What impact do assumptions about missing data have on conclusions? A practical sensitivity analysis for a cancer survival registry.
Within epidemiological and clinical research, missing data are a common issue and often over looked in publications. When the issue of missing observations is addressed it is usually assumed that the missing data are 'missing at random' (MAR). This assumption should be checked for plausibility, however it is untestable, thus inferences should be assessed for robustness to departures from missing at random.



We highlight the method of pattern mixture sensitivity analysis after multiple imputation using colorectal cancer data as an example. We focus on the Dukes' stage variable which has the highest proportion of missing observations. First, we find the probability of being in each Dukes' stage given the MAR imputed dataset. We use these probabilities in a questionnaire to elicit prior beliefs from experts on what they believe the probability would be in the missing data. The questionnaire responses are then used in a Dirichlet draw to create a Bayesian 'missing not at random' (MNAR) prior to impute the missing observations. The model of interest is applied and inferences are compared to those from the MAR imputed data.



The inferences were largely insensitive to departure from MAR. Inferences under MNAR suggested a smaller association between Dukes' stage and death, though the association remained positive and with similarly low p values.



We conclude by discussing the positives and negatives of our method and highlight the importance of making people aware of the need to test the MAR assumption.
Centre for Psychiatry, Queen Mary University of London, Charterhouse Sqaure, London, EC1M 6BQ, UK. m.smuk@qmul.ac.uk.
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0000-0002-1594-1458
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Smuk
Medical Statistics Department, London School of Hygiene and Tropical Medicine, London, UK.|London Hub for Trials Methodology Research, MRC Clinical Trials Unit at UCL, London, UK.
J R
JR
Carpenter
Medical Statistics Department, London School of Hygiene and Tropical Medicine, London, UK.|London Hub for Trials Methodology Research, MRC Clinical Trials Unit at UCL, London, UK.
T P
TP
Morris
D000368:Aged; D000465:Algorithms; D035843:Biomedical Research / Q000379:methods / Q000706:statistics & numerical data*; D015179:Colorectal Neoplasms / Q000175:diagnosis / Q000628:therapy; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D008962:Models, Theoretical; D009367:Neoplasm Staging; D009369:Neoplasms / Q000175:diagnosis / Q000628:therapy*; D017063:Outcome Assessment, Health Care / Q000379:methods / Q000706:statistics & numerical data; D011379:Prognosis; D012042:Registries / Q000706:statistics & numerical data*; D058028:Research Report / Q000592:standards*; D016019:Survival Analysis
Elicitation; Missing at random; Missing data; Missing not at random; Pattern-mixture model; Sensitivity analysis