The model-based approach to inference from multivariate data with missingvalues is reviewed. Regression prediction is most useful when the covariates are

predictive of the missing values and the probability of being missing, and in these

circumstances predictions are particularly sensitive to model misspecification. The

use of penalized splines of the propensity score is proposed to yield robust modelbased

inference under the missing at random (MAR) assumption, assuming monotone

missing data. Simulation comparisons with other methods suggest that the

method works well in a wide range of populations, with little loss of efficiency relative

to parametric models when the latter are correct. Extensions to more general

patterns are outlined.