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Controlling The False Discovery Rate - A Practical And Powerful Approach To Multiple Testing
Abstract
The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses – the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferroni-type procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.
... The aim of this study was not to compare the brain-behavior relationships across the 3 racial/ethnic groups, but to generate associations that are inclusive and reproducible within races and ethnicities across the sample. The brain-behavior relationships were obtained from the strongest edge (R s ) in the functional connectome after applying the Benjamini-Hochberg False Discovery Rate (q = 0.05) 36 to correct for multiple comparisons across 61,776 edges (Supplementary Figure 2). While 17,854 edges shared a significant association with the NIH Toolbox, 65 edges yielded similar relationships with CBCL-externalizing. ...
... The standard, motion-ordered, and bagged brain-behavior associations were computed using the edge that produced the strongest R s in the functional connectome after surviving the Benjamini-Hochberg False Discovery Rate (q = 0.05) 36 . The strongest edges respectively had a correlation strength of |R s | = 0.20 for the NIH Toolbox and |R s | = 0.093 for the CBCL-externalizing. ...
... To detect the standard brain-behavior relationships across the low-motion youth, we computed the partial Spearman's Rank correlation (R s ) between functional connectivity and NIH Toolbox as well as CBCL externalizing and internalizing at the edge level using the full timeseries while adjusting for sex assigned at birth and head motion (indexed by mean FD). The edge that shared the strongest brain-behavior relationship (highest R s ) was selected after applying the Benjamini-Hochberg False Discovery Rate (q = 0.05) 36 to correct for multiple comparisons across 61,776 edges. The strongest R s was chosen based on its magnitude rather than sign to prevent penalizing negatively correlated edges (e.g., an edge's R s = -0.16 is stronger than another edge's R s = 0.15). ...
Population neuroscience datasets allow researchers to estimate reliable effect sizes for brain-behavior associations because of their large sample sizes. However, these datasets undergo strict quality control to mitigate sources of noise, such as head motion. This practice often excludes a disproportionate number of minoritized individuals. We employ motion-ordering and motion-ordering+resampling (bagging) to test if these methods preserve functional MRI (fMRI) data in the Adolescent Brain Cognitive Development Study (N=5,733). Black and Hispanic youth exhibited excess head motion relative to data collected from White youth, and were discarded disproportionately when using conventional approaches. Both methods retained more than 99% of Black and Hispanic youth. They produced reproducible brain-behavior associations across low-/high-motion racial/ethnic groups based on motion-limited fMRI data. The motion-ordering and bagging methods are two feasible approaches that can enhance sample representation for testing brain-behavior associations and fulfill the promise of consortia datasets to produce generalizable effect sizes across diverse populations.
... The resulting distance matrices served as inputs for principal coordinates analysis (PCoA) and significance of sample clustering was analyzed by permutational multivariate analysis of variance (PERMANOVA) with 9,999 permutations. Regarding MaAsLin2, Benjamini-Hochberg FDR [86] adjusted Q-values < 0.1 were considered as significant. LEfSe uses a nonparametric factorial Kruskal Wallis and Wilcoxon rank sum test followed by a linear discriminate analysis to estimate the effect size of each taxon [78]. ...
... The variable importance in projection method (VIP) was Y ijk = µ + A i + P j + +T k + (PT) jk + ε ijk applied to assess the relevance of each metabolite considering the ordinary VIP ≥ 1.5 threshold, in order to identify the most important features. P values were corrected for FDR [86] and P < 0.05 and 0.05 ≤ P < 0.01 were considered as significant and tendency effects, respectively. Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH ("Springer Nature"). ...
Background
Pinus koraiensis cone essential oil (PEO) contains functional compounds such as monoterpene hydrocarbons, and the administration of PEO reduced methane (CH4) emissions during growing phase of goats. However, the mode of action of PEO driven CH4 reduction is not known, especially how the administration of PEO can affect rumen microbiota and host metabolism in goats during the fattening phase. This study aimed to elucidate the potential microbial and host responses PEO supplementation in goats using metataxonomics (prokaryotes and protozoa) and metabolomics (rumen fluid and serum).
