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We examined the setting in which a variable that is subject to missingness is used both as an inclusion/exclusion criterion for creating the analytic sample and subsequently as the primary exposure in the analysis model that is of scientific interest. An example is cancer stage, where patients with stage IV cancer are often excluded from the analytic sample, and cancer stage (I to III) is an exposure variable in the analysis model. We considered two analytic strategies. The first strategy, referred to as "exclude-then-impute," excludes subjects for whom the observed value of the target variable is equal to the specified value and then uses multiple imputation to complete the data in the resultant sample. The second strategy, referred to as "impute-then-exclude," first uses multiple imputation to complete the data and then excludes subjects based on the observed or filled-in values in the completed samples. Monte Carlo simulations were used to compare five methods (one based on "exclude-then-impute" and four based on "impute-then-exclude") along with the use of a complete case analysis. We considered both missing completely at random and missing at random missing data mechanisms. We found that an impute-then-exclude strategy using substantive model compatible fully conditional specification tended to have superior performance across 72 different scenarios. We illustrated the application of these methods using empirical data on patients hospitalized with heart failure when heart failure subtype was used for cohort creation (excluding subjects with heart failure with preserved ejection fraction) and was also an exposure in the analysis model., (© 2023 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

In healthcare cost-effectiveness analysis, probability distributions are typically skewed and missing data are frequent. Bootstrap and multiple imputation are well-established resampling methods for handling skewed and missing data. However, it is not clear how these techniques should be combined. This paper addresses combining multiple imputation and bootstrap to obtain confidence intervals of the mean difference in outcome for two independent treatment groups. We assessed statistical validity and efficiency of 10 candidate methods and applied these methods to a clinical data set. Single imputation nested in the bootstrap percentile method (with added noise to reflect the uncertainty of the imputation) emerged as the method with the best statistical properties. However, this method can require extensive computation times and the lack of standard software makes this method not accessible for a larger group of researchers. Using a standard unpaired t-test with standard multiple imputation without bootstrap appears to be a robust alternative with acceptable statistical performance for which standard multiple imputation software is available., (© 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

Individual participant data meta-analyses (IPD-MA) are increasingly used for developing and validating multivariable (diagnostic or prognostic) risk prediction models. Unfortunately, some predictors or even outcomes may not have been measured in each study and are thus systematically missing in some individual studies of the IPD-MA. As a consequence, it is no longer possible to evaluate between-study heterogeneity and to estimate study-specific predictor effects, or to include all individual studies, which severely hampers the development and validation of prediction models. Here, we describe a novel approach for imputing systematically missing data and adopt a generalized linear mixed model to allow for between-study heterogeneity. This approach can be viewed as an extension of Resche-Rigon's method (Stat Med 2013), relaxing their assumptions regarding variance components and allowing imputation of linear and nonlinear predictors. We illustrate our approach using a case study with IPD-MA of 13 studies to develop and validate a diagnostic prediction model for the presence of deep venous thrombosis. We compare the results after applying four methods for dealing with systematically missing predictors in one or more individual studies: complete case analysis where studies with systematically missing predictors are removed, traditional multiple imputation ignoring heterogeneity across studies, stratified multiple imputation accounting for heterogeneity in predictor prevalence, and multilevel multiple imputation (MLMI) fully accounting for between-study heterogeneity. We conclude that MLMI may substantially improve the estimation of between-study heterogeneity parameters and allow for imputation of systematically missing predictors in IPD-MA aimed at the development and validation of prediction models., (Copyright © 2015 John Wiley & Sons, Ltd.)

Regional or national growth distributions can provide vital information on the health status of populations. In most resource poor countries, however, the required anthropometric data from purpose-designed growth surveys are not readily available. We propose a practical method for estimating regional (multi-country) age-conditional weight distributions based on existing survey data from different countries. We developed a two-step method by which one is able to model data with widely different age ranges and sample sizes. The method produces references both at the country level and at the regional (multi-country) level. The first step models country-specific centile curves by Box-Cox t and Box-Cox power exponential distributions implemented in generalized additive model for location, scale and shape through a common model. Individual countries may vary in location and spread. The second step defines the regional reference from a finite mixture of the country distributions, weighted by population size. To demonstrate the method we fitted the weight-for-age distribution of 12 countries in South East Asia and the Western Pacific, based on 273 270 observations. We modeled both the raw body weight and the corresponding Z score, and obtained a good fit between the final models and the original data for both solutions. We briefly discuss an application of the generated regional references to obtain appropriate, region specific, age-based dosing regimens of drugs used in the tropics. The method is an affordable and efficient strategy to estimate regional growth distributions where the standard costly alternatives are not an option., (Copyright (c) 2009 John Wiley & Sons, Ltd.)

