Analysis of Repeated Measures Under Second-Stage Sphericity: An Empirical Bayes Approach

1997 ◽  
Vol 22 (2) ◽  
pp. 155-192 ◽  
Author(s):  
Robert J. Boik
Keyword(s):  
Multivariate Analysis ◽  
Sample Size ◽  
Covariance Matrix ◽  
Repeated Measures ◽  
Empirical Bayes ◽  
Univariate Analysis ◽  
Sample Sizes ◽  
Multivariate Test ◽  
Orthogonal Contrasts ◽  
Wide Range

The conventional multivariate analysis of repeated measures is applicable in a wide variety of circumstances, in part, because assumptions regarding the pattern of covariances among the repeated measures are not required. If sample sizes are small, however, then the estimators of the covariance parameters lack precision and, as a result, the power of the multivariate analysis is low. If the covariance matrix associated with estimators of orthogonal contrasts is spherical, then the conventional univariate analysis of repeated measures is applicable and has greater power than the multivariate analysis. If sphericity is not satisfied, an adjusted univariate analysis can be conducted, and this adjusted analysis may still be more powerful than the multivariate analysis. As sample size increases, the power advantage of the adjusted univariate test decreases, and, for moderate sample sizes, the multivariate test can be more powerful. This article proposes a hybrid analysis that takes advantage of the strengths of each of the two procedures. The proposed analysis employs an empirical Bayes estimator of the covariance matrix. Existing software for conventional multivariate analyses can, with minor modifications, be used to perform the proposed analysis. The new analysis behaves like the univariate analysis when samples size is small or sphericity is nearly satisfied. When sample size is large or sphericity is strongly violated, then the proposed analysis behaves like the multivariate analysis. Simulation results suggest that the proposed analysis controls test size adequately and can be more powerful than either of the other two analyses under a wide range of non-null conditions.

scholarly journals CMET-07. TUMOR RELATED IMPAIRMENTS OF NEUROCOGNITIVE FUNCTIONS IN PATIENTS WITH BRAIN METASTASES

2019 ◽  
Vol 21 (Supplement_6) ◽  
pp. vi52-vi52
Author(s):  
Junjie Zhen ◽  
Shaoqun Li ◽  
Zhangrui Peng ◽  
Lei Wen ◽  
Mingyao Lai ◽  
...  
Keyword(s):  
Risk Factors ◽  
Multivariate Analysis ◽  
Brain Metastases ◽  
Physical Examination ◽  
Univariate Analysis ◽  
Neurocognitive Impairment ◽  
Neurocognitive Functions ◽  
Neurocognitive Assessment ◽  
Wide Range ◽  
Assessment Results

Abstract OBJECTIVE To study whether the neurocognitive functions were affected by brain metastases in patients, and what are the potential risk factors. METHODS A total of 172 patients with brain metastases were retrospectively analyzed. Prior to radiotherapy of brain metastases, the neurocognitive functions were evaluated by a wide range of tests including MOCA, VFT, HVLT-R, TMT-A, TMT-B and TOL. Kappa test was used to analyze the consistency of physical examination and neurocognitive assessment results. The related factors were analyzed with univariate and multivariate analysis. RESULTS 53 out of 172 patients (30.8%) were identified with cognitive impairments by physical examination. The assessment with neurocognitive scales revealed that there were 148 cases of cognitive impairment (86.0%) and 24 cases of normal cognition (14.0%). Kappa=0.025, indicating that the difference between neurocognitive assessment results and physical examination was significant. The univariate analysis on the factors related to neurocognitive impairment revealed that the risk factors that may affect the neurocognitive functions included age, KPS, m-GPA score, RPA classification, whether the original tumor was under control, with or without brain metastases. After adjusting for education, the multivariate analysis showed that age≥45 years old, KPS≤70, RPA classification >2 and m-GPA score< 3 were independent risk factors for neurocognitive impairment. CONCLUSION Patients with brain metastases were found to have various degrees of neurocognitive impairment prior to radiotherapy. The neurocognitive functions of patients can be more precisely evaluated by a comprehensive scale assessment. Age, KPS, RPA classification and m-GPA score are the main factors associated with neurocognitive impairment.