Results
Ten fattening Korean native goats were divided into two dietary groups: control (CON; basal diet without additives) and PEO (basal diet + 1.5 g/d of PEO) with a 2 × 2 crossover design and the treatment lasted for 11 weeks. Administration of PEO reduced CH4 concentrations in the exhaled gas from eructation by 12.0–13.6% (P < 0.05). Although the microbial composition of prokaryotes (bacteria and archaea) and protozoa in the rumen was not altered after PEO administration. MaAsLin2 analysis revealed that the abundance of Selenomonas, Christensenellaceae R-7 group, and Anaerovibrio were enriched in the rumen of PEO supplemented goats (Q < 0.1). Co-occurrence network analysis revealed that Lachnospiraceae AC2044 group and Anaerovibrio were the keystone taxa in the CON and PEO groups, respectively. Methane metabolism (P < 0.05) was enriched in the CON group, whereas metabolism of sulfur (P < 0.001) and propionate (P < 0.1) were enriched in the PEO group based on microbial predicted functions. After PEO administration, the abundance of 11 rumen and 4 serum metabolites increased, whereas that of 25 rumen and 14 serum metabolites decreased (P < 0.1). Random forest analysis identified eight ruminal metabolites that were altered after PEO administration, among which four were associated with propionate production, with predictive accuracy ranging from 0.75 to 0.88. Additionally, we found that serum sarcosine (serum metabolite) was positively correlated with CH4 emission parameters and abundance of Methanobrevibacter in the rumen (|r|≥ 0.5, P < 0.05).
Conclusions
This study revealed that PEO administration reduced CH4 emission from of fattening goats with altered microbial interactions and metabolites in the rumen and host. Importantly, PEO administration affected utilizes various mechanisms such as formate, sulfur, methylated amines metabolism, and propionate production, collectively leading to CH4 reduction. The knowledge is important for future management strategies to maintain animal production and health while mitigate CH4 emission.
... For vascular risk factors, we meta-analyzed the coefficients of the primary and secondary linear models. P-values were adjusted for multiple comparisons using Benjamini-Hochberg false discovery rate correction (FDR) with pFDR < 5% for inference [61]. 120 tests were included for vascular/genetic analyses, 64 cognitive and 40 for dementia/stroke analyses. ...
INTRODUCTION: White matter hyperintensities (WMH), a major cerebral small vessel disease marker, may arise from different pathologies depending on their location. We explored clinical and genetic correlates of agnostically derived spatial WMH patterns in two longitudinal population-based cohorts (3C-Dijon, LIFE-Adult).
METHODS: We derived seven WMH spatial patterns using Bullseye segmentation in 2,736 individuals aged 65+ and explored their associations with vascular and genetic risk factors, cognitive performance, dementia and stroke incidence.
RESULTS: WMH in the fronto-parietal and anterior periventricular region were associated with blood pressure traits, WMH genetic risk score (GRS), baseline and decline in general cognitive performance, incident all-cause dementia and ischemic stroke. Juxtacortical-deep occipital WMH were not associated with vascular risk factors and WMH GRS, but with incident all-cause dementia and intracerebral hemorrhage.
CONCLUSION: Accounting for WMH spatial distribution is key to decipher mechanisms underlying cerebral small vessel disease subtypes, an essential step towards personalized therapeutic approaches.
... Its standard deviation is determined as the median of LFQ intensity sample standard deviations calculated within and then averaged over each triplicate. Proteins were tested for differential expression using the limma package for the indicated pairwise comparison of samples and a Benjamini-Hochberg procedure was used to account for multiple testing (71). All relevant test results are listed in Table S4. ...
The biogenesis of mitochondria relies on the import of hundreds of different precursor proteins from the cytosol. Most of these proteins are synthesized with N-terminal presequences which serve as mitochondrial targeting signals. Presequences consistently form amphipathic helices, but they considerably differ in respect to their primary structure and length. Here we show that presequences can be classified into seven different groups based on their specific features. Using a test set of different presequences, we observed that group A presequences endow precursor proteins with improved in vitro import characteristics. We developed IQ-Compete (for Import and de-Quenching Competition assay), a novel assay based on fluorescence de-quenching, to monitor the import efficiencies of mitochondrial precursors in vivo. With this assay, we confirmed the increased import competence of group A presequences. Using mass spectrometry, we found that the presequence of the group A protein Oxa1 specifically recruits the tetratricopeptide repeat (TPR) containing protein TOMM34 to the cytosolic precursor protein. TOMM34 apparently serves as a presequence-specific targeting factor which increases the import efficiency of a specific subset of mitochondrial precursor proteins. Our results suggest that presequences contain a protein-specific priority code that encrypts the targeting mechanism of individual mitochondrial precursor proteins.
