Surgical Management of G3 Gastroenteropancreatic Neuroendocrine Neoplasms: A Systematic Review and Meta-analysis.

BACKGROUND: Grade 3 (G3) gastroenteropancreatic (GEP) neuroendocrine neoplasms (NENs) are rare, aggressive tumors with poor prognosis. The World Health Organization 2017 and 2019 classifications further subdivided G3 NENs into G3 neuroendocrine tumors (NETs) and neuroendocrine carcinomas (NECs). Current guidelines favor medical management in most of these patients, and the role of surgical management is not well defined. We performed a systematic literature review and meta-analysis of surgical management versus nonsurgical management for G3 GEP NENs. MATERIALS AND METHODS: A PRISMA-compliant systematic review of the MEDLINE, Embase, Scopus, and Cochrane Library databases (end-of-search date: 16 July 2021) was conducted. Individual patient survival data were reconstructed, and random-effects meta-analyses were performed. RESULTS: Fourteen studies comprising 1810 surgical and 910 nonsurgical patients were systematically reviewed. Publication bias adjusted meta-analysis of 12 studies (1788 surgical and 857 nonsurgical patients) showed increased overall survival (OS) after surgical compared with nonsurgical management for G3 GEP NENs [hazard ratio (HR) 0.40, 95% confidence interval (CI) 0.31-0.53]. Subgroup meta-analyses showed increased OS after surgical management for both pancreatic and gastrointestinal primary sites separately. In another subgroup meta-analysis of G3 GEP NETs (not NECs), surgical management was associated with increased OS compared with nonsurgical management (HR 0.26, 95% CI 0.11-0.61). CONCLUSIONS: Surgical management of G3 GEP NENs may provide a potential survival benefit in well-selected cases. Further research is needed to define which patients will benefit most from surgical versus nonsurgical management. The current literature is limited by inconsistent reporting of survival outcomes in surgical versus nonsurgical groups, tumor grade, differentiation, primary tumor site, and selection criteria for surgical and nonsurgical management.

Feature-specific inference for penalized regression using local false discovery rates.

Penalized regression methods such as the lasso are a popular approach to analyzing high-dimensional data. One attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is the reliability of these selections. Motivated by local false discovery rate methodology from the large-scale hypothesis testing literature, we propose a method for calculating a local false discovery rate for each variable under consideration by the lasso model. These rates can be used to assess the reliability of an individual feature, or to estimate the model's overall false discovery rate. The method can be used for any level of regularization. This is particularly useful for models with a few highly significant features but a high overall false discovery rate, a relatively common occurrence when using cross validation to select a model. It is also flexible enough to be applied to many varieties of penalized likelihoods including generalized linear models and Cox regression, and a variety of penalties, including the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) penalty. We demonstrate the validity of this approach and contrast it with other inferential methods for penalized regression as well as with local false discovery rates for univariate hypothesis tests. Finally, we show the practical utility of our method by applying it to a case study involving gene expression in breast cancer patients.

Penalized linear mixed models for structured genetic data.

Many genetic studies that aim to identify genetic variants associated with complex phenotypes are subject to unobserved confounding factors arising from environmental heterogeneity. This poses a challenge to detecting associations of interest and is known to induce spurious associations when left unaccounted for. Penalized linear mixed models (LMMs) are an attractive method to correct for unobserved confounding. These methods correct for varying levels of relatedness and population structure by modeling it as a random effect with a covariance structure estimated from observed genetic data. Despite an extensive literature on penalized regression and LMMs separately, the two are rarely discussed together. The aim of this review is to do so while examining the statistical properties of penalized LMMs in the genetic association setting. Specifically, the ability of penalized LMMs to accurately estimate genetic effects in the presence of environmental confounding has not been well studied. To clarify the important yet subtle distinction between population structure and environmental heterogeneity, we present a detailed review of relevant concepts and methods. In addition, we evaluate the performance of penalized LMMs and competing methods in terms of estimation and selection accuracy in the presence of a number of confounding structures.

Encoding the Odor of Cigarette Smoke.

