Inverse-observation-weighted estimating equations for longitudinal dropout (${\sum }_{i,j}{w}_{ij}\frac{R_{ij}}{{\rho }_{ij}}(Y_{ij}-m_{ij})=0$)

For monotone missing data, let $R_{ij}$ indicate observation and let ${\rho }_{ij}$ be the product of the conditional retention probabilities through visit $j$. Under sequential missing at random, conditioning on the complete response history makes these retention probabilities depend only on the history already observed at each decision. Therefore $\mathbb{E}(R_{ij}/{\rho }_{ij}\mid Y_i,X_i)=1$. Weighting a working-independence generalized estimating equation by $R_{ij}/{\rho }_{ij}$ restores its mean-zero property. This needs correct retention probabilities, positivity and regularity; uncertainty must account for estimating the weights.