Billions of people throughout the world are bilingual and can understand semantic concepts in multiple languages. However, there is little agreement about how the brains of bilinguals represent semantic information from different languages. Some theories suggest that bilingual speakers' brains contain separate representations for semantic information from different languages, while others suggest that different languages evoke the same semantic representations in the brain. To determine how the brains of bilinguals represent semantic information from different languages, we used functional magnetic resonance imaging (fMRI) to record brain responses while participants who are fluent in both English and Chinese read several hours of natural narratives in each language. We then used this data to specifically and comprehensively compare semantic representations between the two languages. We show that while semantic representations are largely shared between languages, these representations undergo fine-grained shifts between languages. These shifts systematically alter how different concept categories are represented in each language. Our results suggest that for bilinguals, semantic brain representations are shared across languages but modulated by each language. These results reconcile competing theories of bilingual language processing.
Cancers evolve in a dynamic ecosystem. Thus, characterizing cancer's ecological dynamics is crucial to understanding cancer evolution and can lead to discovering novel biomarkers to predict disease progression. Ductal carcinoma in situ (DCIS) is an early-stage breast cancer characterized by abnormal epithelial cell growth confined within the milk ducts. Although there has been extensive research on genetic and epigenetic causes of breast carcinogenesis, none of these studies have successfully identified a biomarker for the progression and/or upstaging of DCIS. In this study, we show that ecological habitat analysis of hypoxia and acidosis biomarkers can significantly improve prediction of DCIS upstaging. First, we developed a novel eco-evolutionary designed approach to define habitats in the tumor intra-ductal microenvironment based on oxygen diffusion distance in our DCIS cohort of 84 patients. Then, we identify cancer cells with metabolic phenotypes attributed to their habitat conditions, such as the expression of CA9 indicating hypoxia responding phenotype, and LAMP2b indicating a hypoxia-induced acid adaptation. Traditionally these markers have shown limited predictive capabilities for DCIS upstaging, if any. However, when analyzed from an ecological perspective, their power to differentiate between indolent and upstaged DCIS increased significantly. Second, using eco-evolutionary guided computational and digital pathology techniques, we discovered distinct spatial patterns of these biomarkers and used the distribution of such patterns to predict patient upstaging. The patterns were characterized by both cellular features and spatial features. With a 5-fold validation on the biopsy cohort, we trained a random forest classifier to achieve the area under curve(AUC) of 0.74. Our results affirm the importance of using eco-evolutionary-designed approaches in biomarkers discovery studies in the era of digital pathology by demonstrating the role of eco-evolution dynamics in predicting cancer progression.
Anthropogenic climate change has led to globally increasing temperatures at an unprecedented pace and, to persist, wild species have to adapt to their changing world. We, however, often fail to derive reliable predictions of species' adaptive potential. Genomic selection represents a powerful tool to investigate the adaptive potential of a species, but constitutes a ‘blind process’ with regard to the underlying genomic architecture of the relevant phenotypes. Here, we used great tit (Parus major) females from a genomic selection experiment for avian lay date to zoom into this blind process. We aimed to identify the genetic variants that responded to genomic selection and epigenetic variants that accompanied this response and, this way, might reflect heritable genetic variation at the epigenetic level. We applied whole genome bisulfite sequencing to blood samples of individual great tit females from the third generation of bidirectional genomic selection lines for early and late lay date. Genomic selection resulted in differences at both the genetic and epigenetic level. Genetic variants that showed signatures of selection were located within genes mostly linked to brain development and functioning, including LOC107203824 (SOX3‐like). SOX3 is a transcription factor that is required for normal hypothalamo‐pituitary axis development and functioning, an essential part of the reproductive axis. As for epigenetic differentiation, the early selection line showed hypomethylation relative to the late selection line. Sites with differential DNA methylation were located in genes important for various biological processes, including gonadal functioning (e.g., MSTN and PIK3CB). Overall, genomic selection for avian lay date provided insights into where within the genome the heritable genetic variation for lay date, on which selection can operate, resides and indicates that some of this variation might be reflected by epigenetic variants.
