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The nature of the recovery process of posttraumatic stress disorder (PTSD) symptoms is multifactorial. The Massive Parallel Limitless-Arity Multiple-testing Procedure (MP-LAMP), which was developed to detect significant combinational risk factors comprehensively, was utilized to reveal hidden combinational risk factors to explain the long-term trajectory of the PTSD symptoms. In 624 population-based subjects severely affected by the Great East Japan Earthquake, 61 potential risk factors encompassing sociodemographics, lifestyle, and traumatic experiences were analyzed by MP-LAMP regarding combinational associations with the trajectory of PTSD symptoms, as evaluated by the Impact of Event Scale-Revised score after eight years adjusted by the baseline score. The comprehensive combinational analysis detected 56 significant combinational risk factors, including 15 independent variables, although the conventional bivariate analysis between single risk factors and the trajectory detected no significant risk factors. The strongest association was observed with the combination of short resting time, short walking time, unemployment, and evacuation without preparation (adjusted P value = 2.2 × 10−4, and raw P value = 3.1 × 10−9). Although short resting time had no association with the poor trajectory, it had a significant interaction with short walking time (P value = 1.2 × 10−3), which was further strengthened by the other two components (P value = 9.7 × 10−5). Likewise, components that were not associated with a poor trajectory in bivariate analysis were included in every observed significant risk combination due to their interactions with other components. Comprehensive combination detection by MP-LAMP is essential for explaining multifactorial psychiatric symptoms by revealing the hidden combinations of risk factors.

To solve major limitations in algorithms for the metabolite-based prediction of psychiatric phenotypes, a novel prediction model for depressive symptoms based on nonlinear feature selection machine learning, the Hilbert–Schmidt independence criterion least absolute shrinkage and selection operator (HSIC Lasso) algorithm, was developed and applied to a metabolomic dataset with the largest sample size to date. In total, 897 population-based subjects were recruited from the communities affected by the Great East Japan Earthquake; 306 metabolite features (37 metabolites identified by nuclear magnetic resonance measurements and 269 characterized metabolites based on the intensities from mass spectrometry) were utilized to build prediction models for depressive symptoms as evaluated by the Center for Epidemiologic Studies-Depression Scale (CES-D). The nested fivefold cross-validation was used for developing and evaluating the prediction models. The HSIC Lasso-based prediction model showed better predictive power than the other prediction models, including Lasso, support vector machine, partial least squares, random forest, and neural network. l-leucine, 3-hydroxyisobutyrate, and gamma-linolenyl carnitine frequently contributed to the prediction. We have demonstrated that the HSIC Lasso-based prediction model integrating nonlinear feature selection showed improved predictive power for depressive symptoms based on metabolome data as well as on risk metabolites based on nonlinear statistics in the Japanese population. Further studies should use HSIC Lasso-based prediction models with different ethnicities to investigate the generality of each risk metabolite for predicting depressive symptoms.

Functional connectivity (FC) and neural excitability may interact to affect symptoms of autism spectrum disorder (ASD). We tested this hypothesis with neural network simulations, and applied it with functional magnetic resonance imaging (fMRI). A hierarchical recurrent neural network embodying predictive processing theory was subjected to a facial emotion recognition task. Neural network simulations examined the effects of FC and neural excitability on changes in neural representations by developmental learning, and eventually on ASD-like performance. Next, by mapping each neural network condition to subject subgroups on the basis of fMRI parameters, the association between ASD-like performance in the simulation and ASD diagnosis in the corresponding subject subgroup was examined. In the neural network simulation, the more homogeneous the neural excitability of the lower-level network, the more ASD-like the performance (reduced generalization and emotion recognition capability). In addition, in homogeneous networks, the higher the FC, the more ASD-like performance, while in heterogeneous networks, the higher the FC, the less ASD-like performance, demonstrating that FC and neural excitability interact. As an underlying mechanism, neural excitability determines the generalization capability of top-down prediction, and FC determines whether the model’s information processing will be top-down prediction-dependent or bottom-up sensory-input dependent. In fMRI datasets, ASD was actually more prevalent in subject subgroups corresponding to the network condition showing ASD-like performance. The current study suggests an interaction between FC and neural excitability, and presents a novel framework for computational modeling and biological application of a developmental learning process underlying cognitive alterations in ASD.