The encoding of odors is believed to begin as a combinatorial code consisting of distinct patterns of responses from odorant receptors (ORs), trace-amine associated receptors (TAARs), or both. To determine how specific response patterns arise requires detecting patterns in vivo and understanding how the components of an odor, which are nearly always mixtures of odorants, give rise to parts of the pattern. Cigarette smoke, a common and clinically relevant odor consisting of >400 odorants, evokes responses from 144 ORs and 3 TAARs in freely behaving male and female mice, the first example of in vivo responses of both ORs and TAARs to an odor. As expected, a simplified artificial mimic of cigarette smoke odor tested at low concentration to identify highly sensitive receptors evokes responses from four ORs, all also responsive to cigarette smoke. Human subjects of either sex identify 1-pentanethiol as the odorant most critical for perception of the artificial mimic; and in mice the OR response patterns to these two odors are significantly similar. Fifty-eight ORs respond to the headspace above 25% 1-pentanethiol, including 9 ORs responsive to cigarette smoke. The response patterns to both cigarette smoke and 1-pentanethiol have strongly responsive ORs spread widely across OR sequence diversity, consistent with most other combinatorial codes previously measured in vivo The encoding of cigarette smoke is accomplished by a broad receptor response pattern, and 1-pentanethiol is responsible for a small subset of the responsive ORs in this combinatorial code.SIGNIFICANCE STATEMENT Complex odors are usually perceived as distinct odor objects. Cigarette smoke is the first complex odor whose in vivo receptor response pattern has been measured. It is also the first pattern shown to include responses from both odorant receptors and trace-amine associated receptors, confirming that the encoding of complex odors can be enriched by signals coming through both families of receptors. Measures of human perception and mouse receptor physiology agree that 1-pentanethiol is a critical component of a simplified odorant mixture designed to mimic cigarette smoke odor. Its receptor response pattern helps to link those of the artificial mimic and real cigarette smoke, consistent with expectations about perceptual similarity arising from shared elements in receptor response patterns.

Presacral neuroendocrine tumors associated with the Currarino syndrome.

Currarino syndrome (CS) is an autosomal dominant syndrome caused by mutations in MNX1 and characterized by anorectal abnormalities, partial sacral agenesis, and presacral masses. The presacral masses are typically benign; however, malignant degeneration can occur, and presacral neuroendocrine tumors (NETs) have been reported in six cases. We report three individuals from two families affected by CS in which multiple individuals developed presacral NETs. The first family, 491, had six members with features of CS, including two siblings who presented with presacral, Grade 2 NETs, one of which had metastasized to bone and lymph nodes. A germline c.874C>T (p.Arg292Trp) mutation was found in a highly conserved region of MNX1 in three affected members who underwent sequencing. A second somatic variant/deletion in MNX1 was not detected in either patient's tumor. In the second family, 342, the proband presented with an incidentally discovered presacral NET. The proband's father had previously undergone resection of a presacral NET, and so genetic testing was performed, which did not reveal an MNX1 mutation or copy number variants. The lack of a second, somatic mutation in the tumors from family 491 argues against MNX1 acting as a tumor suppressor, and the absence of a germline MNX1 mutation in family 342 suggests that other genetic and anatomic factors contribute to the development of presacral NETs. These cases highlight the variable presentation of CS, and the potential for malignancy in these patients.

Modulation of the combinatorial code of odorant receptor response patterns in odorant mixtures.

The perception of odors relies on combinatorial codes consisting of odorant receptor (OR) response patterns to encode odor identity. Modulation of these patterns by odorant interactions at ORs potentially explains several olfactory phenomena: mixture suppression, unpredictable sensory outcomes, and the perception of odorant mixtures as unique objects. We determined OR response patterns to 4 odorants and 3 binary mixtures in vivo in mice, identifying 30 responsive ORs. These patterns typically had a few strongly responsive ORs and a greater number of weakly responsive ORs. ORs responsive to an odorant were often unrelated sequences distributed across several OR subfamilies. Mixture responses predicted pharmacological interactions between odorants, which were tested in vitro by heterologous expression of ORs in cultured cells, providing independent evidence confirming odorant agonists for 13 ORs and identifying both suppressive and additive effects. This included 11 instances of antagonism of ORs by an odorant, 1 instance of additive responses to a binary mixture, 1 instance of suppression of a strong agonist by a weak agonist, and the discovery of an inverse agonist for an OR. Interactions between odorants at ORs are common even when the odorants are not known to interact perceptually in humans, and in some cases interactions at mouse ORs correlate with the ability of humans to perceive an odorant in a mixture.