Background
Attention‐deficit/hyperactivity disorder (ADHD) traits often co‐occur in autistic children. The presence of subclinical ADHD traits can significantly impact upon different aspects of daily living. As such, understanding the distribution of these traits in autistic children may have important implications for the validity of diagnostic tools and subsequent intervention choices. This study builds on previous latent models of parent‐reported autistic and ADHD traits to propose a preliminary model of their distribution in two independent samples of autistic and neurotypical children.
Methods
Factor mixture modelling was applied to caregiver responses to the Social Responsiveness Scale ‐ 2nd edition and the Strengths and Weaknesses of ADHD Symptoms and Normal Behaviour Scale (SWAN) of participants aged 4–18 years who participated in one of two studies in Australia or in the United States.
Results
A 2‐factor, 3‐class factor mixture model demonstrated the best fit to the data across both independent samples. The factors represented the latent constructs of ‘autism’ and ‘ADHD’. The latent classes represented subtypes of children with different levels of autistic traits, with higher levels of ADHD traits as autistic trait endorsement increased. Some sample‐specific differences were observed for each model's item thresholds and factor covariance matrices.
Conclusions
Our findings suggest that the endorsement of subclinical ADHD traits tends to increase alongside autistic trait endorsement across neurotypical and autistic presentations. There may be clinical utility in routinely screening for ADHD traits in children with clinically elevated levels of autistic traits.
Brain geometry impacts brain function. A quantitative encoding of form is provided by the Laplace-Beltrami operator’s spectrum of eigenvalues (LBS). We examined LBS genetics of 22 subcortical brain structures including cerebellum in 19,862 healthy White-British UK Biobank participants by multivariate GWAS (MOSTest) on the first 49 eigenvalues each. Controlling for surface and volume, we identified 80 unique variants (p<1/22*5E-8) influencing the shapes of one or several structures, with the highest yield (37 variants) for brain stem. The previously known influence of several of these loci on basic morphology, such as volume, is thus shown to also influence complex shape. Known associations of observed loci with blood pressure, neurodegeneration, alcohol consumption, and mental disorders hint at preclinical stages of these conditions potentially mediating the genetic effect on brain morphology. Significant correlations between LBS of several brain structures and the polygenic risks of hypertension, ischemic stroke and schizophrenia evince brain shapes as early biomarkers.
Net global losses of seagrasses have accelerated efforts to understand recovery from disturbances. Stressors causing disturbances (e.g., storms, heatwaves, boating) vary temporally and spatially within meadows potentially affecting recovery. To test differential recovery, we conducted a removal experiment at sites that differed in thermal stress for a temperate seagrass (Zostera marina). We also synthesized prior studies of seagrass recovery to assess general patterns. Seagrass shoots were removed from 28.3 m² plots at edge and central sites of a meadow in South Bay, Virginia, USA. We hypothesized faster recovery for edge plots where greater oceanic exchange reduces thermal stress. Contrary to our hypothesis recovery was most rapid in the central meadow matching control site shoot density in 24 months. Recovery was incomplete at the meadow edge and estimated to require 158 months. Differences in recovery were likely due to storm‐driven sediment erosion at the edge sites. Based on data from prior recovery studies, which were primarily on monospecific meadows of Zostera, seagrasses recover across a broad range of conditions with a positive, nonlinear relationship between disturbance area and recovery time. Our experiment indicates position within a seagrass meadow affects disturbance susceptibility and length of recovery. Linking this finding to our literature synthesis suggests increased attention to spatial context will contribute to better understanding variation in recovery rates.