BackgroundBiobanks increasingly collect, process and store omics with more conventional epidemiologic information necessitating considerable effort in data cleaning. An efficient outlier detection method that reduces manual labour is highly desirable.MethodWe develop an unsupervised machine-learning method for outlier detection, namely kurPCA, that uses principal component analysis combined with kurtosis to ascertain the existence of outliers. In addition, we propose a novel regression adjustment approach to improve detection, namely the regression adjustment for data by systematic missing patterns (RAMP).ResultApplication to epidemiological record data in a large-scale biobank (Tohoku Medical Megabank Organization, Japan) shows that a combination of kurPCA and RAMP effectively detects known errors or inconsistent patterns.ConclusionsWe confirm through the results of the simulation and the application that our methods showed good performance. The proposed methods are useful for many practical analysis scenarios.

BackgroundAutism spectrum disorder (ASD) has phenotypically and genetically heterogeneous characteristics. A simulation study demonstrated that attempts to categorize patients with a complex disease into more homogeneous subgroups could have more power to elucidate hidden heritability.MethodsWe conducted cluster analyses using the k-means algorithm with a cluster number of 15 based on phenotypic variables from the Simons Simplex Collection (SSC). As a preliminary study, we conducted a conventional genome-wide association study (GWAS) with a dataset of 597 ASD cases and 370 controls. In the second step, we divided cases based on the clustering results and conducted GWAS in each of the subgroups vs controls (cluster-based GWAS). We also conducted cluster-based GWAS on another SSC dataset of 712 probands and 354 controls in the replication stage.ResultsIn the preliminary study, we observed no significant associations. In the second step of cluster-based GWASs, we identified 65 chromosomal loci, which included 30 intragenic loci located in 21 genes and 35 intergenic loci that satisfied the threshold of P−8. Some of these loci were located within or near previously reported candidate genes for ASD: CDH5, CNTN5, CNTNAP5, DNAH17, DPP10, DSCAM, FOXK1, GABBR2, GRIN2A5, ITPR1, NTM, SDK1, SNCA and SRRM4. Of these 65 significant chromosomal loci, rs11064685 located within the SRRM4 gene had a significantly different distribution in the cases vs. controls in the replication cohort.ConclusionsThese findings suggest that clustering may successfully identify subgroups with relatively homogeneous disease etiologies. Further cluster validation and replication studies are warranted in larger cohorts.

The fused lasso penalizes a loss function by the $L_1$ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed into the difference of successive regression coefficients. The proposed method enables us to construct a more versatile sparse model than the ordinary fused lasso by using a flexible regularization term. We also propose a sparse fused algorithm to produce exact sparse solutions. Simulation studies and real data analyses show that the proposed method has superior performance to the ordinary fused lasso., Comment: 26 pages

Genome-wide association studies (GWASs) commonly use marginal association tests for each single nucleotide polymorphism (SNP). Because these tests treat SNPs as independent, their power will be suboptimal for detecting SNPs hidden by linkage disequilibrium (LD). One way to improve power is to use a multiple regression model. However, the large number of SNPs preclude simultaneous fitting with multiple regression, and subset regression is infeasible because of an exorbitant number of candidate subsets. We therefore propose a new method for detecting hidden SNPs having significant yet weak marginal association in a multiple regression model. Our method begins by constructing a bi-directed graph locally around each SNP that demonstrates a moderately sized marginal association signal, the focal SNPs. Vertexes correspond to SNPs, and adjacency between vertexes is defined by an LD measure. Subsequently, the method collects from each graph all shortest paths to the focal SNP. Finally, for each shortest path the method fits a multiple regression model to all of the SNPs lying in the path and tests the significance of the regression coefficient corresponding to the terminal SNP in the path. Simulation studies show that the proposed method can detect susceptibility SNPs hidden by LD that go undetected with marginal-association testing or with existing multivariate methods, including lasso. When applied to real GWAS data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), our method detected two groups of SNPs: one in a region containing the apolipoprotein E (APOE) gene, and another in a region close to the semaphorin 5A (SEMA5A) gene.

