Transcript Placebo Response - NCSU Bioinformatics Research Center

An Analytic Road Map for
Incomplete Longitudinal Clinical
Trial Data
Craig Mallinckrodt
ICSA
June 4, 2007
Raleigh, NC
Context
Road map ≠ driving directions
 provides info about alternatives
 framework to plan route, doesn’t choose it
Route to valid analyses of incomplete
longitudinal data can be problematic
Many advances in missing data theory and
implementation
We can do better than LOCF
Need framework to plan use of newer methods
Outline
Missing
data mechanisms
Modeling
philosophies
Example
of developing an analytic road map
Example
of implementing an analytic road
map
 Today’s
focus is on missing data. Concepts easily extended to
include modeling of time and correlation
Starting Point
• No universally best method for analyzing
longitudinal data
• This implies analysis must be tailored to the
specific situation at hand
• Consider the desired attributes of the analysis
and the characteristics of the data
Missing Data Mechanisms
• MCAR - missing completely at random
• Conditional on the model, neither observed
or unobserved outcomes are related to
dropout
• MAR - missing at random
• Conditional on the model, observed
outcomes are related to dropout, but
unobserved outcomes are not
• MNAR - missing not at random
• Unobserved outcomes are related to dropout
Missing Data Mechanisms
• MCAR - missing completely at random
• Conditional on independent variables in the
model, neither observed or unobserved
outcomes of the dependent variable are
related to dropout
• MAR - missing at random
• Conditional on the independent variables in
the model, observed outcomes of the
dependent variable are related to dropout,
but unobserved outcomes are not
Consequences
• Missing data mechanism is a characteristic of
the data AND the model
•
•
Differential dropout by treatment indicates covariate
dependence, not mechanism
Mechanism can vary from one outcome to another
• Terms like ignorable missingness and
informative censoring must also consider the
method
• What is ignorable with likelihood-based
analysis is non-ignorable with GEE
Analytic Approaches for Continuous
Outcomes
• MCAR
• ANOVA, GEE
• MAR
• Likelihood-based mixed-effects models (LBMEM), Multiple imputation (MI), Propensity
scoring, Weighted analyses
• MNAR
• Selection models, Pattern mixture models,
Shared parameter models, sensitivity analyses
Note that if missing values are imputed other
assumptions also need to be considered
Modeling Philosophies
• Restrictive modeling
• Inclusive modeling
Restrictive Modeling
• Simple models with few independent
variables
• Often include only the design factors of the
experiment
Inclusive Modeling
• In addition to the design factors of the
experiment, models include auxiliary variables
• Auxiliary variables included to improve
performance of the missing data
procedure – expand the scope of MAR
• baseline covariates
• time varying post-baseline covariates
Rationale For Inclusive Modeling
• MAR: conditional on the dependent and
independent variables in the analysis,
unobserved values of the dependent variable
are independent of dropout
• Hence adding more variables that explain
dropout can make missingness MAR that
would otherwise be MNAR
Inclusive Modeling with LB-MEM
• Add auxiliary variables to analysis model
• Adding baseline covariates is straightforward
• Adding post-baseline time varying covariates
that are also influenced by treatment often
dilute the treatment effect
• Could conduct a multivariate analysis where the
auxiliary variable is a second dependent
variable
Inclusive Modeling with MI
• Include auxiliary variables in the imputation
model
• Typically analyze complete data sets using a
restrictive model, but could use the same
inclusive model to analyze the data
• Similar approaches can be used in propensity
scoring and weighted analyses where a dropout
model is used to develop propensity score bins
or inverse probability of dropout weights,
followed by a second analysis step
Developing An Analytic Road Map:
Example From A Depression Trial
• Confirmatory clinical trial of an antidepressant.
Primary analysis should be simple and
dependable
•
MAR with restrictive modeling as primary
•
Use MAR with inclusive modeling and
MNAR methods as sensitivity analyses
•
Use local influence to investigate impact of
influential patients
Why MAR?
• Data in clinical trials are seldom MCAR because
the observed outcomes typically influence
dropout (lack of efficacy)
• Trials are designed to observe all the relevant
information, which minimizes MNAR data
• Hence in the highly controlled scenario of
clinical trials missing data may be mostly MAR
Why not MNAR?
Rubin (1994): “…, even inferences for the data
parameters generally depend on the posited missingness
mechanism, a fact that typically implies greatly increased
sensitivity of inference…”
Laird (1994): “estimating the unestimable can be
accomplished only by making modeling assumptions,
The consequences of model misspecification will be
more severe in the non-random case.”
Molenberghs, Kenward & Lesaffre (1997): “conclusions
are conditional on the appropriateness of the assumed
model, which in a fundamental sense is not testable.”
Why Restrictive Modeling?
• Historically favor simple models, with impact of
other factors addressed via secondary analyses
• No strong a priori evidence of important
auxiliary variables
• Cost of including unnecessary variables?
