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"Correlation (Statistics)"
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Intraclass correlation – A discussion and demonstration of basic features
A re-analysis of intraclass correlation (ICC) theory is presented together with Monte Carlo simulations of ICC probability distributions. A partly revised and simplified theory of the single-score ICC is obtained, together with an alternative and simple recipe for its use in reliability studies. Our main, practical conclusion is that in the analysis of a reliability study it is neither necessary nor convenient to start from an initial choice of a specified statistical model. Rather, one may impartially use all three single-score ICC formulas. A near equality of the three ICC values indicates the absence of bias (systematic error), in which case the classical (one-way random) ICC may be used. A consistency ICC larger than absolute agreement ICC indicates the presence of non-negligible bias; if so, classical ICC is invalid and misleading. An F-test may be used to confirm whether biases are present. From the resulting model (without or with bias) variances and confidence intervals may then be calculated. In presence of bias, both absolute agreement ICC and consistency ICC should be reported, since they give different and complementary information about the reliability of the method. A clinical example with data from the literature is given.
Journal Article
A Comparison Study of Canonical Correlation Analysis Based Methods for Detecting Steady-State Visual Evoked Potentials
Canonical correlation analysis (CCA) has been widely used in the detection of the steady-state visual evoked potentials (SSVEPs) in brain-computer interfaces (BCIs). The standard CCA method, which uses sinusoidal signals as reference signals, was first proposed for SSVEP detection without calibration. However, the detection performance can be deteriorated by the interference from the spontaneous EEG activities. Recently, various extended methods have been developed to incorporate individual EEG calibration data in CCA to improve the detection performance. Although advantages of the extended CCA methods have been demonstrated in separate studies, a comprehensive comparison between these methods is still missing. This study performed a comparison of the existing CCA-based SSVEP detection methods using a 12-class SSVEP dataset recorded from 10 subjects in a simulated online BCI experiment. Classification accuracy and information transfer rate (ITR) were used for performance evaluation. The results suggest that individual calibration data can significantly improve the detection performance. Furthermore, the results showed that the combination method based on the standard CCA and the individual template based CCA (IT-CCA) achieved the highest performance.
Journal Article
Estimation of an inter-rater intra-class correlation coefficient that overcomes common assumption violations in the assessment of health measurement scales
Background
Intraclass correlation coefficients (ICC) are recommended for the assessment of the reliability of measurement scales. However, the ICC is subject to a variety of statistical assumptions such as normality and stable variance, which are rarely considered in health applications.
Methods
A Bayesian approach using hierarchical regression and variance-function modeling is proposed to estimate the ICC with emphasis on accounting for heterogeneous variances across a measurement scale. As an application, we review the implementation of using an ICC to evaluate the reliability of Observer OPTION
5
, an instrument which used trained raters to evaluate the level of Shared Decision Making between clinicians and patients. The study used two raters to evaluate recordings of 311 clinical encounters across three studies to evaluate the impact of using a Personal Decision Aid over usual care. We particularly focus on deriving an estimate for the ICC when multiple studies are being considered as part of the data.
Results
The results demonstrate that ICC varies substantially across studies and patient-physician encounters within studies. Using the new framework we developed, the study-specific ICCs were estimated to be 0.821, 0.295, and 0.644. If the within- and between-encounter variances were assumed to be the same across studies, the estimated within-study ICC was 0.609. If heteroscedasticity is not properly adjusted for, the within-study ICC estimate was inflated to be as high as 0.640. Finally, if the data were pooled across studies without accounting for the variability between studies then ICC estimates were further inflated by approximately 0.02 while formerly allowing for between study variation in the ICC inflated its estimated value by approximately 0.066 to 0.072 depending on the model.
Conclusion
We demonstrated that misuse of the ICC statistics under common assumption violations leads to misleading and likely inflated estimates of interrater reliability. A statistical analysis that overcomes these violations by expanding the standard statistical model to account for them leads to estimates that are a better reflection of a measurement scale’s reliability while maintaining ease of interpretation. Bayesian methods are particularly well suited to estimating the expanded statistical model.