The first step towards realizing personalized healthcare is to catalog the genetic variations in a population. Since the dissemination of individual-level genomic information is strictly controlled, it will be useful to construct population-level allele frequency panels with easy-to-use interfaces. In the Tohoku Medical Megabank Project, we sequenced nearly 4000 individuals from a Japanese population and constructed an allele frequency panel of 3552 individuals after removing related samples. The panel is called the 3.5KJPNv2. It was constructed by using a standard pipeline including the 1KGP and gnomAD algorithms to reduce technical biases and to allow comparisons to other populations. Our database is the first large-scale panel providing the frequencies of variants present on the X chromosome and on the mitochondria in the Japanese population. All the data are available on our original database at https://jmorp.megabank.tohoku.ac.jp., Population genetics: large database of Japanese gene variations constructed A new database provides information on the frequency of genetic variations within 3552 Japanese individuals, and facilitates comparisons with other populations. The reference panel, constructed by Kengo Kinoshita of Tohoku University, Sendai, and colleagues in Japan is also the first large-scale database to provide genetic variation frequency information on the X chromosome and mitochondrial DNA in the Japanese population. The methods used to sequence the genetic data are similar to those used in other large databases, allowing comparisons with other populations. The population size and methods used to compile the database overcome limitations in previous Japanese reference panels. This and similar databases that catalog genetic variations within populations can improve efforts towards personalizing healthcare and contribute to the study of human population genetics. The database is publicly available online.

We develop a new genetic prediction method, smooth-threshold multivariate genetic prediction, using single nucleotide polymorphisms (SNPs) data in genome-wide association studies (GWASs). Our method consists of two stages. At the first stage, unlike the usual discontinuous SNP screening as used in the gene score method, our method continuously screens SNPs based on the output from standard univariate analysis for marginal association of each SNP. At the second stage, the predictive model is built by a generalized ridge regression simultaneously using the screened SNPs with SNP weight determined by the strength of marginal association. Continuous SNP screening by the smooth-thresholding not only makes prediction stable but also leads to a closed form expression of generalized degrees of freedom (GDF). The GDF leads to the Stein’s unbiased risk estimation (SURE) which enables data-dependent choice of optimal SNP screening cutoff without using cross-validation. Our method is very rapid because computationally expensive genome-wide scan is required only once in contrast to the penalized regression methods including lasso and elastic net. Simulation studies which mimic real GWAS data with quantitative and binary traits demonstrate that the proposed method outperforms the gene score method and genomic best linear unbiased prediction (GBLUP), and also shows comparable or sometimes improved performance with the lasso and elastic net being known to have good predictive ability but with heavy computational cost. Application to whole-genome sequencing (WGS) data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) exhibits that the proposed method shows higher predictive power than the gene score and GBLUP methods.

Deep learning algorithms have been successfully used in medical image classification and cancer detection. In the next stage, the technology of acquiring explainable knowledge from medical images is highly desired. Herein, fully automated acquisition of explainable features from annotation-free histopathological images is achieved via revealing statistical distortions in datasets by introducing the way of pathologists’ examination into a set of deep neural networks. As validation, we compared the prediction accuracy of prostate cancer recurrence using our algorithm-generated features with that of diagnosis by an expert pathologist using established criteria on 13,188 whole-mount pathology images. Our method found not only the findings established by humans but also features that have not been recognized so far, and showed higher accuracy than human in prognostic prediction. This study provides a new field to the deep learning approach as a novel tool for discovering uncharted knowledge, leading to effective treatments and drug discovery.

The accuracy of previous genetic studies in predicting polygenic psychiatric phenotypes has been limited mainly due to the limited power in distinguishing truly susceptible variants from null variants and the resulting overfitting. A novel prediction algorithm, Smooth-Threshold Multivariate Genetic Prediction (STMGP), was applied to improve the genome-based prediction of psychiatric phenotypes by decreasing overfitting through selecting variants and building a penalized regression model. Prediction models were trained using a cohort of 3685 subjects in Miyagi prefecture and validated with an independently recruited cohort of 3048 subjects in Iwate prefecture in Japan. Genotyping was performed using HumanOmniExpressExome BeadChip Arrays. We used the target phenotype of depressive symptoms and simulated phenotypes with varying complexity and various effect-size distributions of risk alleles. The prediction accuracy and the degree of overfitting of STMGP were compared with those of state-of-the-art models (polygenic risk scores, genomic best linear-unbiased prediction, summary-data-based best linear-unbiased prediction, BayesR, and ridge regression). In the prediction of depressive symptoms, compared with the other models, STMGP showed the highest prediction accuracy with the lowest degree of overfitting, although there was no significant difference in prediction accuracy. Simulation studies suggested that STMGP has a better prediction accuracy for moderately polygenic phenotypes. Our investigations suggest the potential usefulness of STMGP for predicting polygenic psychiatric conditions while avoiding overfitting.

