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A Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.

ABSTRACT: In contrast to the classical "one size fits all" approach, precision medicine proposes the customization of individualized treatment regimes to account for patients' heterogeneity in response to treatments. Most of existing works in the literature focused on estimating optimal individualized treatment regimes. However, there has been less attention devoted to hypothesis testing regarding the existence of overall qualitative treatment effects, especially when there is a large number of prognostic covariates. When covariates don't have qualitative treatment effects, the optimal treatment regime will assign the same treatment to all patients regardless of their covariate values. In this paper, we consider testing the overall qualitative treatment effects of patients' prognostic covariates in a high dimensional setting. We propose a sample splitting method to construct the test statistic, based on a nonparametric estimator of the contrast function. When the dimension of covariates is large, we construct the test based on sparse random projections of covariates into a low-dimensional space. We prove the consistency of our test statistic. In the regular cases, we show the asymptotic power function of our test statistic is asymptotically the same as the "oracle" test statistic which is constructed based on the "optimal" projection matrix. Simulation studies and real data applications validate our theoretical findings.

SUBMITTER: Shi C

PROVIDER: S-EPMC7730172 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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A Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.

Shi Chengchun C Lu Wenbin W Song Rui R

Journal of the American Statistical Association 20190619 531

In contrast to the classical "one size fits all" approach, precision medicine proposes the customization of individualized treatment regimes to account for patients' heterogeneity in response to treatments. Most of existing works in the literature focused on estimating optimal individualized treatment regimes. However, there has been less attention devoted to hypothesis testing regarding the existence of overall qualitative treatment effects, especially when there is a large number of prognostic ...[more]

PMID: 33311818

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Project description:BackgroundComputed tomography (CT) is an advanced medical imaging technology. The images obtained by CT are helpful for improving diagnostic accuracy. Currently, CT is widely used in clinical settings for diagnosis and health examinations. However, full angle CT scanning has the disadvantage of causing radiation damage to the human body. Sparse angle projection CT scanning is the most effective way to minimize this damage, but the quality of the reconstructed image is reduced. Therefore, it is important to improve the reconstructed image quality produced by sparse angle projection.MethodsIn this paper, we focused on the algebraic reconstruction algorithm. To reduce the accumulation of random noise, we formulated a modified algebraic reconstruction algorithm. Firstly, the algebraic reconstruction algorithm was used to compute two consecutive results, and then the weighted sum of these two results was used to correct the reconstructed image, and an iterative result was obtained. Using this method, we aimed to reduce the noise accumulation caused by iteration.ResultsIn this study, 20 angle projections were used for the reconstruction. The experimental object was the Shepp-Logan phantom test image. The experiments were implemented under two conditions: without noise and with noise. The peak signal to noise ratio (PSNR) and the mean squared error (MSE) of the reconstructed image from projections without noise were 76.0896 and 0.0016, respectively. The PSNR and MSE of the reconstructed image from projections with noise were 75.8263 and 0.0017, respectively. The reconstructed performance was superior to the previous algebraic reconstruction algorithm.ConclusionsThe performance of the proposed method was superior to other algorithms, which confirms that noise accumulation caused by iteration can be effectively reduced by the weighted summation of two consecutive reconstruction results. Moreover, the reconstruction performance under noisy projection is superior to other algorithms, which demonstrates that the proposed method improves anti-noise performance.

Project description:BackgroundFor dichotomous traits, the generalized disequilibrium test with the moment estimate of the variance (GDT-ME) is a powerful family-based association method. Genomic imprinting is an important epigenetic phenomenon and currently, there has been increasing interest of incorporating imprinting to improve the test power of association analysis. However, GDT-ME does not take imprinting effects into account, and it has not been investigated whether it can be used for association analysis when the effects indeed exist.ResultsIn this article, based on a novel decomposition of the genotype score according to the paternal or maternal source of the allele, we propose the generalized disequilibrium test with imprinting (GDTI) for complete pedigrees without any missing genotypes. Then, we extend GDTI and GDT-ME to accommodate incomplete pedigrees with some pedigrees having missing genotypes, by using a Monte Carlo (MC) sampling and estimation scheme to infer missing genotypes given available genotypes in each pedigree, denoted by MCGDTI and MCGDT-ME, respectively. The proposed GDTI and MCGDTI methods evaluate the differences of the paternal as well as maternal allele scores for all discordant relative pairs in a pedigree, including beyond first-degree relative pairs. Advantages of the proposed GDTI and MCGDTI test statistics over existing methods are demonstrated by simulation studies under various simulation settings and by application to the rheumatoid arthritis dataset. Simulation results show that the proposed tests control the size well under the null hypothesis of no association, and outperform the existing methods under various imprinting effect models. The existing GDT-ME and the proposed MCGDT-ME can be used to test for association even when imprinting effects exist. For the application to the rheumatoid arthritis data, compared to the existing methods, MCGDTI identifies more loci statistically significantly associated with the disease.ConclusionsUnder complete and incomplete imprinting effect models, our proposed GDTI and MCGDTI methods, by considering the information on imprinting effects and all discordant relative pairs within each pedigree, outperform all the existing test statistics and MCGDTI can recapture much of the missing information. Therefore, MCGDTI is recommended in practice.

Dataset Information

A Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.

Publications

A Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.

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