Feasibility of the Radner reading chards in low vision patients

Background: Being unable to read is a major problem for visually impaired patients. Since distance visual acuity (VA) does not adequately reflect reading ability, it is important to also evaluate near VA. The Radner Reading Charts (RRCs) are available to measure patients' reading performance. The present study tested the inter-chart and test-retest reliability of the RRCs in Dutch low-vision patients (i.e., visual acuity ≥0.3 logMAR) with various eye disorders. Methods: Thirty-eight patients read the three RRCs in random order. Then, about 1 month after the initial measurements, a test-retest procedure was performed in 15 of the 38 patients. Tested variables were reading acuity (logRAD), logRAD score, logRAD/logMAR ratio, maximum reading speed (MRS), and critical print size (CPS). Both MRS and CPS were calculated in two different ways. To determine the variability, a mixed-model analysis was used. Results: For all variables, the largest part of the variance was explained by the individual subject (86-89%) whereas the chart accounted for only 0-0.78% of the variability. Therefore, the inter-chart and test-retest reliability was high, except for the CPS which had a poor to moderate reliability (31-62%) when calculated in the two different ways. Conclusions: The inter-chart and test-retest results showed high reliability in patients with low vision due to various diseases; therefore, the charts are feasible to determine effects in large groups. © 2010 Springer-Verlag

A simulation study comparing weighted estimating equations with multiple imputation based estimating equations for longitudinal binary data

Missingness frequently complicates the analysis of longitudinal data. A popular solution for dealing with incomplete longitudinal data is the use of likelihood-based methods, when, for example, linear, generalized linear, or non-linear mixed models are considered, due to their validity under the assumption of missing at random (MAR). Semi-parametric methods such as generalized estimating equations (GEEs) offer another attractive approach but require the assumption of missing completely at random (MCAR). Weighted GEE (WGEE) has been proposed as an elegant way to ensure validity under MAR. Alternatively, multiple imputation (MI) can be used to pre-process incomplete data, after which GEE is applied (MI-GEE). Focusing on incomplete binary repeated measures, both methods are compared using the so-called asymptotic, as well as small-sample, simulations, in a variety of correctly specified as well as incorrectly specified models. In spite of the asymptotic unbiasedness of WGEE, results provide striking evidence that MI-GEE is both less biased and more accurate in the small to moderate sample sizes which typically arise in clinical trials. © 2007 Elsevier B.V. All rights reserved.status: publishe

Tutorial: Direct likelihood analysis versus simple forms of imputation for missing data in randomized clinical trials

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A latent-class mixture model for incomplete longitudinal Gaussian data

In the analyses of incomplete longitudinal clinical trial data, there has been a shift, away from simple methods that are valid only if the data are missing completely at random, to more principled ignorable analyses, which are valid under the less restrictive missing at random assumption. The availability of the necessary standard statistical software nowadays allows for such analyses in practice. While the possibility of data missing not at random (MNAR) cannot be ruled out, it is argued that analyses valid under MNAR are not well suited for the primary analysis in clinical trials. Rather than either forgetting about or blindly shifting to an MNAR framework, the optimal place for MNAR analyses is within a sensitivity-analysis context. One such route for sensitivity analysis is to consider, next to selection models, pattern-mixture models or shared-parameter models. The latter can also be extended to a latent-class mixture model, the approach taken in this article. The performance of the so-obtained flexible model is assessed through simulations and the model is applied to data from a depression trial.status: publishe

Marginalizing pattern-mixture models for categorical data subject to monotone missingness

Many models to analyze incomplete data that allow the missingness to be non-random have been developed. Since such models necessarily rely on unverifiable assumptions, considerable research nowadays is devoted to assess the sensitivity of resulting inferences. A popular sensitivity route, next to local influence (Cook in J Roy Stat Soc Ser B 2:133-169, 1986; Jansen et al. in Biometrics 59:410-419, 2003) and so-called intervals of ignorance (Molenberghs et al. in Appl Stat 50:15-29, 2001), is based on contrasting more conventional selection models with members from the pattern-mixture model family. In the first family, the outcome of interest is modeled directly, while in the second family the natural parameter describes the measurement process, conditional on the missingness pattern. This implies that a direct comparison ought not to be done in terms of parameter estimates, but rather should pass by marginalizing the pattern-mixture model over the patterns. While this is relatively straightforward for linear models, the picture is less clear for the nevertheless important setting of categorical outcomes, since models ordinarily exhibit a certain amount of non-linearity. Following ideas laid out in Jansen and Molenberghs (Pattern-mixture models for categorical outcomes with non-monotone missingness. Submitted for publication, 2007), we offer ways to marginalize pattern-mixture-model-based parameter estimates, and supplement these with asymptotic variance formulas. The modeling context is provided by the multivariate Dale model. The performance of the method and its usefulness for sensitivity analysis is scrutinized using simulations. © 2008 Springer-Verlag.status: publishe

Analyzing incomplete discrete longitudinal clinical trial data

Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after dropout for LOCF. Such assumptions are too strong to generally hold. Over the last decades, a number of full longitudinal data analysis methods have become available, such as the linear mixed model for Gaussian outcomes, that are valid under the much weaker missing at random (MAR) assumption. Such a method is useful, even if the scientific question is in terms of a single time point, for example, the last planned measurement occasion, and it is generally consistent with the intention-to-treat principle. The validity of such a method rests on the use of maximum likelihood, under which the missing data mechanism is ignorable as soon as it is MAR. In this paper, we will focus on non-Gaussian outcomes, such as binary, categorical or count data. This setting is less straightforward since there is no unambiguous counterpart to the linear mixed model. We first provide an overview of the various modeling frameworks for non-Gaussian longitudinal data, and subsequently focus on generalized linear mixed-effects models, on the one hand, of which the parameters can be estimated using full likelihood, and on generalized estimating equations, on the other hand, which is a nonlikelihood method and hence requires a modification to be valid under MAR. We briefly comment on the position of models that assume missingness not at random and argue they are most useful to perform sensitivity analysis. Our developments are underscored using data from two studies. While the case studies feature binary outcomes, the methodology applies equally well to other discrete-data settings, hence the qualifier "discrete" in the title.Published at http://dx.doi.org/10.1214/088342305000000322 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)status: publishe