Gene-environment (GxE) interaction is one potential explanation for the missing heritability problem. A popular approach to genome-wide environment interaction studies (GWEIS) is based on regression models involving interactions between genetic variants and environment variables. Unfortunately, GWEIS encounters systematically inflated (or deflated) test statistics more frequently than a marginal association study. The problematic behavior may occur due to poor specification of the null model (i.e. the model without genetic effect) in GWEIS. Improved null model specification may resolve the problem, but the investigation requires many time-consuming analyses of genome-wide scans, e.g. by trying out several transformations of the phenotype. It is therefore helpful if we can predict such problematic behavior beforehand. We present a simple closed-form formula to assess problematic behavior of GWEIS under the null hypothesis of no genetic effects. It requires only phenotype, environment variables, and covariates, enabling quick identification of systematic test statistic inflation or deflation. Applied to real data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), our formula identified problematic studies from among hundreds GWEIS considering each metabolite as the environment variable in GxE interaction. Our formula is useful to quickly identify problematic GWEIS without requiring a genome-wide scan.

Citrin deficiency causes neonatal intrahepatic cholestasis (NICCD), failure to thrive and dyslipidemia (FTTDCD), and adult-onset type II citrullinemia (CTLN2). Owing to a defect in the NADH-shuttle, citrin deficiency impairs hepatic glycolysis and de novo lipogenesis leading to hepatic energy deficit. To investigate the physiological role of citrin, we studied the growth of 111 NICCD-affected subjects (51 males and 60 females) and 12 NICCD-unaffected subjects (five males and seven females), including the body weight, height, and genotype. We constructed growth charts using the lambda-mu-sigma (LMS) method. The NICCD-affected subjects showed statistically significant growth impairment, including low birth weight and length, low body weight until 6 to 9 months of age, low height until 11 to 13 years of age, and low body weight in 7 to 12-year-old males and 8-year-old females. NICCD-unaffected subjects showed similar growth impairment, including low birth weight and height, and growth impairment during adolescence. In the third trimester, de novo lipogenesis is required for deposition of body fat and myelination of the developing central nervous system, and its impairment likely causes low birth weight and length. The growth rate is the highest during the first 6 months of life and slows down after 6 months of age, which is probably associated with the onset and recovery of NICCD. Adolescence is the second catch-up growth period, and the proportion and distribution of body fat change depending on age and sex. Characteristic growth impairment in citrin deficiency suggests a significant role of citrin in the catch-up growth via lipogenesis.

Charcot-Marie-Tooth disease (CMT) is the most common inherited neuropathy characterized by clinical and genetic heterogeneity. Although more than 30 loci harboring CMT-causing mutations have been identified, many other genes still remain to be discovered for many affected individuals. For two consanguineous families with CMT (axonal and mixed phenotypes), a parametric linkage analysis using genome-wide SNP chip identified a 4.3 Mb region on 12q24 showing a maximum multipoint LOD score of 4.23. Subsequent whole-genome sequencing study in one of the probands, followed by mutation screening in the two families, revealed a disease-specific 5 bp deletion (c.247−10_247−6delCACTC) in a splicing element (pyrimidine tract) of intron 2 adjacent to the third exon of cytochrome c oxidase subunit VIa polypeptide 1 (COX6A1), which is a component of mitochondrial respiratory complex IV (cytochrome c oxidase [COX]), within the autozygous linkage region. Functional analysis showed that expression of COX6A1 in peripheral white blood cells from the affected individuals and COX activity in their EB-virus-transformed lymphoblastoid cell lines were significantly reduced. In addition, Cox6a1-null mice showed significantly reduced COX activity and neurogenic muscular atrophy leading to a difficulty in walking. Those data indicated that COX6A1 mutation causes the autosomal-recessive axonal or mixed CMT.

