Quantile regression for incomplete longitudinal data with selection by death

Quantile regressions are increasingly used to provide population norms for quantitative variables. Indeed, they do not require any Gaussian assumption for the response and allow to characterize its entire distribution through different quantiles. Quantile regressions are especially useful to provide norms of cognitive scores in the elderly that may help general practitioners to identify subjects with unexpectedly low cognitive level in routine examinations. These norms may be estimated from cohorts of elderly using quantile regression for longitudinal data, but this requires to properly account for selection by death, dropout and intermittent missing data. In this work, we extend the weighted estimating equation approach to estimate conditional quantiles in the population currently alive from mortal cohorts with dropout and intermittent missing data. Suitable weight estimation procedures are provided for both monotone and intermittent missing data and under two missing-at-random assumptions, when the observation probability given that the subject is alive depends on the survival time (p-MAR assumption) or not (u-MAR assumption). Inference is performed through subject-level bootstrap. The method is validated in a simulation study and applied to the French cohort Paquid to estimate quantiles of a cognitive test in the elderly population currently alive. On one hand, the simulations show that the u-MAR analysis is quite robust when the true missingness mechanism is p-MAR. This is a useful result because computation of suitable weights for intermittent missing data under the p-MAR assumption is untractable. On the other hand, the simulations highlight, along with the real data analysis, the usefulness of suitable weights for intermittent missing data. This method is implemented in the R package weightQuant.