Repeated-Measures Designs: Univariate or Multivariate Analysis of Variance?

1997 ◽  
Vol 85 (1) ◽  
pp. 193-194
Author(s):  
Peter Hassmén
Keyword(s):  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Repeated Measures ◽  
Type I Error ◽  
Univariate Analysis ◽  
Type I ◽  
Multivariate Analysis Of Variance ◽  
Repeated Measures Analysis ◽  
Alpha Level ◽  
Repeated Measures Designs

Violation of the sphericity assumption in repeated-measures analysis of variance can lead to positively biased tests, i.e., the likelihood of a Type I error exceeds the alpha level set by the user. Two widely applicable solutions exist, the use of an epsilon-corrected univariate analysis of variance or the use of a multivariate analysis of variance. It is argued that the latter method offers advantages over the former.

scholarly journals Comparative evaluation of goodness of fit tests for normal distribution using simulation and empirical data

2020 ◽  
Vol 57 (2) ◽  
pp. 237-251
Author(s):  
Achilleas Anastasiou ◽  
Alex Karagrigoriou ◽  
Anastasios Katsileros
Keyword(s):  
Sample Size ◽  
Normal Distribution ◽  
Empirical Data ◽  
Goodness Of Fit ◽  
Small Sample Size ◽  
Small Sample ◽  
Type I ◽  
Sample Sizes ◽  
Omnibus Test ◽  
Wide Range

SummaryThe normal distribution is considered to be one of the most important distributions, with numerous applications in various fields, including the field of agricultural sciences. The purpose of this study is to evaluate the most popular normality tests, comparing the performance in terms of the size (type I error) and the power against a large spectrum of distributions with simulations for various sample sizes and significance levels, as well as through empirical data from agricultural experiments. The simulation results show that the power of all normality tests is low for small sample size, but as the sample size increases, the power increases as well. Also, the results show that the Shapiro–Wilk test is powerful over a wide range of alternative distributions and sample sizes and especially in asymmetric distributions. Moreover the D’Agostino–Pearson Omnibus test is powerful for small sample sizes against symmetric alternative distributions, while the same is true for the Kurtosis test for moderate and large sample sizes.

scholarly journals Repeated measures in randomized block and split-plot experiments

1993 ◽  
Vol 23 (4) ◽  
pp. 625-639 ◽  
Author(s):  
M.L. Gumpertz ◽  
C. Brownie
Keyword(s):  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Loblolly Pine ◽  
Repeated Measures ◽  
Univariate Analysis ◽  
Complete Analysis ◽  
Phosphorus Fertilization ◽  
Multivariate Analysis Of Variance ◽  
Repeated Measures Data ◽  
Split Plot

Randomized block and split-plot designs are among the most commonly used experimental designs in forest research. Measurements for plots in a block (or subplots in a whole plot) are correlated with each other, and these correlations must be taken into account when analyzing repeated-measures data from blocked designs. The analysis is similar to repeated-measures analysis for a completely randomized design, but test statistics must allow for random block × time effects, and standard errors for treatment means must also incorporate block to block variation and variation among plots within a block. Two types of statistical analysis are often recommended for repeated-measures data: analysis of contrasts of the repeated factor and multivariate analysis of variance. A complete analysis of repeated measures should usually contain both of these components, just as in univariate analysis of variance it is often necessary to decompose the main effects into single degree of freedom contrasts to answer the research objectives. We demonstrate the multivariate analysis of variance and the analysis of contrasts in detail for two experiments. In addition, estimation of coefficients assuming a polynomial growth curve is discussed in detail for one of these experiments. The first experiment, a randomized complete block design, is a forest nutrition study of the long-term effects of midrotation nitrogen and phosphorus fertilization on loblolly pine (Pinustaeda L.); the second experiment, a split-plot design, is an air-pollution study of the effects of ozone and acid precipitation on loblolly pine growth.