In the Brassicaceae, intraspecific non-self pollen (compatible pollen) can germinate and grow into stigmatic papilla cells, while self-pollen or interspecific pollen is rejected at this stage. However, the mechanisms underlying this selective acceptance of compatible pollen remain unclear. Here, using a cell-impermeant calcium indicator, we showed that the compatible pollen coat contains signaling molecules that stimulate Ca2+ export from the papilla cells. Transcriptome analyses of stigmas suggested that autoinhibited Ca2+-ATPase13 (ACA13) was induced after both compatible pollination and compatible pollen coat treatment. A complementation test using a yeast Saccharomyces cerevisiae strain lacking major Ca2+ transport systems suggested that ACA13 indeed functions as an autoinhibited Ca2+ transporter. ACA13 transcription increased in papilla cells and in transmitting tracts after pollination. ACA13 protein localized to the plasma membrane and to vesicles near the Golgi body and accumulated at the pollen tube penetration site after pollination. The stigma of a T-DNA insertion line of ACA13 exhibited reduced Ca2+ export, as well as defects in compatible pollen germination and seed production. These findings suggest that stigmatic ACA13 functions in the export of Ca2+ to the compatible pollen tube, which promotes successful fertilization.

The impact of cryptic relatedness (CR) on genomic association studies is well studied and known to inflate false-positive rates as reported by several groups. In contrast, conventional epidemiological studies for environmental risks, the confounding effect of CR is still uninvestigated. In this study, we investigated the confounding effect of unadjusted CR among a rural cohort in the relationship between environmental risk factors (body mass index, smoking status, alcohol consumption) and systolic blood pressure. We applied the methods of population-based whole-genome association studies for the analysis of the genome-wide single nucleotide polymorphism data in 1622 subjects, and detected 20.2% CR in this cohort population. In the case of the sample size, approximately 1000, the ratio of CR to the population was 20.2%, the population prevalence 25%, the prevalence in the CR 26%, heritability for liability 14.3% and prevalence in the subpopulation without CR 26%, the difference of estimated regression coefficient between samples with and without CR was not significant (P-value = 0.55). On the other hand, in another case with approximately >20% heritability for liability, we showed that confounding due to CR biased the estimation of exposure effects.

Objective Age is known to influence the risk of both cerebral ischemic lesions and impaired cognitive function. Diabetes mellitus (DM) can also be associated with cognitive impairment. However, there has been no study of neuropsychological performance in association with glucose metabolism status and cerebral ischemic lesions in same-aged, community-dwelling elderly persons. The present study was performed to clarify which cognitive domains are associated with impaired glucose metabolism/DM and whether the association is independent of cerebral ischemic lesions. Subjects and Methods A total of 172 residents in Takahata, Japan, all of whom were 78 years old, were evaluated in multiple domains through neuropsychological tests and brain MR images, as well as a medical check-up including tests for glucose metabolism status and conventional vascular risk factors. Glucose metabolism status was determined by analysis of HbA1c level. Results In multiple regression analyses, performance on a verbal fluency (VF) test and the Trail Making Test-Part B, both of which represent executive function, was associated with HbA1c level, even after adjustment for sex, education, cerebral ischemic lesions, and conventional vascular risk factors. The subjects with DM also showed lower VF scores than did those without DM. Conclusion The results of the present study demonstrate that impaired glucose metabolism, independent of the conventional vascular risk factors and cerebral ischemic lesions, may be associated with a decline in executive function in community-dwelling elderly.

For testing the problem of regions in the space of distribution functions, this paper considers approaches to modify the bootstrap probability to be a second-order accurate p -value based on the familiar bias correction and acceleration method. It is shown that Shimodaira's [2004a. Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling. Ann. Statist. 32, 2616–2641] twostep-multiscale bootstrap method works even in the problem of regions in functional space. In this paper the bias correction quantity is estimated by his onestep-multiscale bootstrap method. Instead of using the twostep-multiscale bootstrap method, the acceleration constant is estimated by a newly proposed jackknife method which requires first-level bootstrap resamplings only. Some numerical examples are illustrated, in which an application to testing significance in model selection is included.

This paper develops smooth-threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero. The resulting estimator enjoys the oracle property in the sense of Fan & Li (2001), even in estimators for which the covariance assumption of Wang & Leng (2007) is violated, such as the Buckley--James estimator. Furthermore, the estimator can be obtained without solving a convex optimization problem. A bic -type criterion for tuning parameter selection is also proposed. It is shown that the criterion achieves consistent model selection. A numerical study confirms the performance of the method. Copyright 2009, Oxford University Press.

