A fast and efficient smoothing approach to Lasso regression and an application in statistical genetics: polygenic risk scores for chronic obstructive pulmonary disease (COPD)

Hahn, Georg; Lutz, Sharon M.; Laha, Nilanjana; Cho, Michael H.; Silverman, Edwin K.; Lange, Christoph

doi:10.1101/2020.03.06.980953

Cited by 3 publications

(9 citation statements)

References 16 publications

(25 reference statements)

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“…Section 2.2 applies the Nesterov methodology to Lassosum and introduces our proposed smoothed Lassosum objective function. The proposed smoothed Lassosum actually follows from the more general framework of Hahn et al (2020a,b). We demonstrate this in Section 2.3, where we also state the theoretical guarantees following from the framework.…”

Section: Methodsmentioning

confidence: 99%

“…The first derivative of is explicitly given by see also Hahn et al (2020a,b), from which the closed-form gradient of the smoothed Lassosum objective function of eq. (7) immediately follows as …”

Section: Methodsmentioning

confidence: 99%

“…We employ the glmnet package on CRAN, see Friedman et al (2010, 2020). We will refer to this method as “Glmnet”. We employ the unsmooted and smoothed Lasso of Hahn et al (2020a), implemented in the R package smoothedLasso on CRAN (Hahn et al, 2020c). We will refer to these methods as “Lasso” and “smoothed Lasso”. We train a neural network with the Keras interface (Falbel et al, 2020a) to the Tensorflow machine learning platform (Falbel et al, 2020b).…”

Section: Experimental Studiesmentioning

confidence: 99%

“…We employ the unsmooted and smoothed Lasso of Hahn et al (2020a), implemented in the R package smoothedLasso on CRAN (Hahn et al, 2020c). We will refer to these methods as “Lasso” and “smoothed Lasso”.…”

Section: Experimental Studiesmentioning

confidence: 99%

“…Besides enabling a more efficient and more accurate computation of the score, our work extends the one of Mak et al (2017) in that we do not solely consider polygenic risk scores, but the more general integrated risk models. Our approach follows as a special case from Hahn et al (2020b,a), who propose a general framework to smooth L1 penalties in linear regression. Importantly, employing a smoothing approach has a variety of theoretical advantages following directly from Hahn et al (2020b).…”

Section: Introductionmentioning

confidence: 99%

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A smoothed version of the Lassosum penalty for fitting integrated risk models

Hahn

Prokopenko

Lutz

et al. 2021

Preprint

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Polygenic risk scores are a popular means to predict the disease risk or disease susceptibility of an individual based on its genotype information. When adding other important epidemiological covariates such as age or sex, we speak of an integrated risk model. Methodological advances for fitting more accurate integrated risk models are of immediate importance to improve the precision of risk prediction, thereby potentially identifying patients at high risk early on when they are still able to benefit from preventive steps/interventions targeted at increasing their odds of survival, or at reducing their chance of getting a disease in the first place. This article proposes a smoothed version of the "Lassosum" penalty used to fit polygenic risk scores and integrated risk models. The smoothing allows one to obtain explicit gradients everywhere for efficient minimization of the Lassosum objective function while guaranteeing bounds on the accuracy of the fit. An experimental section demonstrates the increased accuracy of the proposed smoothed Lassosum penalty compared to the original Lassosum algorithm, allowing it to draw equal with state-of-the-art methodology such as LDpred when evaluated via the AUC (area under the ROC curve) metric.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Experimental Studiesmentioning

confidence: 99%

Section: Experimental Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A smoothed version of the Lassosum penalty for fitting integrated risk models

Hahn

Prokopenko

Lutz

et al. 2021

Preprint

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A framework to efficiently smoothL₁penalties for linear regression

