Dynamic modelling of kidney function with interventions at acute

Dynamic modelling of kidney function with
interventions at acute kidney injury occurrences
¨ ur Asar
Ozg¨
[email protected]
with Peter J. Diggle, James Ritchie and Philip Kalra
25 March 2014
MRC Conference on Biostatistics, Cambridge
CHICAS
combining
health information,
computation and statistics
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Outline
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Motivation
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CRISIS Cohort
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Clinical Identification of AKI
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Statistical Modelling
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Results
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Discussion
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Motivation
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Chronic kidney disease (CKD) is defined based on
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kidney damage, e.g. increased albuminuria or proteinuria
decreased kidney function, e.g. GFR < 60 mL/min per 1.73m2
Early stages of CKD are
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reversible
mostly asymptomatic
usually detected during the assessment of comorbid conditions
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Mostly gradual decline in kidney function
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If progressive might lead to kidney failure within months
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CKD patients are in risk of abrupt changes in kidney function
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Motivation
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Acute Kidney Injury (AKI): sudden falls in kidney function
(in hours to days)
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Ranges between
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renal impairment due to mild alterations w/o actual damage
complete renal failure
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Common and potentially catastrophic in hospitalised patients
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Mostly associated with diabetes and/or cardivascular diseases
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No specific treatment, treatment is only supportive
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CKD is a risk factor for AKI
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The influence of AKI on long-term kidney function is unknown
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10
?
5
?
0
GFR
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20
Motivation
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1
2
3
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5
time
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CRISIS Cohort
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Chronic Renal Insufficiency Standards Implementation Study
(CRISIS), Salford Royal Hospital, Manchester, UK
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A cohort of CKD patients, staggered entry, irregular follow-up
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2,221 patients, followed between 15 Nov 2000 - 28 Feb 2013
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1,376 (62.0%) were male, 845 (38%) were female
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2,139 (96.3%) were Caucasian, 82 (3.7%) were non-Caucasian
Total amount of 46,149 hospital visits
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40,877 (88.6%) out-patient
5,272 (11.4%) in-patient
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Number of visits: 1 - 195, median of 13
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Total follow-up time: 0 - 10.9, median of 2.6 (in years)
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Baseline age: 20.0 - 94.3, median of 66.9 (in years)
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1
2
log(eGFR)
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4
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CRISIS Cohort
20
40
60
80
100
Age (in years)
eGFR = 175 ×
SCr
88.4
−1.154
× age−0.203 × 0.742 I(female) × 1.21 I(black)
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Clinical Identification of AKI
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101 patients (5%), at least one AKI, any stage ⇒ a rare event
Based on Creatinine observations by comparing
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RC = (Creatininet − Creatinines )/Creatinines (s < t)
AKI was identified by (the AKIN criteria, Mehta et al., 2007)
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most recent OP with first IP
first IP with other IPs
adjacent IPs
two successive OPs taken within 48 hours
stage 1: if 0.5 ≤ RC < 1
stage 2: if 1 ≤ RC < 2
stage 3: if 2 ≤ RC
AKI occuring within 72 hours belong to a single episode
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Clinical Identification of AKI
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Combine stage 1, 2 and 3 into a single stage
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Censor the trajectories at the 2nd AKI
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Omit the observations that belong to the first AKI episode
Total amount of 5,595 hospital visits
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Total follow-up time for
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3,761 (67.2%) belong to pre-AKI
1,834 (32.8%) belong to post-AKI
pre-AKI : 0.003 - 8.3, median of 1.1 (in years)
post-AKI : 0.003 - 6.6, median of 0.3 (in years)
Amongst the 101 patients
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29
12
34
26
(28.7
(11.9
(33.7
(25.7
%)
%)
%)
%)
were censored at 2nd AKI
had RRT (before 2nd AKI)
died (before 2nd AKI and RRT)
were administratively censored
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Clinical Identification of AKI
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log(eGFR)
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3
2
1
log(eGFR)
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Censored at RRT (n2=12)
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Censored at 2nd AKI (n1=29)
−5
0
Years after AKI
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−5
0
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Years after AKI
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Clinical Identification of AKI
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3
log(eGFR)
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2
3
2
1
log(eGFR)
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No 2nd AKI, No RRT, Alive (n5=26)
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Censored by death (n3=34)
−5
0
Years after AKI
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−5
0
5
Years after AKI
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Statistical Modelling
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Based on the preliminary analyses
Yij = Xij α + Ui + Wi (tij ) + Zij
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(1)
Ui : random intercept, ∼ N(0, ω 2 )
Wi (t): non-stationary Gaussian stochastic process
1. Replace Wi (t) by bi tij , (Ui , bi ) ∼ MVN(0, Σ)
2. Brownian motion: cov (W (s), W (t)) = σ 2 min(s, t)
3. Integrated Brownian motion: 2
cov (W (s), W (t)) = σ 2 min2(s,t) max(s, t) − min3(s,t)
4. Integrated Ornstein-Uhlenbeck Process
cov (W (s), W (t)) =
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κ2
2ν 3
2νmin(s, t) + e −νt + e −νs − 1 − e −ν|t−s|
Zij : measurement error, ∼ N(0, τ 2 )
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Results
log(eGFR) = α0 + α1 ∗ tij + α2 ∗ (tij )+ + α3 ∗ (tij − 0.5)+ +
α4 ∗ I(0 ≤ tij < 0.5) + α5 ∗ I(0.5 ≤ tij )+
Ui + Wi (tij ) + Zij (2)
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tij : age at measurement - age at AKI
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(tij − a)+ : 0 if tij ≤ a, tij − a if tij > a
Model with Wi (tij ) as
Random Slope
Brownian Motion
Integrated Ornstein-Uhlenbeck
Integrated Brownian Motion
Max. logLik
-1554.31
-415.44
-415.44
-1108.94
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Results
Parameter
α0
α1
α2
α3
α4
α5
Variable
Intercept
tij
(tij )+
(tij − 0.5)+
I(0 ≤ tij < 0.5)
I(0.5 ≤ tij )
Estimate
3.072
-0.074
0.737
-0.648
-0.245
-0.390
SE
0.067
0.016
0.154
0.184
0.019
0.059
p
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
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Slope(t > 0.5) = 0.014, SE = 0.101
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H0 : Slope(t < 0) - Slope(t > 0.5) = 0, p = 0.386
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Level decrease for t > 0.5: -32.3% (=(exp(-0.390)-1)*100)
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Discussion
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Longer follow-ups after AKI with updated data
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Incorporating survival end-points, with joint models
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Modelling complete cohort
Random change points for
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accelaration before AKI
end of recovery after AKI
Separating AKI stages
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