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 I I
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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 I I I
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 I I
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
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5
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0
GFR
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20
Motivation
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1
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time 5 / 15
CRISIS Cohort I
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
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log(eGFR)
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CRISIS Cohort
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60
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100
Age (in years)
eGFR = 175 ×
SCr 88.4
−1.154
× age−0.203 × 0.742 I(female) × 1.21 I(black) 7 / 15
Clinical Identification of AKI I I
101 patients (5%), at least one AKI, any stage ⇒ a rare event Based on Creatinine observations by comparing I I I I
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RC = (Creatininet − Creatinines )/Creatinines (s < t) AKI was identified by (the AKIN criteria, Mehta et al., 2007) I I I
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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 I
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 I I
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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 I I I I
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
4 3
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
4 3
log(eGFR)
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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
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Years after AKI
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Statistical Modelling I
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 ) 12 / 15
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) I
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