Freudian Symbols on Sexual and Creative Aspects of Stories

1998 ◽  
Vol 82 (3) ◽  
pp. 1059-1072
Author(s):  
Constance J. Larson
Keyword(s):  
College Students ◽  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Repeated Measures ◽  
Univariate Analysis ◽  
Visual Presentation ◽  
Pairwise Comparisons ◽  
Sexual Content ◽  
Multivariate Analysis Of Variance

Sexual content and creativity of stories and story titles was investigated. 96 college students responded to visual presentation of instances of theoretical Freudian symbols. Analyses subjected responses to a 2 (sex) × 2 (symbol) × 2 (mode) × 6 (subscales) analysis of variance with repeated measures on subscales and to multivariate analysis of variance procedures with four dependent measures. These showed men wrote masculine stories and women wrote feminine stories. Certain subscales were more sensitive to sexual content than others. Pairwise comparisons between the subscales among instances of symbols emerged as significant. In addition, subjects exposed to Male symbols wrote stories containing greater latent sexual content than subjects exposed to Female symbols. Creativity of story tides was evident only on a univariate analysis of variance.

Sample Size Effects on Chi Square and Other Statistics Used in Evaluating Causal Models

1982 ◽  
Vol 19 (4) ◽  
pp. 425-430 ◽  
Author(s):  
William O. Bearden ◽  
Subhash Sharma ◽  
Jesse E. Teel
Keyword(s):  
Sample Size ◽  
Simulation Study ◽  
Size Effects ◽  
Causal Models ◽  
Sample Sizes ◽  
Chi Square ◽  
True Value ◽  
Wide Range ◽  
Complex Models ◽  
Simple Models

A simulation study of the effects of sample size on the overall fit statistic provided by the LISREL program indicates the statistic is well behaved over a wide range of sample sizes for simple models. However, this statistic is apparently not chi square distributed for more complex models when samples are relatively small, and will reject the hypothesized model too often. A set of additional measures suggested by various researchers for evaluating causal models also is examined. These statistics are well behaved for both models tested as they converge to the true value and their variance approaches zero as sample size increases.

scholarly journals OTHR-11. TUMOR RELATED IMPAIRMENTS OF NEUROCOGNITIVE FUNCTIONS IN PATIENTS WITH BRAIN METASTASES

2019 ◽  
Vol 1 (Supplement_1) ◽  
pp. i20-i20
Author(s):  
Junjie Zhen ◽  
Shaoqun Li ◽  
Lei Wen ◽  
Zhangrui Peng ◽  
Mingyao Lai ◽  
...  
Keyword(s):  
Risk Factors ◽  
Multivariate Analysis ◽  
Brain Metastases ◽  
Physical Examination ◽  
Univariate Analysis ◽  
Neurocognitive Impairment ◽  
Neurocognitive Functions ◽  
Neurocognitive Assessment ◽  
Wide Range ◽  
Assessment Results

Abstract OBJECTIVE: To study whether the neurocognitive functions were affected by brain metastases in patients, and what are the potential risk factors. METHODS: A total of 172 patients with brain metastases were retrospectively analyzed. Prior to radiotherapy of brain metastases, the neurocognitive function was evaluated by a wide range of tests including MOCA, VFT, HVLT-R, TMT-A, TMT-B and TOL. Kappa test was used to analyze the consistency of physical examination and neurocognitive assessment results. The related factors were analyzed with univariate and multivariate analysis. RESULTS: 53 out of 172 patients (30.8%) were identified with cognitive impairments by physical examination. The assessment with neurocognitive scales revealed that there were 148 cases of cognitive impairment (86.0%) and 24 cases of normal cognition (14.0%). Kappa=0.025, indicating that the difference between neurocognitive assessment results and physical examination was significant. The univariate analysis on the factors related to neurocognitive impairment revealed that the risk factors that may affect the neurocognitive functions included age, KPS, m-GPA score, RPA classification, whether the original tumor was under control, with or without brain metastases. After adjusting for education, the multivariate analysis showed that age≥45 years old, KPS≤70, RPA classification >2 and m-GPA score< 3 were independent risk factors for neurocognitive impairment. CONCLUSION: Patients with brain metastases were found to have various degrees of neurocognitive impairment prior to radiotherapy. The neurocognitive functions of patients can be more precisely evaluated by a comprehensive scale assessment. Age, KPS, RPA classification and m-GPA score are the main factors associated with neurocognitive impairment.