Journal Article
Patterns of intra-cluster correlation coefficients in school-based cluster randomised controlled trials of interventions for improving social-emotional functioning outcomes in pupils: a secondary data analysis of five UK-based studies
Background
The cluster randomised trial (CRT) design is increasingly used to evaluate the impact of school-based interventions for improving social-emotional functioning outcomes in pupils. Good knowledge is required on plausible values of the intra-cluster correlation coefficient (ICC) of the outcome to calculate the required sample size in such studies. Using data from five school-based CRTs in the UK, we estimate, and describe patterns in, ICCs for social-emotional functioning outcomes.
Methods
Mixed effects linear regression models were fitted to estimate the ICC and variance components. Estimates for baseline data were obtained by fitting “null” models that had no predictor variables; estimates at follow-up were adjusted for trial arm status.
Results
Five hundred and twenty-nine (529) ICCs were estimated. Variation across clusters in the outcomes was present at the school, year group and classroom levels. Overall, the ICCs were not markedly different between the primary and secondary school settings. Most of the school- and classroom-level ICCs were less than 0.04 for pupil-reported outcomes and less than 0.035 for parent-reported outcomes; a notable exception for pupil-reported outcomes was for outcomes that reflect a common experience shared by children, such as school climate, where the ICCs were as large as 0.1. The ICCs for teacher-reported outcomes (up to 0.1 at the school level and 0.2 at the classroom level) were larger than for pupil- and parent-reported outcomes. In the CRT that allocated schools to trial arms and only sampled one classroom from each school, the nominal school-level ICCs for teacher-reported outcomes took values up to 0.25. ICCs for teacher-reported measures of internalising behaviour problems and pro-social behaviour were larger than for externalising behaviour problems.
Conclusions
When randomising school clusters, sub-sampling of lower-level clusters such as classrooms should be accounted for in the sample size calculation. Teacher-reported ICCs are likely to be greater than those for pupil- and parent-reported outcomes as teachers will often provide data for many or all pupils in a given school or classroom. Differences across reporter type and across outcomes need to be considered when specifying plausible values of the ICC to calculate sample size.
Trial registration
STARS study (ISRCTN84130388); KiVa study (ISRCTN23999021); PACES study (ISRCTN23563048); PROMISE study (ISRCTN19083628); MYRIAD study (ISRCTN86619085).
Journal Article
Spatial and spatio-temporal bayesian models with R-INLA
Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio-temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations
eBook
Leveraging expression from multiple tissues using sparse canonical correlation analysis and aggregate tests improves the power of transcriptome-wide association studies
Transcriptome-wide association studies (TWAS) test the association between traits and genetically predicted gene expression levels. The power of a TWAS depends in part on the strength of the correlation between a genetic predictor of gene expression and the causally relevant gene expression values. Consequently, TWAS power can be low when expression quantitative trait locus (eQTL) data used to train the genetic predictors have small sample sizes, or when data from causally relevant tissues are not available. Here, we propose to address these issues by integrating multiple tissues in the TWAS using sparse canonical correlation analysis (sCCA). We show that sCCA-TWAS combined with single-tissue TWAS using an aggregate Cauchy association test (ACAT) outperforms traditional single-tissue TWAS. In empirically motivated simulations, the sCCA+ACAT approach yielded the highest power to detect a gene associated with phenotype, even when expression in the causal tissue was not directly measured, while controlling the Type I error when there is no association between gene expression and phenotype. For example, when gene expression explains 2% of the variability in outcome, and the GWAS sample size is 20,000, the average power difference between the ACAT combined test of sCCA features and single-tissue, versus single-tissue combined with Generalized Berk-Jones (GBJ) method, single-tissue combined with S-MultiXcan, UTMOST, or summarizing cross-tissue expression patterns using Principal Component Analysis (PCA) approaches was 5%, 8%, 5% and 38%, respectively. The gain in power is likely due to sCCA cross-tissue features being more likely to be detectably heritable. When applied to publicly available summary statistics from 10 complex traits, the sCCA+ACAT test was able to increase the number of testable genes and identify on average an additional 400 additional gene-trait associations that single-trait TWAS missed. Our results suggest that aggregating eQTL data across multiple tissues using sCCA can improve the sensitivity of TWAS while controlling for the false positive rate.
