Yoga participation associated with changes in dietary patterns and stress: A pilot study in stressed adults with poor diet.

BACKGROUND AND PURPOSE: Stress contributes to dietary patterns that impede health. Yoga is an integrative stress management approach associated with improved dietary patterns in burgeoning research. Yet, no research has examined change in dietary patterns, body mass index (BMI), and stress during a yoga intervention among stressed adults with poor diet. MATERIALS AND METHODS: Objectively-measured BMI and a battery of self-report questionnaires were collected at four time points during and following a 12-week yoga intervention (N = 78, 71% women, mean BMI = 25.69 kg/m2±4.59) - pre-treatment (T1), mid-treatment (6 weeks; T2), post-treatment (12 weeks; T3), and at 3-month follow-up (24 weeks; T4). RESULTS: T1 to T3 fruit and vegetable intake, BMI, and stress significantly declined in the overall sample. Reduction in vegetable intake was no longer significant after accounting for reductions in caloric intake, and reduction in caloric intake remained significant after accounting for reductions in stress. CONCLUSION: Findings may be interpreted as yoga either encouraging or adversely impacting healthy dietary patterns (i.e., minimizing likelihood of future weight gain vs. decreasing vegetable intake and overall caloric intake among individuals who may not need to lose weight, respectively). Continued research is warranted, utilizing causal designs.

BinomiRare: A robust test for association of a rare genetic variant with a binary outcome for mixed models and any case-control proportion.

Whole-genome sequencing (WGS) and whole-exome sequencing studies have become increasingly available and are being used to identify rare genetic variants associated with health and disease outcomes. Investigators routinely use mixed models to account for genetic relatedness or other clustering variables (e.g., family or household) when testing genetic associations. However, no existing tests of the association of a rare variant with a binary outcome in the presence of correlated data control the type 1 error where there are (1) few individuals harboring the rare allele, (2) a small proportion of cases relative to controls, and (3) covariates to adjust for. Here, we address all three issues in developing a framework for testing rare variant association with a binary trait in individuals harboring at least one risk allele. In this framework, we estimate outcome probabilities under the null hypothesis and then use them, within the individuals with at least one risk allele, to test variant associations. We extend the BinomiRare test, which was previously proposed for independent observations, and develop the Conway-Maxwell-Poisson (CMP) test and study their properties in simulations. We show that the BinomiRare test always controls the type 1 error, while the CMP test sometimes does not. We then use the BinomiRare test to test the association of rare genetic variants in target genes with small-vessel disease (SVD) stroke, short sleep, and venous thromboembolism (VTE), in whole-genome sequence data from the Trans-Omics for Precision Medicine (TOPMed) program.

Simultaneous monitoring for regression coefficients and baseline hazard profile in Cox modeling of time-to-event data.

The Cox model is the most popular tool for analyzing time-to-event data. The nonparametric baseline hazard function can be as important as the regression coefficients in practice, especially when prediction is needed. In the context of stochastic process control, we propose a simultaneous monitoring method that combines a multivariate control chart for the regression coefficients and a profile control chart for the cumulative baseline hazard function that allows for data blocks of possibly different censoring rates and sample sizes. The method can detect changes in either the parametric or the nonparametric part of the Cox model. In simulation studies, the proposed method maintains its size and has substantial power in detecting changes in either part of the Cox model. An application in lymphoma survival analysis in which patients were enrolled by 2-month intervals in the Surveillance, Epidemiology, and End Results program identifies data blocks with structural model changes.

Online Updating of Survival Analysis.

When large amounts of survival data arrive in streams, conventional estimation methods become computationally infeasible since they require access to all observations at each accumulation point. We develop online updating methods for carrying out survival analysis under the Cox proportional hazards model in an online-update framework. Our methods are also applicable with time-dependent covariates. Specifically, we propose online-updating estimators as well as their standard errors for both the regression coefficients and the baseline hazard function. Extensive simulation studies are conducted to investigate the empirical performance of the proposed estimators. A large colon cancer data set from the Surveillance, Epidemiology, and End Results (SEER) program and a large venture capital (VC) data set with time-dependent covariates are analyzed to demonstrate the utility of the proposed methodologies.

An online updating approach for testing the proportional hazards assumption with streams of survival data.