scholarly journals The risk of incomplete functional recovery and sustained disability in patients treated in an integrated stroke unit

2019 ◽  
Vol 27 (1) ◽  
pp. 21-31
Author(s):  
Yu.V. Flomin
Keyword(s):  
Risk Factors ◽  
Multivariate Analysis ◽  
Functional Recovery ◽  
Stroke Unit ◽  
Univariate Analysis ◽  
Stroke Onset ◽  
Stroke Severity ◽  
Nihss Score ◽  
Wide Range ◽  
Stroke Type

Objective – to identify factors that are associated with incomplete functional recovery or sustained disability in patients managed at a Comprehensive Stroke Unit (CSU).Materials and methods. We included 764 patients (41.7 % of women) aged from 20 to 95 years (median – 66 years, interquartile interval 57–75 years), who were in period from 2010 to 2018 admitted to our Stroke Center (SC) operating as a CSU. Upon admission all participants were examined by a Neurologist. Work-up and treatment were in line with recommendations of clinical guidelines. Ischemic stroke was diagnosed in 80.5 % of the patients, hemorrhagic stroke – in 19.5 %. Univariate and multivariate analyses were performed. The functional state was assessed using a modified Rankin scale (MRS). We The considered that the desired outcome was achieved if, at the time of discharge from the hospital, the initial MRS score decreased by ≥ 2 or reached ≤ 2.Results. The baseline NIHSS score ranged from 0 to 39 (median – 10, interquartile interval 6–17). 17.5 % of patients were admitted to our SC in the 1st day, 19.0 % – between 2 and 7 days, 7.5 % – between 8 and 14 days, 14.7 % – between 15 and 30 days, 10.3 % – between 31 and 60 days, 13.0 % – between 61 and 180 days, and 18.0 % – later than 180 days after the stroke onset. According to the univariate analysis, the risk of not achieving the desired outcome was associated with many factors: stroke type and subtype, the patient’s age, time delay before SC admission, the initial severity of stroke, cognitive impairment, limitations of mobility and ADLs, the presence and severity of certain types of neurological deficit, in addition to certain vascular risk factors (atrial fibrillation, smo-king) and signs of inflammation (increased erythrocyte sedimentation rate and C-reactive protein) on admission. Multivariate analysis revealed 4 independent predictors that are strongly associated with the lack of the desired functional outcome: patient age (odds ratio (OR) – 1.03, on average, for each additional year), initial stroke severity (after adjustment to the rest of factors, OR – 1.05, on average, for each additional point of the baseline NIHSS score), global disability on admission (OR – 2.3, on average for each point of the initial MRS score) and the time from stroke onset to the SC admission (compared with a shorter delay, OR – 3.3–4.2, if the patient was hospitalized between 15 and 180 days from the onset, OR – 9.2 if admitted later than 6 months after the onset). The area under the curve of operational characteristics – 0.92 (95 % CI 0.89–0.94) proved the excellent quality of the prediction model and the strong link of this set of factors to the risk of incomplete functional recovery at the time of discharge.Conclusions. According to the results of univariate analysis, the risk of incomplete functional recovery and sustained disability after treatment is associated with a wide range of factors, such as stroke type and subtype, severity of neurological and cognitive deficit, activities limitations, certain risk factors and laboratory abnormalities. Multivariate analysis identified 4 independent predictors of sustained disability, which may help us better predict the length of stay and the outcome of treatment.

