Although recent guidelines for dealing with missing data emphasize the need for sensitivity analyses and such analyses have a long history in statistics universal recommendations for conducting and displaying these analyses are AKAP13 scarce. formal sensitivity analyses more comprehensible to practitioners thereby helping them assess the BI-D1870 robustness of the experiment’s conclusions to plausible missingness BI-D1870 mechanisms. We also present a recent example of these enhanced displays in a medical device clinical trial that helped lead to FDA approval. = (denotes a value of an outcome variable for unit and let = (= 1 for units that are missing and = 0 for units with observed = (of the response only predictors of the missingness indicator only and common predictors for BI-D1870 BI-D1870 and do not overlap. The BI-D1870 triplet (to simplify notation in this section. Let the conditional probability distribution of the outcome for each unit be | | ?) for each ? and for all and and are empty and the missingness is independent of the response itself. MAR: | | and for each ?. MNAR: | | ; ?). Note that MNAR implies that there are unobserved variables that are associated with both the response and the missingness indicator such that | | ; ?) but because we failed to measure itself. In practice many studies with missing data either use complete-case analysis (i.e. discard units with partially missing data) which is generally invalid except in very special cases of MCAR mechanism or analyze the data under the MAR assumption. The latter is usually regarded as a more sound approach than the former especially when the MCAR assumption is implausible given observed data. The MAR assumption allows us to avoid specifying a model for missingness mechanism for Bayesian or direct-likelihood inferences assuming ? and θ are distinct [7 8 However although the MCAR assumption may be tested empirically [7 9 the MAR assumption is generally unassessable because it implies comparing | = 0; θ) with | = 1; θ) and the latter can not be estimated from the observed data without making additional assumptions; detailed formalization of this statement is given in [10]. Therefore a sensitivity analysis is desirable to assess the influence of various assumptions about the missingness mechanism. Here focusing on binary outcomes we describe convenient graphical displays that reveal the effects of all possible combinations of the values of missing data in the first arm (‘treatment’ group) and the second arm (‘control’ group) of a two-arm study on various quantities of interest typically on of a study to be particular combinations of missing data values that would change the study’s conclusions as summarized by its subjects randomly divided into a treatment group of size and a control group of size = 1 if subject is treated and 0 if not treated = (∈ {0 1 indicate whether each subject would be a ‘success’ () = 0) under treatment assignment can be expressed as = (= (and and under the chosen model | obtained under models with alternative assumptions. 4 Simulated example with a binary outcome We generated data for = 100 subjects with two predictors representing sex = (= (= (= (was simulated from was simulated uniformly between 18 and 55 (rounding to the nearest integer). The following models were used BI-D1870 to generate the outcomes and the missingness: = (and are empty. As evident from (3c) the missingness mechanism is MNAR. The model for = 40 were randomly assigned to the treatment group and and subjects missing the outcome in each group respectively. Choosing unequal numbers of treated and control units was intentional to illustrate the generality of the idea. Among the respondents the success rates were 0.48 (or 12 out of 25) in the treatment group and 0.21 (or 8 out of 39) in the control group. Figure 2 shows the heat map of for the generated data set calculated according to (2). If we perform a one-sided hypothesis test for the difference in proportions of successes between the completed treatment group and the completed control group the results may also be demonstrated using the ETP-display: Figure 3 shows the heat map of + θ2+ θ3treatment assignment of the treatment effect as it is evident from Figure 4. Among the advantages of the ETP-displays is that they allow the assessment of other.

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