Transcript Missing values in longitudinal data

To discuss problems with
clinical development team
Kentaro Sakamaki
Yokohama City University
[email protected]
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Two books introduce statistical methods
for understanding problems related with estimands
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Analysis of Longitudinal Data
(Diggle PJ, et al., 2002)
Modern epidemiology
(Rothman KJ, et al., 2008)
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Introduction
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Design considerations
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Exploring longitudinal data
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General linear models
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Parametric models for covariance structure
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Analysis of variance methods
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Generalized linear models for longitudinal data
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Marginal models
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Random effects models
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Transition models
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Likelihood-based methods for categorical data
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Time-dependent covariates
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Missing values in longitudinal data
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Additional topics
BASIC CONCEPTS
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STUDY DESIGN AND CONDUCT
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Modern Epidemiology
Causation and Causal Inference
Measures of Occurrence
Measures of Effect and Measures of Association
Concepts of Interaction
Types of Epidemiologic Studies
Cohort Studies
Case-control Studies
Validity in Epidemiologic Studies
Precision and Statistics in Epidemiologic Studies
Design Strategies to Improve Study Accuracy
Causal Diagrams
DATA ANALYSIS
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Fundamentals of Epidemiologic Data Analysis
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13. Missing values in
longitudinal data
12. Causal Diagrams
• Introduction
• Introduction
• Classification of missing value mechanisms
• Preliminaries for Causal Graphs
• Intermittent missing values and dropouts
• Graphical Models
• Simple solutions and their limitations
• Graphical Representation of Bias and its
Control
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Last observation carried forward
Complete case analysis
• Testing for completely random dropouts
• Generalized estimating equations under a
random missingness mechanism
• Modelling the dropout process
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Selection models
Pattern mixture models
Random effect models
Contrasting assumptions: a graphical
representation
• Some Applications
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Graphical Analysis of Selection Bias
…
Survivor Bias
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• Caveats and Extensions
• Conclusion
• A longitudinal trial of drug therapies for
schizophrenia
• Discussion
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What is new?
• Are Estimands new concepts?
• It is well known in epidemiology.
• Are statistical methods related to Estimands new?
• Diggle PJ, et al ., Analysis of Longitudinal Data, 2002.
• Rothman KJ, et al., Modern epidemiology, 2008.
I think our situation has changed;
Biostatisticians need to know a wide variety of topics.
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Is it important to learn about causal Inference?
https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/
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Effectiveness versus efficacy
(Chapter 9 in “Causal Inference”)
• Some authors refer to the per-protocol effect as the treatment’s “efficacy,” and to the ITT effect
as the treatment’s “effectiveness.”
• A treatment’s “efficacy” closely corresponds to what we have referred to as the average causal
effect of treatment A in an ideal randomized experiment.
• In contrast, a treatment’s “effectiveness” would correspond to the effect of assigning treatment
Z in a setting in which the interventions under study will no be optimally implemented, typically
because a fraction of study subjects will not comply.
• Using this terminology, it is often argued that “effectiveness” is the most realistic measure of a
treatment’s effect because “effectiveness” includes any effects of treatment assignment Z not
mediated through the received treatment A, and already incorporates the fact that people will
not perfectly adhere to the assigned treatment.
• A treatment’s “efficacy,” on the other hand, does not reflect a treatment’s effect in real
conditions.
• Thus one is justified to report the ITT effect as the primary finding from a randomized
experiment not only because it is easy to compute, but also because “effectiveness” is the truly
interesting effect measure.
• Unfortunately, the above argumentation is problematic.
“Effectiveness” is related to “treatment policy” effect
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Effectiveness versus efficacy
(Chapter 9 in “Causal Inference”)
• First, the ITT effect measures the effect of assigned treatment under the
adherence conditions observed in a particular experiment.
• The actual adherence in real life may be different (e.g., participants in a study
may comply better if they are closely monitored), and may actually be affected
by the findings from that particular experiment (e.g., people will be more likely
to comply with a treatment after they learn it works).
• Second, the above argumentation implies that we should refrain from
conducting double-blind randomized clinical trials because, in real life,
both patients and doctors are aware of the received treatment.
• Thus a true “effectiveness” measure should incorporate the effects stemming
from assignment awareness (e.g., behavioral changes) that are eliminated in
double-blind randomized experiments.
• Third, individual patients who are planning to adhere to the treatment
prescribed by their doctors will be more interested in the per-protocol
effect–the “efficacy” of treatment–than in the ITT effect.
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Population
B’
A
A: Target population for treatment
B: Eligible population for Phase III trial
B’: Population in Phase III trial
C: Investigational drug group
D: Standard drug group
B
C
C’: Complier,
Survivor, …
D
Randomization
D’: Complier,
Survivor, …
We should be careful of Generalizability, Comparability,…
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What is problems in estimation?
Baseline characteristics
(Age, sex, performance status, …)
Random allocation
Time dependent factors
(Response, complication,…)
Actual treatment
(E.g. Adherence)
Post treatment
(E.g. treatment switching)
Outcome
・Comparison between treatment groups based on randomization may be valid.
・Is estimation of treatment effect based on randomization also valid?
(Causal diagram can be helpful to answer this question)
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What is “true” value?
Switching treatment because of progression
Investigational drug group
Q
O
L
0
Standard drug group
24
weeks
We know that last observation carried forward method is bad.
However, if we know “true” value ( ), should we use that value?
Is QOL at 24 weeks an adequate endpoint?
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Messages
• There is no clear answer about estimands.
• Clarify the objective of the clinical trial.
• Clarify the problems in the clinical trial.
• Clarify the assumptions of the method for the problem.
• We should have a broad perspective to discuss
estimands.
• Statistical perspective
• Clinical perspective
• Regulator’s perspective
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