A modification of the Bonferroni procedure for testing multiple hypotheses is presented. The method, based on the ordered p-values of the individual tests, is less conservative than the classical Bonferroni procedure but is still simple to apply. A simulation study shows that the probability of a type I error of the procedure does not exceed the nominal significance level, α, for a variety of multivariate normal and multivariate gamma test statistics. For independent tests the procedure has type I error probability equal to α. The method appears particularly advantageous over the classical Bonferroni procedure when several highly-correlated test statistics are involved.
Current methods of statistical inference are correct but incomplete. Small probability (α) of wrong null-hypothesis rejections can be misunderstood. Definitive rejections of null hypotheses, as well as interval assessments of effect sizes, are impossible in single cases with significance probabilities like .05. Sufficiently large sets of independent experiments and attained significance levels (p-values) should be registered. From such data it is possible to calculate least upper bounds for proportions of fallacies in sets of null-hypothesis rejections or effect-size assessments. A provisional rejection of a null hypothesis in a one-tailed test, or a one-sided confidence interval showing a nonzero effect, is here called a discovery. Consider a large number n of independent experiments with r discoveries. For r rejections of null hypotheses the proportion of fallacies Q has least upper bound Qmax = (n/r — 1)α/(1 — α) < 1. For r confidence intervals, the proportion of fallacies is E = αn/r (assuming that no alternative is in the “wrong” direction).
A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to five of the more common multiple comparison procedures. All of the procedures are found to be inconsistent except the simplest procedure, the unrestricted least significant difference (LSD) procedure (or multiple t test). For this and other reasons the unrestricted LSD procedure is recommended for general use, with the proviso that it should be viewed as a hypothesis generator rather than as a method for simultaneous hypothesis generation and testing. The implications for Scheffé's test for general contrasts are also discussed, and a new recommendation is made.
A simple procedure for multiple tests of significance based on individual p-values is derived. This simple procedure is sharper than Holm's (1979) sequentially rejective procedure. Both procedures contrast the ordered p- values with the same set of critical values. Holm's procedure rejects an hypothesis only if its p-value and each of the smaller p-values are less than their corresponding critical-values. The new procedure rejects all hypotheses with smaller or equal p-values to that of any one found less than its critical value.
This paper presents a simple and widely ap- plicable multiple test procedure of the sequentially rejective type, i.e. hypotheses are rejected one at a tine until no further rejections can be done. It is shown that the test has a prescribed level of significance protection against error of the first kind for any combination of true hypotheses. The power properties of the test and a number of possible applications are also discussed.
Optimality criteria formulated in terms of the power functions of the individual tests are given for problems where several hypotheses are tested simultaneously. Subject to the constraint that the expected number of false rejections is less than a given constant $\gamma$ when all null hypotheses are true, tests are found which maximize the minimum average power and the minimum power of the individual tests over certain alternatives. In the common situations in the analysis of variance this leads to application of multiple $t$-tests. In that case the resulting procedure is to use Fisher's "least significant difference," but without a preliminary $F$-test and with a smaller level of significance. Recommendations for choosing the value of $\gamma$ are given by relating $\gamma$ to the probability of no false rejections if all hypotheses are true. Based upon the optimality of the tests, a similar optimality property of joint confidence sets is also derived.
Simes (1986) has proposed a modified Bonferroni procedure for the test of an overall hypothesis which is the combination of
n individual hypotheses. In contrast to the classical Bonferroni procedure, it is not obvious how statements about individual
hypotheses are to be made for this procedure. In the present paper a multiple test procedure allowing statements on individual
hypotheses is proposed. It is based on the principle of closed test procedures (Marcus, Peritz & Gabriel, 1976) and controls
the multiple level α.