Correction: Whole exome sequencing reveals HSPA1L as a genetic risk factor for spontaneous preterm birth.

[This corrects the article DOI: 10.1371/journal.pgen.1007394.].

Whole exome sequencing reveals HSPA1L as a genetic risk factor for spontaneous preterm birth.

Preterm birth is a leading cause of morbidity and mortality in infants. Genetic and environmental factors play a role in the susceptibility to preterm birth, but despite many investigations, the genetic basis for preterm birth remain largely unknown. Our objective was to identify rare, possibly damaging, nucleotide variants in mothers from families with recurrent spontaneous preterm births (SPTB). DNA samples from 17 Finnish mothers who delivered at least one infant preterm were subjected to whole exome sequencing. All mothers were of northern Finnish origin and were from seven multiplex families. Additional replication samples of European origin consisted of 93 Danish sister pairs (and two sister triads), all with a history of a preterm delivery. Rare exonic variants (frequency <1%) were analyzed to identify genes and pathways likely to affect SPTB susceptibility. We identified rare, possibly damaging, variants in genes that were common to multiple affected individuals. The glucocorticoid receptor signaling pathway was the most significant (p<1.7e-8) with genes containing these variants in a subgroup of ten Finnish mothers, each having had 2-4 SPTBs. This pathway was replicated among the Danish sister pairs. A gene in this pathway, heat shock protein family A (Hsp70) member 1 like (HSPA1L), contains two likely damaging missense alleles that were found in four different Finnish families. One of the variants (rs34620296) had a higher frequency in cases compared to controls (0.0025 vs. 0.0010, p = 0.002) in a large preterm birth genome-wide association study (GWAS) consisting of mothers of general European ancestry. Sister pairs in replication samples also shared rare, likely damaging HSPA1L variants. Furthermore, in silico analysis predicted an additional phosphorylation site generated by rs34620296 that could potentially affect chaperone activity or HSPA1L protein stability. Finally, in vitro functional experiment showed a link between HSPA1L activity and decidualization. In conclusion, rare, likely damaging, variants in HSPA1L were observed in multiple families with recurrent SPTB.

Outdoor light at night and postmenopausal breast cancer risk in the NIH-AARP diet and health study.

Circadian disruption may play a role in breast carcinogenesis. Previous studies reported relationships between outdoor light at night (LAN) and the breast cancer risk, but their findings are mixed. There is also a need to examine LAN and breast cancer incidence according to different individual and environmental characteristics to identify subpopulations at greater risk associated with LAN exposure. We studied residential outdoor LAN estimated from satellite imagery at baseline (1996) in relation to postmenopausal breast cancer incidence over ~16 years of follow-up in 186 981 postmenopausal women including 12 318 incident postmenopausal breast cancer cases in the NIH-AARP Diet and Health Study. We used Cox proportional hazards models to estimate hazard ratios (HR) and two-sided 95% confidence intervals (CI) of the relationship between quintiles of LAN and postmenopausal breast cancer risk, overall and by hormone receptor status and cancer stage. We found that when compared to women in the lowest quintile of baseline LAN, those in the highest quintile had a 10% increase in postmenopausal breast cancer risk (HR (95% CI), 1.10 (1.02, 1.18), P-trend, .002). The association appeared to be stronger for estrogen receptor (ER) positive breast cancer (1.12 [1.02, 1.24], .007) than for ER-negative cancer (1.07 [0.85, 1.34], .66). Our findings also suggested that the relationship between LAN and breast cancer risk may differ by individual characteristics, such as smoking, alcohol drinking, sleep duration and BMI, and neighborhood environment. In conclusion, our study suggests that higher outdoor LAN exposure may be a risk factor for postmenopausal breast cancer.

Marginal false discovery rates for penalized regression models.

Penalized regression methods are an attractive tool for high-dimensional data analysis, but their widespread adoption has been hampered by the difficulty of applying inferential tools. In particular, the question "How reliable is the selection of those features?" has proved difficult to address. In part, this difficulty arises from defining false discoveries in the classical, fully conditional sense, which is possible in low dimensions but does not scale well to high-dimensional settings. Here, we consider the analysis of marginal false discovery rates (mFDRs) for penalized regression methods. Restricting attention to the mFDR permits straightforward estimation of the number of selections that would likely have occurred by chance alone, and therefore provides a useful summary of selection reliability. Theoretical analysis and simulation studies demonstrate that this approach is quite accurate when the correlation among predictors is mild, and only slightly conservative when the correlation is stronger. Finally, the practical utility of the proposed method and its considerable advantages over other approaches are illustrated using gene expression data from The Cancer Genome Atlas and genome-wide association study data from the Myocardial Applied Genomics Network.

