Missing data

How many imputations with mice? Assessing Monte-Carlo error after multiple imputation in R

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When using multiple imputation to handle missing data, one must, if not immediately, but eventually, decide how many imputations to base inferences on. The validity of inferences does not rely on how many imputations are used, but the statistical efficiency of the inference can be increased by using more imputations. Moreover, we may want our results to be reproducible to a given precision, in the sense that if someone were to re-impute the same data using the same number of imputations but with a different random number seed, they would obtain the same estimates to the desired precision. For a great summary on considerations on how many imputations to use, see the corresponding section from Stef van Buuren’s book.

In this post I provide a small bit of R code which, given a pooled analysis after performing imputation using the mice package in R, calculates the so called Monte-Carlo standard error of the multiple imputation point estimates. Stata has really nice functionality for doing this built into mi estimate.

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Conditional mean reference-based multiple imputation

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The reference-based approach to imputing missing data has become popular in clinical trials, as I’ve blogged about previously. In the standard approach, the multiple imputations are generated as draws from the posterior distribution under a Bayesian model. With a continuous outcome, each of the imputed datasets is analysed using a linear regression model for the outcome (typically measured at the final time point), with treatment group and some baseline variables as covariates.

In a new pre-print available on arXiv, in work by Marcel Wolbers and colleagues at Roche, we propose an alternative approach for reference-based imputation for continuous outcomes. This approach results in a treatment effect point estimate and (frequentist) standard error without any Monte-Carlo error.

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Summary statistics after imputation with mice

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Someone recently asked how they could calculate summary statistics after performing multiple imputation with the mice package. The first thing to say is that if you are only interested in calculating a certain summary statistic on each of the imputed datasets, this is easy to achieve. You can extract each imputed dataset using the complete() function, and then apply whatever function you would normally use to calculate the summary statistic in question.

In the rest of this post, I’ll consider the situation where you are interested in performing inference for the summary statistic (or functional if you will). That is, if you are interested in say the median in your data, you are interested because ultimately you are interested in the median of the variable in the population (from which your sample data came from). Viewed this way, the summary statistic is an estimator of a population parameter, and so we should apply the usual procedure for multiple imputation: estimate the parameter on each imputed dataset and its corresponding complete data variance, and then pool these using Rubin’s rules. For some quantities (e.g. the mean), this is pretty easy. For others, at least as far as I can see, it requires a bit more work.

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