The nature of sensitivity in monotone missing not at random models

Abstract

Models for incomplete longitudinal data under missingness not at random have gained some popularity. At the same time, cautionary remarks have been issued regarding their sensitivity to often unverifiable modeling assumptions. Consequently, there is evidence for a shift towards using ignorable methodology, supplemented with sensitivity analyses to explore the impact of potential deviations of this assumption in the direction of missingness at random. One such tool is local influence. It is shown that local influence tends to pick up a lot of different anomalies in the data at hand, not just deviations in the MNAR mechanism. This particular behavior is described and insight offered in terms of the non-standard behavior of the likelihood ratio test statistic for MAR missingness versus MNAR missingness within a model of the Diggle and Kenward type.

An Analysis of Selection Models for Incomplete Longitudinal Clinical Trials Due to Dropout: An Application to Multi-centre Trial Data

“…On the other hand, when all the other modeling assumptions can be guaranteed to hold, the use of the LRT, in a well-defined sense, is inappropriate for hypothesis test for MNAR versus MAR [4]. This is certainly true for the model based on Diggle and Kenward [5] who investigated the tests of MAR null hypothesis against MNAR, but it is important to note that their tests are conditional on the alternative model holding.…”

“…In equation (4), the covariates for the measurement process are assumed measured but suppressed for simplicity sake. The form in equation (4) can be discussed as follows: when the missingness process is independent of the responses, i.e.,…”

“…The LRT statistic is used to test the hypothesis of ψ 2 =0 (i.e., MAR), where dropout is no longer dependent upon the current measurement, and similarly to test the hypothesis of ψ 1 =ψ 2 =0 (i.e., MCAR), where dropout is assumed to be at random, the dropout therefore, does not depend upon the outcome altogether. However, the use of the LRT is inappropriate for hypothesis test for MNAR versus MAR when all the other modeling assumptions hold, due to the fact that the behavior of the LRT statistic for the MNAR parameter ψ 2 is non-standard, since the availability of the information on ψ 2 is very rare and interwoven with other features of both measurement and dropout models [4]. In addition Little and Rotnitzky et al [24,25] illustrated that the limiting distribution is a χ 2 mixture with characteristics controlled by the singular information matrix.…”

“…Therefore, for the ψ 2 associated with MNAR model, the score equation creates a quasilinear dependence structure in the system of score equations. This issue is studied in detail by Jansen et al [4], while, in the context of an onychomycosis study [26] have stated that excluding a small amount of measurement error can change drastically the LRT statistic for the MAR null hypothesis, see also for example [8]. In practice, such a distinction (MAR/MNAR) can only be made using untestable modeling assumptions such a distributional form, see, [12].…”

“…It is possible to consider more general models when one assumes random missingness mechanism to be untrue [4]. Examples on work of MNAR modeling include [5].…”