Mixture and concentration effects on odorant receptor response patterns in vivo.

Natural odors are mixtures of volatile chemicals (odorants). Odors are encoded as responses of distinct subsets of the hundreds of odorant receptors and trace amine-associated receptors expressed monogenically by olfactory sensory neurons. This is an elegantly simple mechanism for differentially encoding odors but it is susceptible to complex dose-response relationships and interactions between odorants at receptors, which may help explain olfactory phenomena such as mixture suppression, synthetic versus elemental odor processing, and poorly predictable perceptual outcomes of new odor mixtures. In this study in vivo tests in freely behaving mice confirm evidence of a characteristic receptor response pattern consisting of a few receptors with strong responses and a greater number of weakly responding receptors. Odorant receptors responsive to an odor are often unrelated and widely divergent in sequence, even when the odor consists of a single species of odorant. Odorant receptor response patterns to a citrus odor broaden with concentration. Some highly sensitive receptors respond only to a low concentration but others respond in proportion to concentration, a feature that may be critical for concentration-invariant perception. Other tests find evidence of interactions between odorants in vivo. All of the odorant receptor responses to a moderate concentration of the fecal malodor indole are suppressed by a high concentration of the floral odorant, α-ionone. Such suppressive effects are consistent with prior evidence that odorant interactions at individual odorant receptors are common.

Marginal false discovery rate control for likelihood-based penalized regression models.

The popularity of penalized regression in high-dimensional data analysis has led to a demand for new inferential tools for these models. False discovery rate control is widely used in high-dimensional hypothesis testing, but has only recently been considered in the context of penalized regression. Almost all of this work, however, has focused on lasso-penalized linear regression. In this paper, we derive a general method for controlling the marginal false discovery rate that can be applied to any penalized likelihood-based model, such as logistic regression and Cox regression. Our approach is fast, flexible and can be used with a variety of penalty functions including lasso, elastic net, MCP, and MNet. We derive theoretical results under which the proposed method is valid, and use simulation studies to demonstrate that the approach is reasonably robust, albeit slightly conservative, when these assumptions are violated. Despite being conservative, we show that our method often offers more power to select causally important features than existing approaches. Finally, the practical utility of the method is demonstrated on gene expression datasets with binary and time-to-event outcomes.

Identification of genetic modifiers of age-at-onset for familial Parkinson's disease.

Parkinson's disease (PD) is the most common cause of neurodegenerative movement disorder and the second most common cause of dementia. Genes are thought to have a stronger effect on age-at-onset of PD than on risk, yet there has been a phenomenal success in identifying risk loci but not age-at-onset modifiers. We conducted a genome-wide study for age-at-onset. We analysed familial and non-familial PD separately, per prior evidence for strong genetic effect on age-at-onset in familial PD. GWAS was conducted in 431 unrelated PD individuals with at least one affected relative (familial PD) and 1544 non-familial PD from the NeuroGenetics Research Consortium (NGRC); an additional 737 familial PD and 2363 non-familial PD were used for replication. In familial PD, two signals were detected and replicated robustly: one mapped to LHFPL2 on 5q14.1 (PNGRC = 3E-8, PReplication = 2E-5, PNGRC + Replication = 1E-11), the second mapped to TPM1 on 15q22.2 (PNGRC = 8E-9, PReplication = 2E-4, PNGRC + Replication = 9E-11). The variants that were associated with accelerated onset had low frequencies (<0.02). The LHFPL2 variant was associated with earlier onset by 12.33 [95% CI: 6.2; 18.45] years in NGRC, 8.03 [2.95; 13.11] years in replication, and 9.79 [5.88; 13.70] years in the combined data. The TPM1 variant was associated with earlier onset by 15.30 [8.10; 22.49] years in NGRC, 9.29 [1.79; 16.79] years in replication, and 12.42 [7.23; 17.61] years in the combined data. Neither LHFPL2 nor TPM1 was associated with age-at-onset in non-familial PD. LHFPL2 (function unknown) is overexpressed in brain tumours. TPM1 encodes a highly conserved protein that regulates muscle contraction, and is a tumour-suppressor gene.