The Cox model-which remains the first choice for analyzing time-to-event data, even for large data sets-relies on the proportional hazards (PH) assumption. When survival data arrive sequentially in chunks, a fast and minimally storage intensive approach to test the PH assumption is desirable. We propose an online updating approach that updates the standard test statistic as each new block of data becomes available and greatly lightens the computational burden. Under the null hypothesis of PH, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data blocks pooled into one data set. In simulation studies, the test and its variant based on most recent data blocks maintain their sizes when the PH assumption holds and have substantial power to detect different violations of the PH assumption. We also show in simulation that our approach can be used successfully with "big data" that exceed a single computer's computational resources. The approach is illustrated with the survival analysis of patients with lymphoma cancer from the Surveillance, Epidemiology, and End Results Program. The proposed test promptly identified deviation from the PH assumption, which was not captured by the test based on the entire data.

A new Bayesian joint model for longitudinal count data with many zeros, intermittent missingness, and dropout with applications to HIV prevention trials.

In longitudinal clinical trials, it is common that subjects may permanently withdraw from the study (dropout), or return to the study after missing one or more visits (intermittent missingness). It is also routinely encountered in HIV prevention clinical trials that there is a large proportion of zeros in count response data. In this paper, a sequential multinomial model is adopted for dropout and subsequently a conditional model is constructed for intermittent missingness. The new model captures the complex structure of missingness and incorporates dropout and intermittent missingness simultaneously. The model also allows us to easily compute the predictive probabilities of different missing data patterns. A zero-inflated Poisson mixed-effects regression model is assumed for the longitudinal count response data. We also propose an approach to assess the overall treatment effects under the zero-inflated Poisson model. We further show that the joint posterior distribution is improper if uniform priors are specified for the regression coefficients under the proposed model. Variations of the g-prior, Jeffreys prior, and maximally dispersed normal prior are thus established as remedies for the improper posterior distribution. An efficient Gibbs sampling algorithm is developed using a hierarchical centering technique. A modified logarithm of the pseudomarginal likelihood and a concordance based area under the curve criterion are used to compare the models under different missing data mechanisms. We then conduct an extensive simulation study to investigate the empirical performance of the proposed methods and further illustrate the methods using real data from an HIV prevention clinical trial.

FURIN variant associations with postexercise hypotension are intensity and race dependent.

FURIN is a proprotein convertase subtilisin/kexin enzyme important in pro-renin receptor processing, and FURIN (furin, paired basic amino acid cleaving enzyme) variants are involved in multiple aspects of blood pressure (BP) regulation. Therefore, we examined associations among FURIN variants and the immediate blood pressure (BP) response to bouts of aerobic exercise, termed postexercise hypotension (PEH). Obese (30.9 ± 3.6 kg  m-2 ) Black- (n = 14) and White- (n = 9) adults 42.0 ± 9.8 year with hypertension (139.8 ± 10.4/84.6 ± 6.2 mmHg) performed three random experiments: bouts of vigorous (VIGOROUS) and moderate (MODERATE) intensity cycling and control. Subjects were then attached to an ambulatory BP monitor for 19 h. We performed deep-targeted exon sequencing with the Illumina TruSeq Custom Amplicon kit. FURIN genotypes were coded as the number of minor alleles (#MA) and selected for additional statistical analysis based upon Bonferonni or Benjamini-Yekutieli multiple testing corrected P-values under time-adjusted linear models for 19 hourly BP measurements. After VIGOROUS over 19 h, as FURIN #MA increased in rs12917264 (P = 2.4E-04) and rs75493298 (P = 6.4E-04), systolic BP (SBP) decreased 30.4-33.7 mmHg; and in rs12917264 (P = 1.6E-03) and rs75493298 (P = 9.7E-05), diastolic BP (DBP) decreased 17.6-20.3 mmHg among Blacks only. In addition, after MODERATE over 19 h in FURIN rs74037507 (P = 8.0E-04), as #MA increased, SBP increased 20.8 mmHg among Blacks only. Whereas, after MODERATE over the awake hours in FURIN rs1573644 (P = 6.2E-04), as #MA increased, DBP decreased 12.5 mmHg among Whites only. FURIN appears to exhibit intensity and race-dependent associations with PEH that merit further exploration among a larger, ethnically diverse sample of adults with hypertension.

Is less more? A randomized comparison of home practice time in a mind-body program.

