The R package mice imputes incomplete multivariate data by chained equations. The software mice 1.0 appeared in the year 2000 as an S-PLUS library, and in 2001 as an R package. mice 1.0 introduced predictor selection, passive imputation and automatic pooling. This article documents mice 2.9, which extends the functionality of mice 1.0 in several ways. In mice 2.9, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. mice 2.9 adds new functionality for imputing multilevel data, automatic predictor selection, data handling, post-processing imputed values, specialized pooling routines, model selection tools, and diagnostic graphs. Imputation of categorical data is improved in order to bypass problems caused by perfect prediction. Special attention is paid to transformations, sum scores, indices and interactions using passive imputation, and to the proper setup of the predictor matrix. mice 2.9 can be downloaded from the Comprehensive R Archive Network. This article provides a hands-on, stepwise approach to solve applied incomplete data problems.

The goal of multiple imputation is to provide valid inferences for statistical estimates from incomplete data. To achieve that goal, imputed values should preserve the structure in the data, as well as the uncertainty about this structure, and include any knowledge about the process that generated the missing data. Two approaches for imputing multivariate data exist: joint modeling (JM) and fully conditional specification (FCS). JM is based on parametric statistical theory, and leads to imputation procedures whose statistical properties are known. JM is theoretically sound, but the joint model may lack flexibility needed to represent typical data features, potentially leading to bias. FCS is a semi-parametric and flexible alternative that specifies the multivariate model by a series of conditional models, one for each incomplete variable. FCS provides tremendous flexibility and is easy to apply, but its statistical properties are difficult to establish. Simulation work shows that FCS behaves very well in the cases studied. The present paper reviews and compares the approaches. JM and FCS were applied to pubertal development data of 3801 Dutch girls that had missing data on menarche (two categories), breast development (five categories) and pubic hair development (six stages). Imputations for these data were created under two models: a multivariate normal model with rounding and a conditionally specified discrete model. The JM approach introduced biases in the reference curves, whereas FCS did not. The paper concludes that FCS is a useful and easily applied flexible alternative to JM when no convenient and realistic joint distribution can be specified.

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This paper studies a non-response problem in survival analysis where the occurrence of missing data in the risk factor is related to mortality. In a study to determine the influence of blood pressure on survival in the very old (85+ years), blood pressure measurements are missing in about 12.5 per cent of the sample. The available data suggest that the process that created the missing data depends jointly on survival and the unknown blood pressure, thereby distorting the relation of interest. Multiple imputation is used to impute missing blood pressure and then analyse the data under a variety of non-response models. One special modelling problem is treated in detail; the construction of a predictive model for drawing imputations if the number of variables is large. Risk estimates for these data appear robust to even large departures from the simplest non-response model, and are similar to those derived under deletion of the incomplete records.

Since 1858, an increase of mean stature has been observed in the Netherlands, reflecting the improving nutritional, hygienic, and health status of the population. In this study, stature, weight, and pubertal development of Dutch youth, derived from four consecutive nationwide cross-sectional growth studies during the past 42 y, are compared to assess the size and rate of the secular growth change. Data on length, height, weight, head circumference, sexual maturation, and demographics of 14,500 boys and girls of Dutch origin in the age range 0-20 y were collected in 1996 and 1997. Growth references for height and weight were constructed with a method that summarizes the distribution by three smooth curves representing skewness (L curve), the median (M curve), and coefficient of variation (S curve). The relationship between height and demographic variables was assessed by multivariate analysis. Reference curves for menarche and secondary sex characteristics were estimated by a generalized additive model using a logit transformation. A positive secular growth change has been present in the past 42 y for children, adolescents, and young adults of Dutch origin, although at a slower rate in the last 17 y. Height differences according to region, educational level of child and parents, and family size have remained. In girls, median age at menarche has decreased by 6 mo during the past four decades to 13.15 y. Environmental conditions have been favorable for many decades in the Netherlands, and the positive secular change in height has not yet come to a halt, in contrast to Scandinavian countries. Main contributors to the increase in height may be improved nutrition, child health, and hygiene, and a reduction of family size.

The use of the Gibbs sampler with fully conditionally specified models, where the distribution of each variable given the other variables is the starting point, has become a popular method to create imputations in incomplete multivariate data. The theoretical weakness of this approach is that the specified conditional densities can be incompatible, and therefore the stationary distribution to which the Gibbs sampler attempts to converge may not exist. This study investigates practical consequences of this problem by means of simulation. Missing data are created under four different missing data mechanisms. Attention is given to the statistical behavior under compatible and incompatible models. The results indicate that multiple imputation produces essentially unbiased estimates with appropriate coverage in the simple cases investigated, even for the incompatible models. Of particular interest is that these results were produced using only five Gibbs iterations starting from a simple draw from observed marginal distributions. It thus appears that, despite the theoretical weaknesses, the actual performance of conditional model specification for multivariate imputation can be quite good, and therefore deserves further study.

This paper studies a non-response problem in survival analysis where the occurrence of missing data in the risk factor is related to mortality. In a study to determine the influence of blood pressure on survival in the very old (85# years), blood pressure measurements are missing in about 12)5 per cent of the sample. The available data suggest that the process that created the missing data depends jointly on survival and the unknown blood pressure, thereby distorting the relation of interest. Multiple imputation is used to impute missing blood pressure and then analyse the data under a variety of non-response models. One special modelling problem is treated in detail; the construction of a predictive model for drawing imputations if the number of variables is large. Risk estimates for these data appear robust to even large departures from the simplest non-response model, and are similar to those derived under deletion of the incomplete records.

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