scholarly journals Association between schizophrenia and an autoimmune bullous skin disease-pemphigus: a population-based large-scale study

2017 ◽  
Vol 28 (2) ◽  
pp. 191-198 ◽  
Author(s):  
K. Kridin ◽  
S. Zelber-Sagi ◽  
D. Comaneshter ◽  
A. D. Cohen
Keyword(s):  
Multivariate Analysis ◽  
Large Scale ◽  
Matched Control ◽  
Univariate Analysis ◽  
Real Life ◽  
Population Based ◽  
Cross Sectional Study ◽  
Control Group ◽  
Cross Sectional ◽  
Wide Range

Aims.Immunological hypotheses have become increasingly prominent suggesting that autoimmunity may be involved in the pathogenesis of schizophrenia. Schizophrenia was found to be associated with a wide range of autoimmune diseases. However, the association between pemphigus and schizophrenia has not been established yet. We aimed to estimate the association between pemphigus and schizophrenia using a large-scale real-life computerised database.Methods.This study was conducted as a cross-sectional study utilising the database of Clalit Health Services. The proportion of schizophrenia was compared between patients diagnosed with pemphigus and age-, gender- and ethnicity-matched control subjects. Univariate analysis was performed usingχ2and Student'st-test and a multivariate analysis was performed using a logistic regression model.Results.A total of 1985 pemphigus patients and 9874 controls were included in the study. The prevalence of schizophrenia was greater in patients with pemphigus as compared to the control group (2.0%v. 1.3%, respectively;p= 0.019). In a multivariate analysis, pemphigus was significantly associated with schizophrenia (OR, 1.5; 95% CI, 1.1–2.2). The association was more prominent among females, patients older than 60 years, and Jews.Conclusions.Pemphigus is significantly associated with schizophrenia. Physicians treating patients with pemphigus should be aware of this possible association. Patients with pemphigus should be carefully assessed for comorbid schizophrenia and be treated appropriately.

scholarly journals Hyperbolic trade-off: the importance of balancing trial and subject sample sizes in neuroimaging

2021 ◽  
Author(s):  
Gang Chen ◽  
Daniel S Pine ◽  
Melissa A Brotman ◽  
Ashley R Smith ◽  
Robert W Cox ◽  
...  
Keyword(s):  
Experimental Design ◽  
Sample Size ◽  
Hierarchical Modeling ◽  
Cognitive Task ◽  
Parameter Estimates ◽  
Effect Estimate ◽  
Sample Sizes ◽  
Statistical Efficiency ◽  
Behavioral Studies ◽  
Wide Range

Big data initiatives have gained popularity for leveraging a large sample of subjects to study a wide range of effect magnitudes in the brain. On the other hand, most task-based FMRI designs feature relatively small number of subjects, so that resulting parameter estimates may be associated with compromised precision. Nevertheless, little attention has been given to another important dimension of experimental design, which can equally boost a study's statistical efficiency: the trial sample size. Here, we systematically explore the different factors that impact effect uncertainty, drawing on evidence from hierarchical modeling, simulations and an FMRI dataset of 42 subjects who completed a large number of trials of a commonly used cognitive task. We find that, due to the presence of relatively large cross-trial variability: 1) trial sample size has nearly the same impact as subject sample size on statistical efficiency; 2) increasing both trials and subjects improves statistical efficiency more effectively than focusing on subjects alone; 3) trial sample size can be leveraged with the number of subjects to improve the cost-effectiveness of an experimental design; 4) for small trial sample sizes, rather than the common practice of condition-level modeling through summary statistics, trial-level modeling may be necessary to accurately assess the standard error of an effect estimate. Lastly, we make practical recommendations for improving experimental designs across neuroimaging and behavioral studies.

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