Home practice is a major component of mind-body programs, yet little is known about how to optimize the amount of prescribed home practice in order to achieve an effective "dose" of practice while minimizing participant burden. This study tested how varying the amount of home practice in a mind-body program impacts compliance and stress reduction, and whether prescribing a flexible home practice schedule increases compliance. Eighty-four stressed participants undergoing a 12-week yoga program were randomized to low, medium, and high home practice conditions. The medium condition allowed participants the flexibility to choose one of two amounts of practice each day. The low practice group exhibited the highest compliance (91%) compared to the medium and low practice groups (∼60%), but exhibited the lowest total practice time, and did not significantly reduce stress. The high practice group was the only group to achieve significant stress-reduction, which was maintained 12 weeks post program. Prescribing a flexible home practice schedule did not increase compliance. Results suggest that prescribing higher practice doses may maximize practice time and symptom reduction despite lower compliance.

Assessing covariate effects using Jeffreys-type prior in the Cox model in the presence of a monotone partial likelihood.

In medical studies, the monotone partial likelihood is frequently encountered in the analysis of time-to-event data using the Cox model. For example, with a binary covariate, the subjects can be classified into two groups. If the event of interest does not occur (zero event) for all the subjects in one of the groups, the resulting partial likelihood is monotone and consequently, the covariate effects are difficult to estimate. In this article, we develop both Bayesian and frequentist approaches using a data-dependent Jeffreys-type prior to handle the monotone partial likelihood problem. We first carry out an in-depth examination of the conditions of the monotone partial likelihood and then characterize sufficient and necessary conditions for the propriety of the Jeffreys-type prior. We further study several theoretical properties of the Jeffreys-type prior for the Cox model. In addition, we propose two variations of the Jeffreys-type prior: the shifted Jeffreys-type prior and the Jeffreys-type prior based on the first risk set. An efficient Markov-chain Monte Carlo algorithm is developed to carry out posterior computation. We perform extensive simulations to examine the performance of parameter estimates and demonstrate the applicability of the proposed method by analyzing real data from the SEER prostate cancer study.

Bayesian Modeling and Inference for Nonignorably Missing Longitudinal Binary Response Data with Applications to HIV Prevention Trials.

Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, one must handle the missing data appropriately and examine whether the missing data mechanism is ignorable or nonignorable. In this article, we develop a new probit model for longitudinal binary response data. It resolves a challenging issue for estimating the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We show that when improper uniform priors are specified for the regression coefficients of the joint multinomial model via a sequence of one-dimensional conditional distributions for the missing data indicators under nonignorable missingness, the joint posterior distribution is improper. A variation of Jeffreys prior is thus established as a remedy for the improper posterior distribution. In addition, an efficient Gibbs sampling algorithm is developed using a collapsing technique. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to guide the choices of prior specifications and to compare the models under different missing data mechanisms. We report on extensive simulations conducted to investigate the empirical performance of the proposed methods. The proposed methodology is further illustrated using data from an HIV prevention clinical trial.

Deep-targeted sequencing of endothelial nitric oxide synthase gene exons uncovers exercise intensity and ethnicity-dependent associations with post-exercise hypotension.

In previous studies, we found an endothelial nitric oxide synthase gene (NOS3) variant rs2070744 associated with the ambulatory blood pressure (BP) response following bouts of moderate and vigorous intensity acute exercise, termed post-exercise hypotension (PEH). In a validation cohort, we sequenced NOS3 exons for associations with PEH Obese (30.9 ± 3.6 kg.m-2) African American (n = 14) [AF] and Caucasian (n = 9) adults 42.0 ± 9.8 years with hypertension (139.8 ± 10.4/84.6 ± 6.2 mmHg) performed three random experiments: bouts of vigorous and moderate intensity cycling and control. Subjects were attached to an ambulatory BP monitor for 19 h. We performed deep-targeted exon sequencing with the Illumina TruSeq Custom Amplicon kit. Variant genotypes were coded as number of minor alleles (#MA) and selected for additional statistical analysis based upon Bonferonni or Benjamini-Yekutieli multiple testing-corrected P-values under time-adjusted linear models for 19 hourly BP measurements for each subject. After vigorous intensity over 19 h, among NOS3 variants passing multiple testing thresholds, as the #MA increased in rs891512 (P = 6.4E-04), rs867225 (P = 6.5E-04), rs743507 (P = 2.6E-06), and rs41483644 (P = 2.4E-04), systolic (SBP) decreased from 17.5 to 33.7 mmHg; and in rs891512 (P = 9.7E-05), rs867225 (P = 2.6E-05), rs41483644 (P = 1.6E-03), rs3730009 (P = 2.6E-04), and rs77325852 (P = 5.6E-04), diastolic BP decreased from 11.1 mmHg to 20.3 mmHg among AF only. In contrast, after moderate intensity over 19 h in NOS3 rs3918164, as the #MA increased, SBP increased by 16.6 mmHg (P = 2.4E-04) among AF only. NOS3 variants exhibited associations with PEH after vigorous, but not moderate intensity exercise among AF only. NOS3 should be studied further for its effects on PEH in a large, ethnically diverse sample of adults with hypertension to confirm our findings.