In maximum penalized or regularized methods, it is important to select a tuning parameter appropriately. This paper proposes a direct plug-in method for tuning parameter selection. The tuning parameters selected using a generalized information criterion (Konishi and Kitagawa, Biometrika, 83, 875–890, 1996) and cross-validation (Stone, Journal of the Royal Statistical Society, Series B, 58, 267–288, 1974) are shown to be asymptotically equivalent to those selected using the proposed method, from the perspective of estimation of an optimal tuning parameter. Because of its directness, the proposed method is superior to the two selection methods mentioned above in terms of computational cost. Some numerical examples which contain the penalized spline generalized linear model regressions are provided.

For likelihood-based regression contexts, including generalized linear models, this paper presents a boosting algorithm for local constant quasi-likelihood estimators. Its advantages are the following: (a) the one-boosted estimator reduces bias in local constant quasi-likelihood estimators without increasing the order of the variance, (b) the boosting algorithm requires only one-dimensional maximization at each boosting step and (c) the resulting estimators can be written explicitly and simply in some practical cases.

This note presents a direct adjustment of the estimative prediction limit to reduce the coverage error from a target value to third-order accuracy. The adjustment is asymptotically equivalent to those of Barndorff-Nielsen & Cox (1994, 1996) and Vidoni (1998). It has a simpler form with a plug-in estimator of the coverage probability of the estimative limit at the target value. Copyright 2007, Oxford University Press.

For forty-three clinical test values presumably associated to common complex human diseases, we carried out a genome-wide association study using 600K SNPs in a general Japanese population of 1,639 individuals (1,252 after quality control procedures) drawn from a regional cohort, followed by a replication study for statistically significant SNPs (p = 1.95 × 10(-9)-8.34 × 10(-39)) using an independent population of 1,671 from another cohort. In this single two-stage study, we newly found strong and robust associations of common variants at the ABO histo-blood glycosyltransferase locus in 9q32 with the plasma levels of pancreatic lipase (P-LIP), in addition to successful confirmation of the known ABO association of angiotensin converting enzyme (ACE) independent of the ACE1 gene in 17q23.2 with the ACE level. Our results are compatible with the previously reported association between the ABO gene and pancreatic cancer, and show that the effect of these common variants at the ABO locus on the P-LIP and ACE levels is largely opposing and pleiotropic.

In gene-gene interaction analysis using single nucleotide polymorphism (SNP) data, empty cells arise in the genotype contingency table more frequently than in single SNP association studies. Empty cells lead to unidentifiable regression coefficients in regression model fitting. It is unclear whether the degrees of freedom (d.f.) for testing interactions are reduced for such sparse contingency tables. Boolean Operation based Screening and Testing is an exhaustive gene-gene interaction search method in which a fixed d.f. of four (the most conservative choice) is used in the chi-squared null distribution for the likelihood ratio test for gene-gene interactions under a logistic regression model. In this paper, the choice of d.f. is investigated theoretically by introducing a decomposition of type I error. An adaptive method using the observed d.f. can be less conservative than the fixed d.f. method, thereby enhancing power. In simulated data, type I error rates for the adaptive method were usually better controlled under various scenarios for Gaussian linear regression and logistic regression, including prospective and retrospective sampling designs, as well as for artificial data that mimic actual genome-wide SNPs. When the adaptive method was applied to public datasets generated from simulations, it exhibited an improvement in power over the fixed method.

Use of redundant statistical model is often the case with practical data analysis. Redundancy widely investigated is inclusion of irrelevant predictors which is resolved by setting their coefficients to zero. On the other hand, it is also useful to consider overlapping parameters of which the values are similar. Grouping by regarding a set of parameters as a single parameter contributes to building intimate parameterization and increasing estimation accuracy by dimension reduction. ¶ The paper proposes a data adaptive automatic grouping of parameters, which simultaneously enables variable selection that can yield sparse solution, by applying the smooth-thresholding. The new procedure is applicable to several estimation equation-based methods, and is shown to possess the oracle property. No convex optimization is needed for its implementation. Numerical examinations including large p small n situation are performed. Proposed automatic grouping applies to interaction modeling for Ohio wheeze data and for credit scoring data.