Abstract
Modeling non-ignorable dropouts in longitudinal studies to alleviate attrition bias: An
illusion instrumental variable approach
Taehyun Jung, M.S
Department of Biostatistics, Yale University, 2014
Longitudinal clinical trials frequently struggle with attritions which arise before the intended
completion time of the study and it leads to the problems of increased bias and reduced statistical power.
Many of the current and commonly used methods focus on marginal models for describing the mean
response and its time trend, assuming dropouts are ignorable. Although this mechanism is often
reasonable, there are situations where this assumption is unlikely to hold and bring out biased estimates
and standard error. Therefore, in the presence of the non-ignorable dropouts, two broad classes of
methods are introduced; selection model and pattern-mixture model depending on the manner in which
the joint distribution of repeated measures and dropout process is partitioned. However, selection model is
computationally intractable in many cases and difficult to implement using existing statistical software.
Also, the assumption for pattern-mixture models is too strong in many circumstances because it regards
same response distribution for same dropout time.
In this article, we use a joint modeling of longitudinal processes subject to non-ignorable
dropouts. The latent variable, the subject-specific random effects, in the linear mixed-effects model was
also used in the discrete-time hazard models to explain the dependence between the longitudinal outcome
and the discrete-time dropouts. To attenuate attrition bias, we proposed an instrumental variable as an
additional covariate in the model. Several literatures suggest instrumental variables as a remarkable tool
to lessen bias under Missing at Random assumption but little research has been showed in the context of
Missing Not at Random. Inverse Mill’s Ratio, a well-known instrumental variable from econometric
literatures, is introduced to account for the probability that a person will leave. This variable is naturally
derived from the probit model which is one of our dropout processes. We first derive the instrumental
variable and then apply it into the mixed-effect part in the joint model and then estimate with the method
of maximum-likelihood. Using data from SPOON trial, we investigate how much attrition bias can be
alleviated by proposed model compared to others.