Association of newborn screening metabolites with risk of wheezing in childhood.

BACKGROUND: There are critical gaps in our understanding of the temporal relationships between metabolites and subsequent asthma development. This is the first study to examine metabolites from newborn screening in the etiology of early childhood wheezing. METHODS: One thousand nine hundred and fifty one infants enrolled between 2012 and 2014 from pediatric practices located in Middle Tennessee in the population-based birth cohort study, the Infant Susceptibility to Pulmonary Infections and Asthma Following RSV Exposure Study (INSPIRE), were linked with metabolite data from the Tennessee Newborn Screening Program. The association between the levels of 37 metabolites and the number of wheezing episodes in the past 12 months was assessed at 1, 2, and 3 years of life. RESULTS: Several metabolites were significantly associated with the number of wheezing episodes. Two acylcarnitines, C10:1 and C18:2, showed robust associations. Increasing levels of C10:1 were associated with increasing number of wheezing episodes at 2 years (OR 2.11, 95% CI 1.41-3.17) and 3 years (OR 2.56, 95% CI 1.59-4.11), while increasing levels of C18:2 were associated with increasing number of wheezing episodes at 1 year (OR 1.38, 95% CI 1.12-1.71) and 2 years (OR 1.47, 95% CI 1.17-1.84). CONCLUSIONS: Identification of specific metabolites and associated pathways involved in wheezing pathogenesis offer insights into potential targets to prevent childhood asthma morbidity.

Increased Grade in Neuroendocrine Tumor Metastases Negatively Impacts Survival.

BACKGROUND: Tumor grade is an important predictor of survival in gastroenteropancreatic (GEP) neuroendocrine tumors (NETs), as determined by Ki-67 expression and mitotic rate. NETs generally grow indolently, but some cells may acquire traits facilitating metastasis. It is unclear how frequently metastases differ in grade from their primary tumors, and whether increasing grade in metastases affects prognosis. METHODS: Ki-67 immunohistochemistry was performed on resected GEPNET specimens and cases with results for both primary tumors and concurrent metastases were identified. Grade was determined using a modified World Health Organization classification (Ki-67: G1 = 0-2%; G2 > 2-20%; G3 > 20%). RESULTS: Ki-67 was performed on both the primary tumor and metastases in 103 patients. Tumor grade was higher in metastases from 25 (24%) patients, 24 increased from G1 to G2, and 1 increased from G2 to G3; 68 (66%) patients had no change in grade (42 G1 and 26 G2), and 10 (10%) decreased from G2 to G1. No clinicopathologic factors were predictive of higher grade in metastases. The 5-year progression-free survival (PFS) was 55% for patients with stable grade versus 8% of patients with increased grade, while 5-year overall survival (OS) was 92 and 54%, respectively. The 5-year OS of patients who had stable grade with G1 and G2 primaries was 92 and 64%, respectively. CONCLUSIONS: Nearly one-third of patients had metastases with a different grade than their primary, and, when grade increased, both PFS and OS significantly decreased. Determining the grade in both the primary tumor and a metastasis is important for estimating prognosis and to help inform decisions regarding additional therapies.

First-time mothers' breast-feeding maintenance: role of experiences and changes in maternal perceptions.

OBJECTIVE: Breast-feeding initiation rates have increased in the USA; however, maintenance of breast-feeding for recommended durations is low. The objective of the present study was to identify factors that may facilitate breast-feeding for longer durations among first-time mothers, including physiological and social experiences and changes in maternal perceptions. DESIGN: Survival analysis and linear regression methods were used to explore the relationship between experiences and breast-feeding duration, and the possible mediating effect of changes in maternal perceptions. SETTING: Secondary data from the Infant Feeding Practices Study II, conducted in the USA between 2005 and 2007. SUBJECTS: Data from 762 first-time mothers who ever breast-fed were analysed. RESULTS: Experiencing trouble with baby's latch, problems with milk flow/supply and painful breast-feeding were significantly associated with breast-feeding duration (64, 26 and 36 % shorter duration, respectively). Meanwhile, positive changes in perception with respect to breast-feeding self-efficacy, opinion about infant feeding and belief about breast milk were associated with 16-27 % longer duration. Furthermore, changes in perception were observed to partially mediate the impact of physiological experiences on breast-feeding duration. CONCLUSIONS: Perceptions of breast-feeding self-efficacy, beliefs and opinions can change over time and are influenced by breast-feeding experiences. The combined effect of experience and perception plays a key role in influencing breast-feeding duration. Future research should explore interventions to maintain or improve these perceptions while accounting for physiological experiences to support breast-feeding for recommended durations among first-time mothers.

