breathing and death as competing events in critical care...
Transcript of breathing and death as competing events in critical care...
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Unassisted breathing and death as competing events in critical care trials
William Checkley, MD, PhDJohns Hopkins University
November 22, [email protected]
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Objectives
• Jointly model the frequency and timing of
unassisted breathing and death in critical care
trials.
• Characterize differences in the frequency,
timing or both of these two clinical events
between study groups.
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ALI
Unassistedbreathing
Discharge from ICU
Dischargehome
Death
Intermediate morbidity outcomes
(Competing event)
Clinical outcomes in acute lung injury
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Ventilator‐free days score (VFDS)
• Most common definition (at 28 days):
–VFDS = 0: death < 28 days.
–VFDS = (28 ‐ x): number of days without
mechanical ventilation in the first 28 days.
–VFDS = 0: Mechanical ventilation > 28 days.
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“Turn a knob, save a life”
• Ventilation with “traditional” tidal volumes (10‐15 ml/kg) may cause stretch‐induced injury.
• Does ventilation with lower tidal volumes improve clinical outcomes in patients with ALI?
• Mortality was lower for 6 ml/kg vs 12 ml/kg (31% vs 40%; p = 0.007).
• VFDS were greater for 6 ml/kg vs 12 ml/kg (mean 12 vs 10; p = 0.007).
ARDS Network. N Engl J Med 2000;342:1301–1308
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“Dry lungs are happy lungs”
• Fluid restriction may improve lung function but jeopardize extrapulmonary organ perfusion.
• Does fluid management with lower vs higher intravascular pressure improve outcomes?
• 60‐day mortality was 26% in the conservative arm vs 28% in the liberal arm (p = 0.30).
• VFDS were greater in the conservative arm vsliberal arm (mean 14.6 vs 12.1; p < 0.001).
ARDS Network. N Engl J Med 2006;354:2564–2575
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= 2 (p=0.007) = 2.6 (p<0.001)6 ml/kg 12 ml/kg
05
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Conservative Liberal
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What does the VFDS measure?
• Similar differences in VFDS between study
groups in both trials.
• How to interpret the difference in VFDS for
each trial?
• What does a difference of “2” VFDS mean?
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Problems with the VFDS
• Strongly “abnormal” distribution.
• Cannot be modeled with any parametric
probability distributions.
• Relies on non‐parametric methods or central‐
limit theorem approximations for analysis.
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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
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Ventilator-free days score
Cou
ntVentilator‐free days score
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Problems with the VFDS
• A difference in VFDS may be due to a lower
mortality and/or more days free of ventilation.
• The word “days” is confusing: cannot be used
to interpret differences in VFDS.
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Survival analysis for multiple events
• Standard methods in survival analysis can only accommodate one type of clinical event.
• Subjects without the event are censored at time of last follow‐up.
• Non‐informative censoring = censored subjects develop the event at the same rate if followed longer. Untenable for critical care outcomes.
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Survival analysis for multiple events
• Censoring at time of death when unassisted
breathing is the event of interest:
– Violates assumption of survival analysis.
– Doesn’t describe realities of critical care outcomes.
– Limited view of complexities of competing events.
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Competing risks
• Modeling strategy that allows multiple,
competing events for time‐to‐event data.
• Competing events:
– Hinder the observation of the primary event.
– Alter the probability of occurrence of the primary
event.
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Competing risks
• Well‐implemented statistical methods for
“classical” competing risks.
• These methods assume that the rate of events
between two groups is proportional over time.
• Therefore, cannot characterize differences in the
“timing” of events (sustained, early, late, none?).
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ALI
Unassistedbreathing
Dischargehome
Death
Competing events of UAB vs death
Event of interest (
Competing event (1‐)
Checkley et al. Epidemiology 2010;21: 557–565.
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Mixture models
• The mixture means a combination of probability
distributions.
• In our application, the mixture model consists of:
– A mixture probability (summary of the frequency
of each competing event)
– Parametric survival distribution (summary of the
times of each competing event).
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Generalized gamma distribution
• 3 parameters: location (), scale () and shape
().
• Probability density function:
fGG(t) = [‐2(e‐t)]exp[‐‐2(e‐t) ]||t(‐2)
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Cumulative incidence function (CIF)
• Cumulative percentage of subjects who develop an
event over a specified time period.
• For 1 event, CIF = 1 – Kaplan‐Meier.
• For competing events:
– CIF ≠ 1 – Kaplan Meier (subdistribution CIF).
– Asymptote is the overall frequency for that event.