Thrombolysis with recombinant tissue-type plasminogen activator (rt-PA) and anisoylated plasminogen streptokinase activator (APSAC) in myocardial infarction has been proved to reduce mortality. A new front-loaded infusion regimen of 100 mg of rt-PA with an initial bolus dose of 15 mg followed by an infusion of 50 mg over 30 min and 35 mg over 60 min has been reported to yield higher patency rates than those achieved with standard regimens of thrombolytic treatment. The effects of this front-loaded administration of rt-PA versus those obtained with APSAC on early patency and reocclusion of infarct-related coronary arteries were investigated in a randomized multicenter trial in 421 patients with acute myocardial infarction. Coronary angiography 90 min after the start of treatment revealed a patent infarct-related artery (Thrombolysis in Myocardial Infarction [TIMI] grade 2 or 3) in 84.4% of 199 patients given rt-PA versus 70.3% of 202 patients given APSAC (p = 0.0007). Early reocclusion within 24 to 48 h was documented in 10.3% of 174 patients given rt-PA versus 2.5% of 163 patients given APSAC. Late reocclusion within 21 days was observed in 2.6% of 152 patients given rt-PA versus 6.3% of 159 patients given APSAC. There were 5 in-hospital deaths (2.4%) in the rt-PA group and 17 deaths (8.1%) in the APSAC group (p = 0.0095). The reinfarction rate was 3.8% and 4.8%, respectively. Peak serum creatine kinase and left ventricular ejection fraction at follow-up angiography were essentially identical in both treatment groups. There were more bleeding complications after APSAC (45% vs. 31%, p = 0.0019).(ABSTRACT TRUNCATED AT 250 WORDS)
We have shown previously that acquired tamoxifen resistance in an in vivo experimental model is associated with reduced tamoxifen accumulation, isomerization of trans-4-hydroxytamoxifen, and tamoxifen-stimulated tumor growth. The purpose of this study is to isolate and verify the presence of estrogenic tamoxifen metabolites in human breast tumors using high-performance liquid chromatography (HPLC) and mass-spectrometry (MS) techniques.
In the present study, we used HPLC and MS to identify the presence of estrogenic metabolites in tumor samples excised from athymic nude mice and in human breast tumors isolated from patients receiving adjuvant tamoxifen therapy.
We identified the presence of metabolite E, a known estrogenic metabolite of tamoxifen, in tamoxifen-resistant MCF-7 human breast tumors implanted in athymic nude mice, as well as in tumors from patients with clinical resistance. Additionally, we separated another estrogenic metabolite, bisphenol, by HPLC, and this was also tentatively confirmed by MS analysis.
These data suggest that cellular tamoxifen metabolism to estrogenic metabolites may in part contribute to stimulating the growth of hormone-responsive breast tumors following prolonged exposure to tamoxifen. Further evaluation of the relationship between cellular metabolism and acquired tamoxifen resistance is warranted.
The antiestrogen tamoxifen is effective in therapy for breast cancer. However, its use is limited by the eventual development of acquired tamoxifen resistance in many patients. The mechanisms responsible for tamoxifen resistance remain unknown; loss of estrogen receptor (ER), selection of hormone-independent breast cancer clones, or alterations in serum tamoxifen levels after long-term use do not explain acquired resistance in most patients. Using an experimental model in which human breast cancer cells develop resistance in athymic mice treated with tamoxifen, we have recently shown that acquired resistance is associated with markedly reduced cellular concentrations of tamoxifen and by isomerization of the trans-4-hydroxy metabolite to the less potent cis isomer.
Using a sensitive high-performance liquid chromatography (HPLC) assay, we have now measured levels of tamoxifen and its major metabolites in a series of 14 tumors from patients treated with tamoxifen. The duration of therapy ranged from 1 month to 6 years.
Tumor tamoxifen levels varied over a wide range. Low concentrations were observed in tumors from eight patients, all demonstrating progressive disease at the time of biopsy after a minimum duration of treatment of 6 months. Six tumors had moderate to high tamoxifen levels, two from patients responding to tamoxifen, one from a patient with stable disease, and three from patients with disease progression. Both the cis and trans isomers of the potent antiestrogenic metabolite 4-hydroxy-tamoxifen were detected in 11 tumors. Six tumors had high ratios of the cis to trans isomer (1.10:2.06), all from patients not responding to tamoxifen. The five tumors with low cis:trans ratios included the two tumors from responding patients and three from patients with progression. All but one of the 11 nonresponding patients had either a low tumor tamoxifen level, a high cis:trans ratio, or both.
This study clearly demonstrates a wide range of tumor tamoxifen levels and accumulation of the less antiestrogenic cis isomer of 4-hydroxytamoxifen in some patients on tamoxifen therapy. Additional study is necessary to determine if these metabolic profiles are related to the development of tamoxifen resistance.