Hahn

Lutz

Laha

et al. 2020

Preprint

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Penalized linear regression approaches that include an L1 term have become an important tool in day-to-day statistical data analysis. One prominent example is the least absolute shrinkage and selection operator (Lasso), though the class of L1 penalized regression operators also includes the fused and graphical Lasso, the elastic net, etc. Although the L1 penalty makes their objective function convex, it is not differentiable everywhere, motivating the development of proximal gradient algorithms such as Fista, the current gold standard in the literature. In this work, we take a different approach based on smoothing. The methodological contribution of our article is threefold: (1) We introduce a unified framework to compute closed-form smooth surrogates of a whole class of L1 penalized regression problems using Nesterov smoothing. The surrogates preserve the convexity of the original (unsmoothed) objective functions, are uniformly close to them, and have closed-form derivatives everywhere for efficient minimization via gradient descent; (2) We prove that the estimates obtained with the smooth surrogates can be made arbitrarily close to the ones of the original (unsmoothed) objective functions, and provide explicitly computable bounds on the accuracy of our estimates; (3) We propose an iterative algorithm to progressively smooth the L1 penalty which increases accuracy and is virtually free of tuning parameters. The proposed methodology is applicable to a large class of L1 penalized regression operators, including all the operators mentioned above. Using simulation studies, we compare our framework to current gold standards such as Fista, glmnet, gLasso, etc. Our simulation results suggest that our proposed smoothing framework provides estimates of equal or higher accuracy than the gold standards while keeping the aforementioned theoretical guarantees and having roughly the same asymptotic runtime scaling.

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The Effect of Teach‐Back Combined with King Interactive Standard Mode on the Life of COPD Patients

Rang

Peng

Wen

et al. 2022

Contrast Media & Molecular Imaging

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Background. COPD is a common clinical chronic airway inflammatory disease that occurs mostly in middle-aged and older adults over the age of 40. The incidence of COPD is increasing year by year and the onset of age is gradually becoming younger. Objective. To observe the effect of teach-back combined with king interaction on the life of patients with chronic obstructive pulmonary disease (COPD). Methods. A total of 100 COPD patients admitted to our hospital from Jan 2021 to Jan 2022 were retrospectively selected to be divided into 50 cases in the control group and 50 cases in the observation group according to the nursing methods. The control group was treated with routine nursing intervention, while the observation group was treated with teach-back combined with king interactive standard mode intervention. The differences in Self-Care Ability Assessment Scale (ESCA) score, St. George’s Respiratory Questionnaire (SGRQ) score, Mental State Assessment Scale (MSSNS) score, 6-minute walking distance (6MWD), and pulmonary function indexes were compared between the two groups before and after the intervention. The success rate and patient compliance of each index in the groups were also recorded. Results. After 3 months and 6 months of intervention, the total SGRO score and its factor scores of self-care skills, self-care responsibility, self-concept, health knowledge level in them were all higher than those before the intervention, while the total SGRO score and its factor scores of respiratory symptoms, activity limitation, disease influence, and so on were all decreased compared with those before the intervention. The ESCA score of the observation group was significantly higher than that of the control one after 3 months and 6 months of intervention, while the SGRQ score was significantly lower than that of the control one, with statistical significance P < 0.05 . After 3 months of intervention, the total score of MSSNS and the scores of anxiety, depression, loneliness, and other factors in both groups were decreased compared with those before intervention. After 6 months of intervention, the total score of MSSNS and scores of each factor in both groups were decreased compared with those before intervention, and the MSSNS scores in the observation group were significantly lower than those in the control group after the intervention, which was statistically significant P < 0.05 . After 3 months and 6 months of intervention, 6MWD, forced vital capacity (FVC), forced expiratory value in 1 second (FEV1), and FVC/FEV1 in them were all higher than those before intervention, and 6MWD and pulmonary function were significantly higher in the observation group than in the control group after 3 and 6 months of intervention, which was statistically significant P < 0.05 . The ESCA score, SGRQ score, MSSNS score, pulmonary function compliance rate, and compliance rate in the observation group were significantly higher than those in the control group, which was statistically significant P < 0.05 . Conclusion. The use of teach-back combined with king interactive standard mode in COPD patients can improve the patient’s self-care ability, reduce psychological negative emotions, and improve the quality of life.

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A fast and efficient smoothing approach to Lasso regression and an application in statistical genetics: polygenic risk scores for chronic obstructive pulmonary disease (COPD)

Cited by 3 publications

References 16 publications

A smoothed version of the Lassosum penalty for fitting integrated risk models

A smoothed version of the Lassosum penalty for fitting integrated risk models

A framework to efficiently smoothL₁penalties for linear regression

The Effect of Teach‐Back Combined with King Interactive Standard Mode on the Life of COPD Patients

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A fast and efficient smoothing approach to Lasso regression and an application in statistical genetics: polygenic risk scores for chronic obstructive pulmonary disease (COPD)

Cited by 3 publications

References 16 publications

A smoothed version of the Lassosum penalty for fitting integrated risk models

A smoothed version of the Lassosum penalty for fitting integrated risk models

A framework to efficiently smoothL1penalties for linear regression

The Effect of Teach‐Back Combined with King Interactive Standard Mode on the Life of COPD Patients

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Product

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A framework to efficiently smoothL₁penalties for linear regression