Using pattern mixture modeling to account for informative attrition in the Whitehall II study: A simulation study

Attrition is one potential bias that occurs in longitudinal studies when participants drop out and is informative when the reason for attrition is associated with the study outcome. However, this is impossible to check because the data we need to confirm informative attrition are missing. When data are missing at random (MAR), the probability of missingness not being associated with the missing values conditional on the observed data, one appropriate approach for handling missing data is multiple imputation (MI). However, when attrition results in the data being missing not at random (MNAR), the probability of missing data is associated with the values missing, so we cannot use MI directly. An alternative approach is pattern mixture modeling, which specifies the distribution of the observed data, which we know, and the missing data, which we dont know. We can estimate the missing data models, using observations about the data, and average the estimates of the two models using MI. Many longitudinal clinical trials have a monotone missing pattern (once participants drop out, they do not return), which simplifies MI, so use pattern mixture modeling as a sensitivity analysis. However, in observational studies, data are missing because of nonresponses and attrition, which is a more complex setting for handling attrition compared with clinical trials. For this study, we used data from the Whitehall II study. Data were first collected on over 10,000 civil servants in 1985 and data collection phases are repeated every 2-3 years. Participants complete a health and lifestyle questionnaire and, at alternate , odd-numbered phases, attend a screening clinic. Over 30 years, many epidemiological studies used these data. One study investigated how smoking status at baseline (Phase 5) was associated with a 10-year cognitive decline using a mixed model with random intercept and slope. In these analyses, the authors replaced missing values in non-responders with last observed values. However, participants with reduced cognitive function may be unable to continue participation in the Whitehall II study, which may bias the statistical analysis. Using Stata, we will simulate 1,000 datasets with the same distributions and associations as Whitehall II to perform the statistical analysis described above. First, we will develop a MAR missingness mechanism (conditional on previously observed values) and change cognitive function values to missing. Next, for attrition, we will use a MNAR missingness mechanism (conditional on measurements at the same phase). For both MAR and MNAR missingness mechanisms, we will compare the bias and precision from an analysis of simulated datasets without any missing data with a complete case analysis and an analysis of data imputed using MI; additionally, for the MNAR missingness mechanism, we will use pattern mixture modeling. We will use the twofold fully conditional specification (FCS) algorithm to impute missing values for nonresponders and to average estimates when using pattern mixture modeling. The twofold FCS algorithm imputes each phase sequentially conditional on observed information at adjacent phases, so is a suitable approach for imputing missing values in longitudinal data. The user-written package for this approach, twofold, is available on the Statistical Software Components (SSC) archive. We will present the methods used to perform the study and results from these comparisons.