In vivo identification of eugenol-responsive and muscone-responsive mouse odorant receptors.

Our understanding of mammalian olfactory coding has been impeded by the paucity of information about the odorant receptors (ORs) that respond to a given odorant ligand in awake, freely behaving animals. Identifying the ORs that respond in vivo to a given odorant ligand from among the ∼1100 ORs in mice is intrinsically challenging but critical for our understanding of olfactory coding at the periphery. Here, we report an in vivo assay that is based on a novel gene-targeted mouse strain, S100a5-tauGFP, in which a fluorescent reporter selectively marks olfactory sensory neurons that have been activated recently in vivo. Because each olfactory sensory neuron expresses a single OR gene, multiple ORs responding to a given odorant ligand can be identified simultaneously by capturing the population of activated olfactory sensory neurons and using expression profiling methods to screen the repertoire of mouse OR genes. We used this in vivo assay to re-identify known eugenol- and muscone-responsive mouse ORs. We identified additional ORs responsive to eugenol or muscone. Heterologous expression assays confirmed nine eugenol-responsive ORs (Olfr73, Olfr178, Olfr432, Olfr610, Olfr958, Olfr960, Olfr961, Olfr913, and Olfr1234) and four muscone-responsive ORs (Olfr74, Olfr235, Olfr816, and Olfr1440). We found that the human ortholog of Olfr235 and Olfr1440 responds to macrocyclic ketone and lactone musk odorants but not to polycyclic musk odorants or a macrocyclic diester musk odorant. This novel assay, called the Kentucky in vivo odorant ligand-receptor assay, should facilitate the in vivo identification of mouse ORs for a given odorant ligand of interest.

Downregulation of dystroglycan glycosyltransferases LARGE2 and ISPD associate with increased mortality in clear cell renal cell carcinoma.

BACKGROUND: Dystroglycan (DG) is a cell-surface laminin receptor that links the cytoskeleton to the extracellular matrix in a variety of epithelial tissues. Its function as a matrix receptor requires extensive glycosylation of its extracellular subunit αDG, which involves at least 13 distinct genes. Prior work has shown loss of αDG glycosylation in an assortment of carcinomas, including clear cell renal cell carcinoma (ccRCC) though the cause (s) and functional consequences of this loss are still unclear. METHODS: Using The Cancer Genome Atlas (TCGA) database, we analyzed the DG glycosylation pathway to identify changes in mRNA expression and correlation with clinical outcomes. We validated our findings with a cohort of 65 patients treated with radical nephrectomy by analyzing DG glycosylation via immunohistochemistry and gene expression via qRT-PCR. RESULTS: Analysis of TCGA database revealed frequent dysregulation of a subset of DG glycosyltransferases. Most notably, there was a frequent, significant downregulation of GYLTL1B (LARGE2) and ISPD. DG glycosylation is frequently impaired in ccRCC patient samples and most strongly associates with downregulation of GYLTL1B. CONCLUSIONS: Reduced levels of GYLTL1B and ISPD mRNA associated with increased patient mortality and are the likely cause of αDG hypoglycosylation in ccRCC.

The group exponential lasso for bi-level variable selection.

In many applications, covariates possess a grouping structure that can be incorporated into the analysis to select important groups as well as important members of those groups. One important example arises in genetic association studies, where genes may have several variants capable of contributing to disease. An ideal penalized regression approach would select variables by balancing both the direct evidence of a feature's importance as well as the indirect evidence offered by the grouping structure. This work proposes a new approach we call the group exponential lasso (GEL) which features a decay parameter controlling the degree to which feature selection is coupled together within groups. We demonstrate that the GEL has a number of statistical and computational advantages over previously proposed group penalties such as the group lasso, group bridge, and composite MCP. Finally, we apply these methods to the problem of detecting rare variants in a genetic association study.