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Days after randomization
Cum
ulat
ive
inci
denc
e fu
nctio
n
0.0
0.5
1.0
0 100 200 300 400
exposed 0.6
1 exposed 0.4unexposed 0.69
1 unexposed 0.31
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Ratio of cumulative incidences (RCI)
• Relative change in the cumulative percentage of
subjects who achieve UAB by day “t”.
• At any given time, the RCI of UAB of A to B:
– Favors A if RCI > 1
– Favors B if RCI < 1
• Asymptote of the RCI of UAB is the relative risk.
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RCI of UAB: interpretation
• On day 5, the RCI of UAB of treatment A to B
was 1.20 (95% CI 1.05 – 1.45).
• The percentage of ventilated patients who
achieved UAB in treatment A on day 5 was
20% greater than that in treatment B.
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Types of censoring
• Right‐censoring for UAB or death = participant
did not achieve UAB (or discharge) nor death.
• Interval‐censoring for UAB = exact day of UAB
unknown but occurred between day 28 and
day of discharge alive with UAB.
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ALI
? ?
?
Right‐censoring
Day unknown Day unknown
Day unknown
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ALI
? Dischargehome
Interval‐censoring
Day unknown Day known
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Mixture model for competing risks
• Two generalized gamma distributions to model the times‐to‐UAB and times‐to‐death.
• The mixing probabilities are the overall frequencies of UAB () and death (1 – ).
f(t) + (1 – )g(t)
f(t) ~ fGG(t; f, ff)
g(t) ~ fGG(t; g, gg)
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Mixture model for competing risks
• f(t) = density function for times‐to‐UAB.
• F(t) = survival function for times‐to‐UAB.
• CIF of UAB = [1 – F(t)]
1 [1 – F1(t)]
0 [1 – F0(t)]• RCI of UAB =
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Statistical inference
• Maximum likelihood estimation of 14 parameters.
– 7 parameters for each study group:
– 3 for times‐to‐UAB (f, ff), 3 for times‐to‐death (g, gg), and 1 for the mixing probability ().
• 1,000 bootstrap replicates to obtain 95% CI.
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Tidal volume trial
Days after randomization
%
12 ml/kg, Unassisted breathing6 ml/kg , Unassisted breathing12 ml/kg, Death6 ml/kg, Death
0
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0
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Days after randomization
%
0 15 30 45 60 75 90
12 ml/kg, Unassisted breathing6 ml/kg , Unassisted breathing12 ml/kg, Death6 ml/kg, Death
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Assisted breathing
Death
Unassisted breathing
Tidal volume trial
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Days after randomization
5 10 15 20 25
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RC
I of u
nass
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d br
eath
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of th
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ml/k
g to
12
ml/k
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gyFavors 6 m
l/kg strategyFavors 12 m
l/kg strategyTidal volume trial
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Results: tidal volume trial
• On average, the cumulative incidence of UAB
was 20% greater for 6 ml/kg than for 12 ml/kg.
• RCI of UAB was not different from the overall
RR of UAB (p=0.477).
• Differences in times‐to‐UAB between
treatments was small.
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Fluid management trial
Days after randomization
%
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Liberal, Unassisted breathingConservative , Unassisted breathingLiberal, DeathConservative, Death
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Days after randomization
%
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Assisted breathing
Death
Unassisted breathing
Fluid management trial
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Days after randomization
5 10 15 20 25
4/5
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5/4
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2/1
RC
I of u
nass
iste
d br
eath
ing
of th
e co
nser
vativ
e to
libe
ral s
trate
gyFavors Conservative strategy
Favors Liberal strategyFluid management trial
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Results: fluid management trial
• Shortly after randomization, cumulative incidence of UAB was 50% greater in the conservative strategy.
• RCI of UAB was statistically greater than RR of UAB in the first 12 days (p<0.001).
• Patients in the conservative strategy achieved UAB earlier than patients in the liberal strategy.
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Overall results
• Difference of “2” VFDS was different in both trials.
• Tidal volume trial: VFDS difference was due to a
difference in mortality and not due to UAB.
• Fluid management trial: VFDS difference was due
to earlier UAB and not due to mortality.
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Advantages of our mixture model
• Fully parametric
• Standard methods to estimate parameters
• Easily accommodates R/L/interval censoring
• Covariates in the form of a regression
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Advantages of our mixture model
• Free from proportionality of hazards.
• Complete description of the hazard function.
• We can calculate relative times.
• We can decompose the frequency and timing of events and interpret them separately.
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Acknowledgements
• Roy Brower, MD
• Alvaro Muñoz, PhD
• ARDS Network Investigators