Journal Article
Accuracy of a screening tool for medication adherence: A systematic review and meta-analysis of the Morisky Medication Adherence Scale-8
This systematic review examined the reliability and validity of the Morisky Medication Adherence Scale-8 (MMAS-8), which has been widely used to assess patient medication adherence in clinical research and medical practice.
Of 418 studies identified through searching 4 electronic databases, we finally analyzed 28 studies meeting the selection criteria of this study regarding the reliability and validity of MMAS-8 including sensitivity and specificity. Meta-analysis for Cronbach's α, intraclass correlation coefficient (ICC), sensitivity and specificity to detect a patient with nonadherence to medication were performed. The pooled estimates for Cronbach's α and ICC were calculated using the random-effects weighted T transformation. A bivariate random-effects model was used to estimate pooled sensitivity and specificity.
The pooled Cronbach's α estimate for type 2 diabetes group in 7 studies and osteoporosis group in 3 studies were 0.67 (95% Confidence Interval(CI), 0.65 to 0.69) and 0.77 (95% CI, 0.72 to 0.83), respectively. With regard to test-retest, the pooled ICC for type 2 diabetes group in 3 studies and osteoporosis group in 2 studies were 0.81 (95% CI, 0.75 to 0.85) and 0.80 (95% CI, 0.74 to 0.85). For a cut-off value of 6, the pooled sensitivity and specificity in 12 studies were 0.43 (95% CI, 0.33 to 0.53) and 0.73 (95% CI, 0.68 to 0.78), respectively.
The MMAS-8 had acceptable internal consistency and reproducibility in a few diseases like type 2 diabetes. Using the cut-off value of 6, criterion validity was not enough good to validly screen a patient with nonadherence to medication. However, this study did not calculated a pooled estimate for criterion validity using the higher values than 6 as a cut-off value since most of included individual studies did not report criterion validity based on those values.
Journal Article
An introduction to new robust linear and monotonic correlation coefficients
Background
The most common measure of association between two continuous variables is the Pearson correlation (Maronna et al. in Safari an OMC. Robust statistics, 2019. https://login.proxy.bib.uottawa.ca/login?url=https://learning.oreilly.com/library/view/-/9781119214687/?ar&orpq&email=^u). When outliers are present, Pearson does not accurately measure association and robust measures are needed. This article introduces three new robust measures of correlation: Taba (T), TabWil (TW), and TabWil rank (TWR). The correlation estimators T and TW measure a linear association between two continuous or ordinal variables; whereas TWR measures a monotonic association. The robustness of these proposed measures in comparison with Pearson (P), Spearman (S), Quadrant (Q), Median (M), and Minimum Covariance Determinant (MCD) are examined through simulation. Taba distance is used to analyze genes, and statistical tests were used to identify those genes most significantly associated with Williams Syndrome (WS).
Results
Based on the root mean square error (RMSE) and bias, the three proposed correlation measures are highly competitive when compared to classical measures such as P and S as well as robust measures such as Q, M, and MCD. Our findings indicate TBL2 was the most significant gene among patients diagnosed with WS and had the most significant reduction in gene expression level when compared with control (
P
value = 6.37E-05).
Conclusions
Overall, when the distribution is bivariate Log-Normal or bivariate Weibull, TWR performs best in terms of bias and T performs best with respect to RMSE. Under the Normal distribution, MCD performs well with respect to bias and RMSE; but TW, TWR, T, S, and P correlations were in close proximity. The identification of TBL2 may serve as a diagnostic tool for WS patients. A
Taba
R package has been developed and is available for use to perform all necessary computations for the proposed methods.
Journal Article