This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and disease staging), psychology (stages of cognitive development), human development (pubertal stages) and chronic diseases (stages of dementia). Transition probabilities between successive stages are modeled as smoothly varying functions of age. Age-conditional references are calculated from the modeled probabilities by the mid-P value. It is possible to eliminate the influence of age by calculating standard deviation scores (SDS). The method is applied to the empirical data to produce reference charts on secondary sexual maturation. The mean of the empirical SDS in the reference population is close to zero, whereas the variance depends on age. The stage line diagram provides quick insight into both status (in SDS) and tempo (in SDS/year) of development of an individual child. Other measures (e.g. height SDS, body mass index SDS) from the same child can be added to the chart. Diagrams for sexual maturation are available as a web application at http://vps.stefvanbuuren.nl/puberty. The stage line diagram expresses status and tempo of discrete changes on a continuous scale. Wider application of these measures scores opens up new analytic possibilities., ((c) 2009 John Wiley & Sons, Ltd.)

The standard deviation score (SDS) is a powerful tool for screening for growth-related problems. However, referral rules of the type 'if SDS(Y)

Measurement of development is often less precise than that of height and weight. Developmental scores are typically based on passing one or more developmental markers, but do not have interval scale so calculating differences between scores can be nonsensical. Age-specific standardized scores are sometimes used, but fail to have a common metric that allows comparison of developmental scores across age. The goal of this study is to develop a quantitative developmental score (D-score) with improved measurement characteristics. The basic assumption of the D-score is the existence of a common continuous scale for the development. Scores of 2151 children between 0 and 2 years on a Dutch developmental instrument were analysed. Application of the Rasch Model resulted in excellent reliability and satisfactory fit. This indicates that the new quantitative D-score succeeds in representing outcomes of the instrument on a common interval scale. Age-conditional reference values for the D-score were derived by means of the LMS method. The definition of the D-scores is not specific to age, so the D-score of a measured person can be compared to the D-score of another person of a different age. Difference scores between sessions can be used to evaluate developmental velocity on the individual level. To our knowledge this is the first developmental scale for children with such properties.

The World Health Organization (WHO), in collaboration with a number of research institutions worldwide, is developing new child growth standards. As part of a broad consultative process for selecting the best statistical methods, WHO convened a group of statisticians and child growth experts to review available methods, develop a strategy for assessing their strengths and weaknesses, and discuss methodological issues likely to be faced in the process of constructing the new growth curves. To select the method(s) to be used, the group proposed a two-stage decision-making process. First, to select a few relevant methods based on a list of set criteria and, second, to compare the methods using available tests or other established procedures. The group reviewed 30 methods for attained growth curves. Using the pre-defined criteria, a few were selected combining five distributions and two smoothing techniques. Because the number of selected methods was considered too large to be fully tested, a preliminary study was recommended to evaluate goodness of fit of the five distributions. Methods based on distributions with poor performance will be eliminated and the remaining methods fully tested and compared., (Copyright (c) 2005 John Wiley & Sons, Ltd.)

A well-known problem in spontaneous reporting systems (SRSs) for adverse drug reactions (ADRs) is under-reporting, that is, the problem that not all occurrences of ADRs are reported to the SRS. We look at the question of how to draw statistical conclusions from analyses of SRS data using reporting odds ratios. We will show that certain under-reporting problems play no role in assessing ADRs from SRSs: the results from the analyses turn out to be biased by some specific under-reporting problems, but not by others. SRS data can be particularly useful for the assessment of drug-drug interactions. If the assumption holds that there is an under-reporting problem for a first drug, and an under-reporting problem for a second drug, but that these two under-reporting problems do not influence each other, then reporting odds ratios estimated from SRSs are useful for signalling drug-drug interactions in the ADR-experiencing population. Similar results hold for covariate-drug interactions. We illustrate our results using two examples., (Copyright 2002 John Wiley & Sons, Ltd.)

The worm plot visualizes differences between two distributions, conditional on the values of a covariate. Though the worm plot is a general diagnostic tool for the analysis of residuals, this paper focuses on an application in constructing growth reference curves, where the covariate of interest is age. The LMS model of Cole and Green is used to construct reference curves in the Fourth Dutch Growth Study 1997. If the model fits, the measurements in the reference sample follow a standard normal distribution on all ages after a suitably chosen Box-Cox transformation. The coefficients of this transformation are modelled as smooth age-dependent parameter curves for the median, variation and skewness, respectively. The major modelling task is to choose the appropriate amount of smoothness of each parameter curve. The worm plot assesses the age-conditional normality of the transformed data under a variety of LMS models. The fit of each parameter curve is closely related to particular features in the worm plot, namely its offset, slope and curvature. Application of the worm plot to the Dutch growth data resulted in satisfactory reference curves for a variety of anthropometric measures. It was found that the LMS method generally models the age-conditional mean and skewness better than the age-related deviation and kurtosis., (Copyright 2001 John Wiley & Sons, Ltd.)