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, which extends the functionality of mice 1.0 in several ways. In mice, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. mice 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 can be downloaded from the Comprehensive R Archive Network. This article provides a hands-on, stepwise approach to solve applied incomplete data problems.

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mice: Multivariate Imputation by Chained Equations in R

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It is important that the medical profession play a significant role in critically evaluating the use of diagnostic procedures and therapies as they are introduced in the detection, management,

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ACC/AHA 2006 Guidelines for the Management of Patients With Valvular Heart Disease

Non-randomised studies of the effects of interventions are critical to many areas of healthcare evaluation, but their results may be biased. It is therefore important to understand and appraise their strengths and weaknesses. We developed ROBINS-I (“Risk Of Bias In Non-randomised Studies - of Interventions”), a new tool for evaluating risk of bias in estimates of the comparative effectiveness (harm or benefit) of interventions from studies that did not use randomisation to allocate units (individuals or clusters of individuals) to comparison groups. The tool will be particularly useful to those undertaking systematic reviews that include non-randomised studies.

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ROBINS-I: a tool for assessing risk of bias in non-randomised studies of interventions.

Multiple imputation by chained equations is a flexible and practical approach to handling missing data. We describe the principles of the method and show how to impute categorical and quantitative variables, including skewed variables. We give guidance on how to specify the imputation model and how many imputations are needed. We describe the practical analysis of multiply imputed data, including model building and model checking. We stress the limitations of the method and discuss the possible pitfalls. We illustrate the ideas using a data set in mental health, giving Stata code fragments. Copyright © 2010 John Wiley & Sons, Ltd.

Multiple imputation using chained equations: Issues and guidance for practice

Most studies have some missing data. Jonathan Sterne and colleagues describe the appropriate use and reporting of the multiple imputation approach to dealing with them

Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls.

Reference intervals are used in laboratory medicine to detect measurements which are extreme, possibly abnormal. Methods of estimating reference intervals and age-specific reference intervals (where the measurement is dependent on a covariate, typically age) are reviewed. The issues of calculating confidence bands, determining appropriate sample sizes and assessing goodness-of-fit are discussed.

Calculating reference intervals for laboratory measurements

The Cox proportional hazards model has become the standard for the analysis of survival time data in cancer and other chronic diseases. In most studies, proportional hazards (PH) are assumed for covariate effects. With long-term follow-up, the PH assumption may be violated, leading to poor model fit. To accommodate non-PH effects, we introduce a new procedure, MFPT, an extension of the multivariable fractional polynomial (MFP) approach, to do the following: (1) select influential variables; (2) determine a sensible dose-response function for continuous variables; (3) investigate time-varying effects; (4) model such time-varying effects on a continuous scale. Assuming PH initially, we start with a detailed model-building step, including a search for possible non-linear functions for continuous covariates. Sometimes a variable with a strong short-term effect may appear weak or non-influential if 'averaged' over time under the PH assumption. To protect against omitting such variables, we repeat the analysis over a restricted time-interval. Any additional prognostic variables identified by this second analysis are added to create our final time-fixed multivariable model. Using a forward-selection algorithm we search for possible improvements in fit by adding time-varying covariates. The first part to create a final time-fixed model does not require the use of MFP. A model may be given from 'outside' or a different strategy may be preferred for this part. This broadens the scope of the time-varying part. To motivate and illustrate the methodology, we create prognostic models from a large database of patients with primary breast cancer. Non-linear time-fixed effects are found for progesterone receptor status and number of positive lymph nodes. Highly statistically significant time-varying effects are present for progesterone receptor status and tumour size.

A New Proposal for Multivariable Modelling of Time‐Varying Effects in Survival Data Based on Fractional Polynomial Time‐Transformation

Departure of a sample from a normal distribution should be assessed by a quantity that is meaningful in terms of the data, rather than merely by the P-value from a test statistic. Indices of departure based on the Shapiro-Francia W' and the Shapiro-Wilk W statistics are derived, and shown to have a natural interpretation in relation to the normal probability plot. A new diagnostic plot is proposed. An example is given which shows the relationship between one of the new indices and errors in calculated reference ranges due to non-normality of the data.

Estimating departure from normality.

Prognostic models that predict the clinical course of a breast cancer patient are important in oncology. We propose an approach to constructing such models based on fractional polynomials in which useful transformations of the continuous factors are determined. The idea may be applied with all types of regression model, including Cox regression, the method of choice for survival-time data. We analyse a prospective study of node-positive breast cancer. Seven standard prognostic factors--age, menopausal status, tumour size, tumour grade, number of positive lymph nodes, progesterone and oestrogen receptor concentrations--were investigated in 686 patients, of whom 299 had an event for recurrence-free survival and 171 died. We determine a final model with transformations of prognostic factors and compare it with the more traditional approaches using categorized variables or assuming a straight line relationship. We conclude that analysis using fractional polynomials can extract important prognostic information which the traditional approaches may miss.

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Modelling the effects of standard prognostic factors in node-positive breast cancer

Logistic regression models are widely used in medicine for predicting patient outcome (prognosis) and constructing diagnostic tests (diagnosis). Multivariable logistic models yield an (approximately) continuous risk score, a transformation of which gives the estimated event probability for an individual. A key aspect of model performance is discrimination, that is, the model's ability to distinguish between patients who have (or will have) an event of interest and those who do not (or will not). Graphical aids are important in understanding a logistic model. The receiver-operating characteristic (ROC) curve is familiar, but not necessarily easy to interpret. We advocate a simple graphic that provides further insight into discrimination, namely a histogram or dot plot of the risk score in the outcome groups. The most popular performance measure for the logistic model is the c-index, numerically equivalent to the area under the ROC curve. We discuss the comparative merits of the c-index and the (standardized) mean difference in risk score between the outcome groups. The latter statistic, sometimes known generically as the effect size, has been computed in slightly different ways by several different authors, including Glass, Cohen and Hedges. An alternative measure is the overlap between the distributions in the outcome groups, defined as the area under the minimum of the two density functions. The larger the overlap, the weaker the discrimination. Under certain assumptions about the distribution of the risk score, the c-index, effect size and overlap are functionally related. We illustrate the ideas with simulated and real data sets.

Patrick Royston

Papers

Calculating reference intervals for laboratory measurements

A New Proposal for Multivariable Modelling of Time‐Varying Effects in Survival Data Based on Fractional Polynomial Time‐Transformation

Estimating departure from normality.

Modelling the effects of standard prognostic factors in node-positive breast cancer

Visualizing and assessing discrimination in the logistic regression model.