Abstract
Linear increments (LI) are used to analyse repeated outcome data with missing values. Previously, two LI methods have been proposed, one allowing non‐monotone missingness but not independent measurement error and one allowing independent measurement error but only monotone missingness. In both, it was suggested that the expected increment could depend on current outcome. We show that LI can allow non‐monotone missingness and either independent measurement error of unknown variance or dependence of expected increment on current outcome but not both. A popular alternative to LI is a multivariate normal model ignoring the missingness pattern. This gives consistent estimation when data are normally distributed and missing at random (MAR). We clarify the relation between MAR and the assumptions of LI and show that for continuous outcomes multivariate normal estimators are also consistent under (non‐MAR and non‐normal) assumptions not much stronger than those of LI. Moreover, when missingness is non‐monotone, they are typically more efficient.
Highlights
Many medical studies involve repeated measurement of an outcome over time on a set of patients
The distributional form of DTIC (dDTIC) assumption, combined with the assumed independence of the measurement error and missingness processes, allows the probability of missingness to depend on all past underlying outcomes but not on future underlying outcomes or the outcomes measured with error
Its results demonstrate that methods that estimatet, rather than constraining it to equal its true value, are biased when there is measurement error, and that, when data are non-monotone missing, linear increments (LI)–rMVN imputation and rMVN imputation can be more efficient than LI–LS imputation witht constrained ast D I
Summary
Many medical studies involve repeated measurement of an outcome over time on a set of patients. A&G allowed for multivariate outcomes and non-monotone missing data and explicitly modelled the increment between times t 1 and t as a function of the outcome at time t 1 They treated the special situation where some missing outcomes result from patients dying, and, as an alternative to estimating the compensator, introduced an imputation method (which we call ‘LI-LS imputation’), which is suitable when some patients die. The LI approach was originally conceived as a computationally simple way to handle data that are missing not at random (MNAR), that is, where the probability an outcome is observed can depend on the unobserved data in a particular way It involves the ‘discretetime independent censoring (DTIC)’ assumption that the expected increment between times t 1 and t given the underlying outcomes up to time t 1 and the missingness pattern in the increments up to time t does not depend on that missingness pattern.
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