Analysis of an incomplete binary outcome derived from frequently recorded longitudinal continuous data: application to daily pain evaluation

Randomized clinical trials increasingly collect daily data, frequently using electronic diaries. Such data are usually summarized into an 'intermediate' continuous outcome (such as the mean of the daily values in a period before a scheduled clinic visit). These are in turn often summarized further into a binary outcome, for example, indicating whether the intermediate continuous outcome has improved by a prespecified amount from randomization. This article compares and contrasts statistical approaches for analyzing such binary outcomes when the underlying study is subject to dropout so that some of the underlying diary data are missing. Such analysis involves rigorous rules for the derivation of outcomes, a thorough data exploration for the selection of covariates, and an elucidation of the missingness mechanism. The investigated statistical methods for treatment-effect analysis are based on direct modeling and on multiple imputation and are applied either to the binary outcome or the intermediate continuous outcome or to the daily diary data. These are compared on the basis of criteria for inferences at prespecified times during the follow-up. We show that multiple-imputation methods are particularly well adapted to our context and that missing data imputation on the daily diary data, rather than the derived outcomes, makes best use of the available information. The data set, which motivated our investigation, comes from a placebo-controlled clinical trial to assess the effect on pain of a new compound.     

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1—Basic theory and simple methods of adjustment

Measurement error and misclassification of variables frequently occur in epidemiology and involve variables important to public health. Their presence can impact strongly on results of statistical analyses involving such variables. However, investigators commonly fail to pay attention to biases resulting from such mismeasurement. We provide, in two parts, an overview of the types of error that occur, their impacts on analytic results, and statistical methods to mitigate the biases that they cause. In this first part, we review different types of measurement error and misclassification, emphasizing the classical, linear, and Berkson models, and on the concepts of nondifferential and differential error. We describe the impacts of these types of error in covariates and in outcome variables on various analyses, including estimation and testing in regression models and estimating distributions. We outline types of ancillary studies required to provide information about such errors and discuss the implications of covariate measurement error for study design. Methods for ascertaining sample size requirements are outlined, both for ancillary studies designed to provide information about measurement error and for main studies where the exposure of interest is measured with error. We describe two of the simpler methods, regression calibration and simulation extrapolation (SIMEX), that adjust for bias in regression coefficients caused by measurement error in continuous covariates, and illustrate their use through examples drawn from the Observing Protein and Energy (OPEN) dietary validation study. Finally, we review software available for implementing these methods. The second part of the article deals with more advanced topics.     

Using Multiple Imputation to Incorporate Cases with Missing Items in a Mental Health Services Study

When data analysis tools require that every variable be observed on each case, then missing items on a subset of variables force investigators either to leave potentially interesting variables out of analysis models or to include these variables but drop incomplete cases from the analysis. For example, in a study considered here, mental health patients were interviewed at two time points about a variety of topics that reflect successful adaptation to outpatient treatment, such as support from family and friends and avoidance of legal problems, although not all patients were successfully interviewed at the second time point. In a previous analysis of these data, logistic regression models were developed to relate baseline patient characteristics and recent treatment cost history to binary outcomes capturing aspects of adaptation. In these models, years of education was omitted as a covariate because it was incompletely observed at baseline. Here, we carry out analyses that include information from partially observed cases. Specifically, we use a multivariate model to produce multiple plausible imputed values for each missing item, and we combine results from separate logistic regression analyses on the completed data sets using the multiple imputation inference technique. Although the majority of inferences about specific regression coefficients paralleled those from the original study, some differences are noted. We discuss the implications of having flexible analysis tools for incomplete data in health services research and comment on issues related to model choice.