinical trial databases
– ADNI: • Observational study with normal, mild cognitively impaired (MCI) and mild AD
subjects • Baseline ADAS-cog data from 819 subjects
– CAMD: • Database with placebo arm data from clinical trials • First visit ADAS-cog data from 6 studies (1832 subjects)
• Estimation: – NONMEM 7.3 beta – LAPLACE method
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Estimated Response Functions
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Item Information
Which test item is most informative with respect to cognitive disability? Calculate item information function:
ℐ𝑖 𝐷𝑖 = −E𝜕2
𝜕𝐷𝑖2log f𝑖 𝑦 𝐷𝑖
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Item Information - Binary Response
g 𝜿𝑖 ,𝐷 = 𝜅𝑖1 + 𝜅𝑖2 − 𝜅𝑖1𝑒𝜅𝑗3 𝐷−𝜅𝑗4
1 + 𝑒𝜅𝑗3 𝐷−𝜅𝑗4
P 𝑦𝑖𝑖 = 1 = g 𝜿𝑖 ,𝐷𝑖 P 𝑦𝑖𝑖 = 0 = 1 − g 𝜿𝑖 ,𝐷𝑖
l 𝜿𝒋,𝐷𝑖 =𝜕𝜕𝐷𝑖2
log g 𝜿𝒋,𝐷𝑖
= −𝜅𝑖32 𝑒𝜅𝑗3 𝐷𝑖−𝜅𝑗4 𝜅𝑖1 − 𝜅𝑖2 𝜅𝑖1 − 𝜅𝑖2𝑒2𝜅𝑗3 𝐷𝑖−𝜅𝑗4
𝑒𝜅𝑗3 𝐷𝑖−𝜅𝑗4 + 12𝜅𝑖1 + 𝜅𝑖2𝑒𝜅𝑗3 𝐷𝑖−𝜅𝑗4
2
h 𝜿𝒋,𝐷𝑖 =𝜕𝜕𝐷𝑖2
log 1 − g 𝜿𝒋,𝐷𝑖
= −𝜅𝑖32 𝑒𝜅𝑗3 𝐷𝑖−𝜅𝑗4 𝜅𝑖1 − 𝜅𝑖2 𝜅𝑖1 + 𝑒2𝜅𝑗3 𝐷𝑖−𝜅𝑗4 − 𝜅𝑖2𝑒2𝜅𝑗3 𝐷𝑖−𝜅𝑗4 − 1
𝑒𝜅𝑗3 𝐷𝑖−𝜅𝑗4 + 12𝜅𝑖1 − 𝑒2𝜅𝑗3 𝐷𝑖−𝜅𝑗4 + 𝜅𝑖2𝑒2𝜅𝑗3 𝐷𝑖−𝜅𝑗4 − 1
2
ℐ𝑖 𝜿𝒋,𝐷𝑖 = −g 𝜿𝒋,𝐷𝑖 l 𝜿𝒋,𝐷𝑖 − 1 − g 𝜿𝒋,𝐷𝑖 h 𝜿𝒋,𝐷𝑖
12
Item Information Functions
13
Population Information
Subjects disability is unknown prior to assessment can’t calculate individual information value calculate expected information for a population to be studied
ℐ�̅� = E ℐ𝑖 𝐷𝑖
= � p 𝐷𝑖; 𝜇pop,𝜎pop2 ℐ𝑖(𝐷𝑖)∞
−∞
𝑑𝐷𝑖
p(𝑥; 𝜇pop,𝜎pop2 )…Probability density function for normal distribution with mean 𝜇pop and variance 𝜎pop2
𝜇pop and 𝜎pop2 are estimated from ADNI data
14
Population Information
15
0
20
40
60
-2 0 2Cognitive Disability
Cou
nt
Population Normal MCI Mild AD
Disability Distribution in ADNI
0
20
40
60
-2 0 2Cognitive Disability
Cou
nt
Item Information
Average Information in Population: 3.81
Population Information
16
Component Ranking
17
MCI Population Component Information %
1 Delayed Word Rec 4.61 29.9 2 Word Recall 3.82 24.8 3 Word Recognition 1.98 12.8 4 Orientation 1.98 12.8 5 Naming Obj&Fing 1.06 6.9
mAD Population Component Information %
1 Orientation 4.92 22.7 2 Word Recall 3.79 17.5 3 Delayed Word Rec 3.26 15.0 4 Naming Obj&Fing 2.83 13.0 5 Number Cancellation 1.48 6.8
87% of total
Adaptive Assessment 𝕋 Set of available cognitive tests 𝑇𝑖 Set of already performed cognitive tests up to step 𝑘 𝑦𝑖 Subject response at step 𝑘 𝐷�𝑖 Disability estimate of subject after step 𝑘 𝜎𝑖2 Associated variance of the estimate Algorithm
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𝐷�0 = 1,𝜎02 = 1,𝑘 = 0 while 𝜎𝑖2 > 𝑡𝑡𝑙 {
𝜏∗ = arg max𝑖∈𝕋\𝑇𝑘
� p 𝑥;𝐷�𝑖 ,𝜎𝑖2 ℐ𝑖(𝑥)∞
−∞
𝑑𝑥
𝑦𝑖 = patient response to τ∗ 𝑇𝑖 = 𝑇𝑖 ∪ 𝜏∗,𝑘 = 𝑘 + 1
𝐷�𝑖 = arg max� log f 𝑖 𝑦𝑖 ,𝐷𝑖
𝑖=0
+ log p 𝐷; 0,1
𝜎𝑖2 =𝑑2
𝑑𝐷2� log f 𝑖 𝑦𝑖 ,𝐷𝑖
𝑖=0
+ log p 𝐷; 0,1
}
AD i.d.e.a.- Alzheimer’s Disease integrated dynamic electronic assessment
Aim: Implement adaptive testing algorithm in a web application Architecture:
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Algorithm Operation
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Benefits of AD i.d.e.a.
Simplified testing procedure Decreased duration Increased sensitivity Assessment history Unique underlying scale
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AD i.d.e.a. Clinical benefits
Routine cognitive testing Improved diagnosis More precise tracking Integration of multiple existing assessments
Algorithm Performance
22
Summary
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Improved Diagnosis &
Clinical Trials
New Treatment Options
Acknowledgements • DDMoRe initiative
• Colleagues in Uppsala, Sweden • Pfizer colleagues in Groton, USA
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The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement n° 115156, resources of which are composed of financial contributions from the European Union's Seventh Framework Programme (FP7/2007-2013) and EFPIA companies’ in kind contribution. The DDMoRe project is also supported by financial contribution from Academic and SME partners. This work does not necessarily represent the view of all DDMoRe partners.
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