In the analysis of clustered data, inverse cluster size weighting has been shown to be resistant to the potentially biasing effects of informative cluster size, where the number of observations within a cluster is associated with the outcome variable of interest. The method of inverse cluster size reweighting has been implemented to establish clustered data analogues of common tests for independent data, but the method has yet to be extended to tests of categorical data. Many variance estimators have been implemented across established cluster-weighted tests, but potential effects of differing methods on test performance has not previously been explored. Here, we develop cluster-weighted estimators of marginal proportions that remain unbiased under informativeness, and derive analogues of three popular tests for clustered categorical data, the one-sample proportion, goodness of fit, and independence chi square tests. We construct these tests using several variance estimators and show substantial differences in the performance of cluster-weighted tests based on variance estimation technique, with variance estimators constructed under the null hypothesis maintaining size closest to nominal. We illustrate the proposed tests through an application to a data set of functional measures from patients with spinal cord injuries participating in a rehabilitation program.
The log rank test is a popular nonparametric test for comparing survival distributions among groups. When data are organized in clusters of potentially correlated observations, adjustments can be made to account for within-cluster dependencies among observations, eg, tests derived from frailty models. Tests for clustered data can be further biased when the number of observations within each cluster and the distribution of groups within cluster are correlated with survival times, phenomena known as informative cluster size and informative within-cluster group size. In this manuscript, we develop a log rank test for clustered data that adjusts for the potentially biasing effect of informative cluster size and within-cluster group size. We provide the results of a simulation study demonstrating that our proposed test remains unbiased under cluster-based informativeness, while other candidate tests not accounting for the clustering structure do not properly maintain size. Furthermore, our test exhibits power advantages under scenarios in which traditional tests are appropriate. We demonstrate an application of our test by comparing time to functional progression between groups defined initial functional status in a spinal cord injury data set.
Background: In synergy with the mounting scientific evidence for the capacity of recovery after spinal cord injury (SCI) and training, new evidence-based therapies advancing neuromuscular recovery are emerging. There is a parallel need for outcome instruments that specifically address recovery. The Pediatric Neuromuscular Recovery Scale (Pediatric NRS) is one example with established content validity to assess neuromuscular capacity within task performance. Objective: The objective of this study was to determine interrater reliability of the Pediatric NRS to classify motor capacity in children after SCI. Methods: Pediatric physicians (3), occupational therapists (5), and physical therapists (6) received standardized training in scoring the scale, then rated video assessments of 32 children post SCI, 2–12 years of age, 78% non-ambulatory. Interrater reliability was analyzed using Kendall coefficient of concordance for individual Pediatric NRS items and overall score. Results: The interrater reliability coefficient was determined to be near 1 for the overall Pediatric NRS score (ICC = 0.966; 95% CI, 0.89–0.98). Twelve of 16 individual items exhibited high concordance coefficients (Kendall's W ≥ 0.8) and four items demonstrated concordance coefficients, < 0.8 and > 0.69. Interrater reliability was equivalent among groups defined by age and neurological level, but lower among non-ambulatory individuals. Conclusion: Strong interrater reliability was demonstrated by pediatric clinicians who scored children with SCI using the Pediatric NRS.
When observations are collected in/organized into observational units, within which observations may be dependent, those observational units are often referred to as "clustered" and the data as "clustered data". Examples of clustered data include repeated measures or hierarchical shared association (e.g., individuals within families). This paper provides an overview of the R package htestClust, a tool for the marginal analysis of such clustered data with potentially informative cluster and/or group sizes. Contained in htestClust are clustered data analogues to the following classical hypothesis tests: rank-sum, signed rank, t-, one-way ANOVA, F, Levene, Pearson/Spearman/Kendall correlation, proportion, goodness-of-fit, independence, and McNemar. Additional functions allow users to visualize and test for informative cluster size. This package has an easy-to-use interface mimicking that of classical hypothesis-testing functions in the R environment. Various features of this package are illustrated through simple examples.
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