Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data

Hu, Zongliang; Tong, Tiejun; Genton, Marc G.

doi:10.1111/biom.12984

Cited by 12 publications

(8 citation statements)

References 37 publications

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“…Our optimized number of trajectories were further confirmed by EC as applied on clustering results provided by PCA + KMA. We also applied a statistical test, HTST, described in Appendix 1 (105) to measure similarities between sub-clusters. Subsequently, in stage two of our efforts (supervised task), prediction of the identified trajectories based on early years (data in year 0 and 1) was performed using multiple HMLSs, including 16 FEAs coupled to 10 CAs, as enlisted previously.…”

Section: Analysis Proceduresmentioning

confidence: 99%

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Longitudinal clustering analysis and prediction of Parkinson’s disease progression using radiomics and hybrid machine learning

Salmanpour¹,

Shamsaei²,

Hajianfar³

et al. 2022

Quant Imaging Med Surg

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Background: We employed machine learning approaches to (I) determine distinct progression trajectories in Parkinson's disease (PD) (unsupervised clustering task), and (II) predict progression trajectories (supervised prediction task), from early (years 0 and 1) data, making use of clinical and imaging features.Methods: We studied PD-subjects derived from longitudinal datasets (years 0, 1, 2 & 4; Parkinson's Progressive Marker Initiative). We extracted and analyzed 981 features, including motor, non-motor, and radiomics features extracted for each region-of-interest (ROIs: left/right caudate and putamen) using our standardized standardized environment for radiomics analysis (SERA) radiomics software. Segmentation of ROIs on dopamine transposer -single photon emission computed tomography (DAT SPECT) images were performed via magnetic resonance images (MRI). After performing cross-sectional clustering on 885 subjects (original dataset) to identify disease subtypes, we identified optimal longitudinal trajectories using hybrid machine learning systems (HMLS), including principal component analysis (PCA) + K-Means algorithms (KMA) followed by Bayesian information criterion (BIC), Calinski-Harabatz criterion (CHC), and elbow criterion (EC). Subsequently, prediction of the identified trajectories from early year data was performed using multiple HMLSs including 16 Dimension Reduction Algorithms (DRA) and 10 classification algorithms.Results: We identified 3 distinct progression trajectories. Hotelling's t squared test (HTST) showed that the identified trajectories were distinct. The trajectories included those with (I, II) disease escalation (2 trajectories, 27% and 38% of patients) and (III) stable disease (1 trajectory, 35% of patients). For trajectory prediction from early year data, HMLSs including the stochastic neighbor embedding algorithm (SNEA, as a DRA) as well as locally linear embedding algorithm (LLEA, as a DRA), linked with the new probabilistic neural network classifier (NPNNC, as a classifier), resulted in accuracies of 78.4% and 79.2% respectively, while other HMLSs such as SNEA + Lib_SVM (library for support vector machines) and t_SNE (t-distributed stochastic neighbor embedding) + NPNNC resulted in 76.5% and 76.1% respectively.Conclusions: This study moves beyond cross-sectional PD subtyping to clustering of longitudinal disease trajectories. We conclude that combining medical information with SPECT-based radiomics features, and optimal utilization of HMLSs, can identify distinct disease trajectories in PD patients, and enable effective prediction of disease trajectories from early year data.

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Section: Analysis Proceduresmentioning

confidence: 99%

“…P n n T T + − ≥. Note that rejecting the null hypothesis concludes that at least one pair of the p sets of group response means are unequal(105).…”

mentioning

confidence: 97%

Longitudinal clustering analysis and prediction of Parkinson’s disease progression using radiomics and hybrid machine learning

Salmanpour¹,

Shamsaei²,

Hajianfar³

et al. 2022

Quant Imaging Med Surg

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“…For ease of presentation, we conduct simulation studies for the twosample test only. We also consider seven other tests for comparison: the unscaled Hotelling's tests including CQ from Chen and Qin (2010) and aSUP from Xu et al (2016); the diagonal Hotelling's tests including PA from Park and Ayyala (2013), GCT from Gregory et al (2015), and DLRT from Hu et al (2019); the composite Hotelling's test CHT from Li (2017); and the regularized Hotelling's test RMPBT from Zoh et al (2018).…”

Section: Monte Carlo Simulation Studiesmentioning

confidence: 99%

“…t are generated from a heavy-tailed distribution to examine the robustness of the proposed tests. Following Gregory et al (2015) and Hu et al (2019), we consider a "double" Pareto distribution with parameters a > 0 and b > 0. The detailed algorithm is as follows:…”

Section: Heavy-tailed Datamentioning

confidence: 99%

“…Cai et al (2014) considered a test based on the maximum of the squared marginal t statistics. Hu et al (2019) proposed a likelihood ratio test based on a diagonal covariance matrix structure. Feng et al (2017) grouped the covariates into many small blocks, and then under the assumption that there is little correlation between these blocks, they constructed their test statistic as the summation of Hotelling's T 2 statistics within each small block.…”

Section: Introductionmentioning

confidence: 99%

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A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors

Hu¹,

Tong²,

Genton³

2020

Preprint

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For high-dimensional small sample size data, Hotelling's T 2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the literature. Note, however, that each of the existing approaches may have serious limitations and only works well in certain situations. Inspired by this, we propose a pairwise Hotelling method for testing high-dimensional mean vectors, which, in essence, provides a good balance between the existing approaches. To effectively utilize the correlation information, we construct the new test statistics as the summation of Hotelling's test statistics for the covariate pairs with strong correlations and the squared t statistics for the individual covariates that have little correlation with others. We further derive the asymptotic null distributions and power functions for the proposed Hotelling tests under some regularity conditions. Numerical results show that our new tests are able to control the type I error rates, and can achieve a higher statistical power compared to existing methods, especially when the covariates are highly correlated. Two real data examples are also analyzed and they both demonstrate the efficacy of our pairwise Hotelling tests.

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Standardized Dempster's non‐exact test for high‐dimensional mean vectors

Fang

Chen

et al. 2022

Stat

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Although the Hotelling's T2 test has been a widely used test for hypothesis testing problems on the mean vectors, it is not well defined when the data dimension is larger than the sample size. Dempster's non‐exact test, as a remedy for the Hotelling's T2 test, is known to be more powerful than the Hotelling's T2 test and is well defined even when the dimension is much larger than the sample size. However, Dempster's non‐exact test will lose power when the variances of the covariates are different. In this paper, we propose a standardized Dempster's non‐exact test for the classical mean testing problem. The proposed test is more powerful for data with heteroscedastic features and is applicable to the high‐dimensional case. An approximate distribution of the test statistic has been established, and to better control the type I error rate when the sample size is small, we further constructed a Monte Carlo version of the proposed standardized Dempster's non‐exact test. Various simulation studies and a real data application were conducted with comparison to other popular tests. The numerical results showed that while the type I error rates were well controlled, the testing power of our proposed test was generally higher than those of other tests.

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Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data

Cited by 12 publications

References 37 publications

Longitudinal clustering analysis and prediction of Parkinson’s disease progression using radiomics and hybrid machine learning

Longitudinal clustering analysis and prediction of Parkinson’s disease progression using radiomics and hybrid machine learning

A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors

Standardized Dempster's non‐exact test for high‐dimensional mean vectors

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