• Avoids any potential confounding of auxiliary
variables with design factors (e.g., treatment)
Implementing The Road Map:
Example From A Depression Trial
259 patients, randomized 1:1 ratio to drug and placebo
Response: Change of HAMD17 score from baseline
6 post-baseline visits (Weeks 1,2,3,5,7,9)
Primary objective: test the difference of mean change in
HAMD17 total score between drug and placebo at the
endpoint
Primary analysis: LB-MEM
Primary Analysis: LB-MEM
proc mixed;
class subject treatment time site;
model Y = baseline treatment time site
treatment*time ;
repeated time / sub = subject type = un;
lsmeans treatment*time / cl diff;
run;
This is a full multivariate model, with unstructured modeling
of time and correlation. More parsimonious approaches
may be useful in other scenarios
Treatment contrast 2.17, p = .024
Patient Disposition
Drug
Placebo
Protocol complete
60.9%
64.7%
Adverse event
12.5%
4.3%
5.5%
13.7%
Lack of efficacy
Differential rates, timing, and/or reasons for
dropout do not necessarily distinguish
between MCAR, MAR, MNAR
Inclusive Modeling in MI:
Including
Auxiliary AE Data
Imputation Models
• *Yih = µ +1 Yi1 +…+ h-1 Yi(h-1) + ih
• Yih = µ + 1 Yi1 +…+ h-1 Yi(h-1) + 1 AEi1 +…+ h-1 AEi(h-1) +
ih
• Yih= µ + 1 Yi1 +…+ h-1 Yi(h-1) + 1 AEi1 +…+ h-1 AEi(h-1)
+11 (Yi1 *AEi1 ) + …+i(h-1) (Yi(h-1) * AEi(h-1) ) + ih
Analysis Model
MMRM as previously described
Result
•
MI results were not sensitive to the different
imputation models
Endpoint contrast
MMRM
2.2
MI Y+AE
2.3
MI Y+AE+Y*AE
2.1
•
Including AE data might be important in other
scenarios. Many ways to define AE
MNAR Modeling
•
Implement a selection model
– Had to simplify model: modeled time as linear + quadratic, and
used ar(1) correlation
•
Compare results from assuming MAR, MNAR
•
Also obtain local influence to assess impact
of influential patients on treatment contrasts
and non-random dropout
Selection Model Results
Contrast
(p-value)
MAR
MNAR
2.20
2.18
(0.0179) (0.0177)
Missingness Parameters
0
1
2
Estimate
-2.46
0.11
-0.08
SE
0.27
0.05
0.06
Local Influence: Influential Patients
12
Ci
6
4
#179
#154
#50
2
#6
0
Ci
8
10
#30
0
50
100
150
Patient
200
250
Individual Profiles with Influential
Patients Highlighted
0
# 30
-30
-20
-10
change in HAMD17
-10
-20
-30
change in HAMD17
0
10
Duloxetine
10
placebo
2
4
6
W eeks
8
2
4
6
W eeks
8
Investigating The Influential
Patients
The most influential patient was #30, a drug-treated
patient that had the unusual profile of a big
improvement but dropped out at week 1
This patient was in his/her first MDD episode when
s/he was enrolled
This patient dropped out based on his/her own
decision claiming that the MDD was caused by high
carbon monoxide level in his/her house
This patient was of dubious value for assessing the
efficacy of the drug
Selection Model: Influential
Patients Removed
( 30, 191)
Removed Subjects
MAR
Diff. at endpoint
(p-value)
(6, 30, 50, 154, 179, 191)
MNAR
MAR
MNAR
2.07
(0.0241)
2.07
(0.0237)
2.40
(0.0082)
2.40
(0.0083)
0
-2.22 (0.14)
-2.44 (0.27)
-2.23 (0.15)
-2.47 (0.28)
1
0.05 (0.02)
0.11 (0.05)
-0.05 (0.02)
0.11 (0.06)
Missingness Parameters
2
-0.07 (0.06)
-0.08 (0.06)
Implications
Comforting that no subjects had a huge
influence on results. Impact bigger if it were
a smaller trial
Similar to other depression trials we have
investigated, results not influenced by MNAR
data
We can be confident in the primary result
Discussion
MAR with restrictive modeling was a
reasonable choice for the primary analysis
MAR with inclusive modeling and MNAR was
useful in assessing sensitivity
Sensitivity analyses promote the appropriate
level of confidence in the primary result and
lead us to an alternative analysis in which we
can have the greatest possible confidence
Opinions
• Inclusive modeling has been under utilized
• More research to understand dropout would be
useful
• Did not discuss pros and cons of various ways
to implement inclusive modeling. Use the one
you know? Be careful to not dilute treatment
• The road map for analyses used in the example
data is specific to that scenario and is not
intended to be a general prescription
Conclusions
• No universally best method for analyzing
longitudinal data
• Analysis must be tailored to the specific
situation at hand
• We can do better than LOCF etc.
• Considering the missingness mechanism and
the modeling philosophy provides the framework
in which to choose an appropriate primary
analysis and appropriate sensitivity analyses