The Northern Ireland group held a meeting at 4pm on Thursday 30th April 2015 in the Queen’s University of Belfast. The speaker was Finbarr Leacy, MRC Biostatistics Unit, Cambridge, UK.
This lucid talk dealt with missing data, noting that it could lead to substantial bias and misleading inference. It defined missing data and the idea of missing data mechanisms: missing completely at random (MCAR) missing at random (MAR), and missing not at random (MNAR). Finbarr listed the various methods of analysis available: (a) complete case analysis (CCA) (b) weighting procedures (c) imputation methods and (c) model-based procedures.
Suppose we have outcome Y, covariates X and Z where Y and X are subject to missingness and let R be the binary missingness indicator (1=complete, 0=missing). Suppose we wish to estimate Y |X, Z. The simplest method of analysis was CCA which he claimed was unbiased if R ┴ Y |X, Z. It was also unbiased if the data were MCAR and under some MAR and MNAR mechanisms. He reminded the audience that MAR had become the de facto standard. Within the likelihood and Bayesian paradigms the missing data mechanism was ignorable, but that it was non-ignorable under MNAR. Unfortunately, MAR was untestable!! Consequently, sensitivity analyses were required.
He explained that missing data analysis was becoming ever more important to medical trial regulators such as the EMA and FDA and that a number of modern and infuential reports on these issues were now available.
Sensitivity analyses could be conducted under the pattern-mixture framework or the in the selection model framework, where the sensitivity parameters quanti.ed the the degree of departure from MAR. EM and Monte-Carlo EM algorithms could be used to fit these models in the maximum likelihood paradigm while the Bayesian alternative had been comprehensively treated in the longitudinal setting (see Daniels and Hogan, 2008). Although theoretically justified, such approaches became computationally infeasible as the number of incomplete variables increased and Finbarr argued that Multiple imputation was an attractive alternative.
He described two broad categories; Joint Modelling imputation and Fully Conditional Speci.cation (FCS) imputation noting that typical implementations assumed data were MAR. He went on to work through sequential regression imputation in longitudinal studies and reference-based imputation before reaching the fully conditional speci.cation. A perceived drawback of FCS was that the chained equations need not correspond to any true joint model. However, he pointed to recent work by Liu et al. (2014) and Hughes et al. (2014) who had provided sufficient conditions for the asymptotic and finite sample equivalence of these imputation distributions, respectively. He went on to deal with FCS and sensitivity analysis giving a detailed method of analysis and example before concluding the talk by referring to possible extensions beyond the categorical data setting via the Hammersley-Clifford theorem (Hammersley and Clifford, 1971).
The talk was very well received and Mr Michael Stevenson, Queens University Belfast, asked about methods for dealing with missingness in undergraduate examinations involving multiple choice papers. There was some discussion about the procedures currently in use, but no clear conclusion was reached. Finbarr was thanked again for a very illuminating and informative talk.