Defining, Evaluating, and Removing Bias Induced by Linear Imputation in Longitudinal Clinical Trials with MNAR Missing Data
Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[ Y ] = X β, leads to the defin...
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| Published in | Journal of biopharmaceutical statistics Vol. 21; no. 2; pp. 226 - 251 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
England
Taylor & Francis Group
01.03.2011
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1054-3406 1520-5711 1520-5711 |
| DOI | 10.1080/10543406.2011.550097 |
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| Abstract | Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[
Y
] = X
β, leads to the definition of the primary parameter β = (X′X)
−1
X′E[
Y
], and the definition of linear secondary parameters of the form θ = L
β = L(X′X)
−1
X′E[
Y
], including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[
Y
], which raises the questions: What is E[
Y
] when some elements of the incomplete random vector
Y
are not observed and MNAR, or when such a
Y
is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[
Y
] in this context that leads directly to definitions of β,
,
, and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial. |
|---|---|
| AbstractList | Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[Y] = Xβ, leads to the definition of the primary parameter ..., and the definition of linear secondary parameters of the form ..., including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[Y], which raises the questions: What is E[Y] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[Y] in this context that leads directly to definitions of β, ..., ..., and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial. (ProQuest: ... denotes formulae/symbols omitted.) Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[Y] = Xβ, leads to the definition of the primary parameter β = (X'X)(-1)X'E[Y], and the definition of linear secondary parameters of the form θ = Lβ = L(X'X)(-1)X'E[Y], including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[Y], which raises the questions: What is E[Y] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[Y] in this context that leads directly to definitions of β, Bias(β) = E[β] - β, Bias(θ) = E[θ] - Lβ, and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial.Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[Y] = Xβ, leads to the definition of the primary parameter β = (X'X)(-1)X'E[Y], and the definition of linear secondary parameters of the form θ = Lβ = L(X'X)(-1)X'E[Y], including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[Y], which raises the questions: What is E[Y] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[Y] in this context that leads directly to definitions of β, Bias(β) = E[β] - β, Bias(θ) = E[θ] - Lβ, and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial. Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[Y] = Xβ, leads to the definition of the primary parameter β = (X'X)(-1)X'E[Y], and the definition of linear secondary parameters of the form θ = Lβ = L(X'X)(-1)X'E[Y], including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[Y], which raises the questions: What is E[Y] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[Y] in this context that leads directly to definitions of β, Bias(β) = E[β] - β, Bias(θ) = E[θ] - Lβ, and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial. Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[Y]=X beta , leads to the definition of the primary parameter beta =(X'X)-1X'E[Y], and the definition of linear secondary parameters of the form [thetas]=L beta =L(X'X)-1X'E[ Y], including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[Y], which raises the questions: What is E[Y] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[Y] in this context that leads directly to definitions of beta , [image omitted], [image omitted], and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial. Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of “biased data”, which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[Y] = Xβ, leads to the definition of the primary parameter β = (X′X)−1X′E[Y], and the definition of linear secondary parameters of the form θ = Lβ = L(X′X)−1X′E[Y], including for example, a parameter representing a “treatment effect”. These parameters depend explicitly on E[Y], which raises the questions: what is E[Y] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is “completed” via imputation? We develop a rigorous, readily interpretable definition of E[Y] in this context that leads directly to definitions of β,Bias(β^)=E[β^]−β,Bias(θ^)=E[θ^ ]−Lβ, and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include “Last Observation Carried Forward” (LOCF) and “Baseline Observation Carried Forward” (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical, but very realistic longitudinal analgesic clinical trial. Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased estimators and tests of corrupted hypotheses. In a full rank linear model analysis the model equation, E[ Y ] = X β, leads to the definition of the primary parameter β = (X′X) −1 X′E[ Y ], and the definition of linear secondary parameters of the form θ = L β = L(X′X) −1 X′E[ Y ], including, for example, a parameter representing a "treatment effect." These parameters depend explicitly on E[ Y ], which raises the questions: What is E[ Y ] when some elements of the incomplete random vector Y are not observed and MNAR, or when such a Y is "completed" via imputation? We develop a rigorous, readily interpretable definition of E[ Y ] in this context that leads directly to definitions of β, , , and the extent of hypothesis corruption. These definitions provide a basis for evaluating, comparing, and removing biases induced by various linear imputation methods for MNAR incomplete data from longitudinal clinical trials. Linear imputation methods use earlier data from a subject to impute values for post-dropout missing values and include "Last Observation Carried Forward" (LOCF) and "Baseline Observation Carried Forward" (BOCF), among others. We illustrate the methods of evaluating, comparing, and removing biases and the effects of testing corresponding corrupted hypotheses via a hypothetical but very realistic longitudinal analgesic clinical trial. |
| Author | Helms, Ronald W. Helms, Russell W. Helms, Mary W. Reece, Laura Helms |
| AuthorAffiliation | b Department of Biostatistics, University of North Carolina a Rho, Inc., Chapel Hill |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/21390998$$D View this record in MEDLINE/PubMed |
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| Snippet | Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of "biased data," which leads to biased... Missing not at random (MNAR) post-dropout missing data from a longitudinal clinical trial result in the collection of “biased data”, which leads to biased... |
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| SubjectTerms | Algorithms Bias BOCF Clinical trial Clinical trials Clinical Trials as Topic Collection Computer Simulation Corrupted hypothesis Data analysis Data Interpretation, Statistical Dropout Estimation bias Estimators Humans Hypotheses Imputation Linear equations LOCF Longitudinal Longitudinal Studies MAR Mathematical analysis Mathematical models Medical statistics Missing at random Missing data Missing not at random MNAR Models, Statistical Parameter definition Parameter estimation Patient Dropouts Statistics Vectors (mathematics) |
| Title | Defining, Evaluating, and Removing Bias Induced by Linear Imputation in Longitudinal Clinical Trials with MNAR Missing Data |
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