Exposure to secondhand smoke and asthma severity among children in Connecticut.

OBJECTIVE: To determine whether secondhand smoke (SHS) exposure is associated with greater asthma severity in children with physician-diagnosed asthma living in CT, and to examine whether area of residence, race/ethnicity or poverty moderate the association. METHODS: A large childhood asthma database in CT (Easy Breathing) was linked by participant zip code to census data to classify participants by area of residence. Multinomial logistic regression models, adjusted for enrollment date, sex, age, race/ethnicity, area of residence, insurance type, family history of asthma, eczema, and exposure to dogs, cats, gas stove, rodents and cockroaches were used to examine the association between self-reported exposure to SHS and clinician-determined asthma severity (mild, moderate, and severe persistent vs. intermittent asthma). RESULTS: Of the 30,163 children with asthma enrolled in Easy Breathing, between 6 months and 18 years old, living in 161 different towns in CT, exposure to SHS was associated with greater asthma severity (adjusted relative risk ratio (aRRR): 1.07 [1.00, 1.15] and aRRR: 1.11 [1.02, 1.22] for mild and moderate persistent asthma, respectively). The odds of Black and Puerto Rican/Hispanic children with asthma being exposed to SHS were twice that of Caucasian children. Though the odds of SHS exposure for publicly insured children with asthma were three times greater than the odds for privately insured children (OR: 3.02 [2.84,3,21]), SHS exposure was associated with persistent asthma only among privately insured children (adjusted odds ratio (aOR): 1.23 [1.11,1.37]). CONCLUSION: This is the first large-scale pragmatic study to demonstrate that children exposed to SHS in Connecticut have greater asthma severity, clinically determined using a systematic approach, and varies by insurance status.

Weighted pseudolikelihood for SNP set analysis with multiple secondary outcomes in case-control genetic association studies.

We propose a weighted pseudolikelihood method for analyzing the association of a SNP set, example, SNPs in a gene or a genetic pathway or network, with multiple secondary phenotypes in case-control genetic association studies. To boost analysis power, we assume that the SNP-specific effects are shared across all secondary phenotypes using a scaled mean model. We estimate regression parameters using Inverse Probability Weighted (IPW) estimating equations obtained from the weighted pseudolikelihood, which accounts for case-control sampling to prevent potential ascertainment bias. To test the effect of a SNP set, we propose a weighted variance component pseudo-score test. We also propose a penalized IPW pseudolikelihood method for selecting a subset of SNPs that are associated with the multiple secondary phenotypes. We show that the proposed variable selection procedure has the oracle properties and is robust to misspecification of the correlation structure among secondary phenotypes. We select the tuning parameter using a weighted Bayesian Information-like Criterion (wBIC). We evaluate the finite sample performance of the proposed methods via simulations, and illustrate the methods by the analysis of the multiple secondary smoking behavior outcomes in a lung cancer case-control genetic association study.

Online Updating of Statistical Inference in the Big Data Setting.

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

Deep-targeted exon sequencing reveals renal polymorphisms associate with postexercise hypotension among African Americans.

We found variants from the Angiotensinogen-Converting Enzyme (ACE), Angiotensin Type 1 Receptor (AGTR1), Aldosterone Synthase (CYP11B2), and Adducin (ADD1) genes exhibited intensity-dependent associations with the ambulatory blood pressure (BP) response following acute exercise, or postexercise hypotension (PEH). In a validation cohort, we sequenced exons from these genes for their associations with PEH Obese (30.9 ± 3.6 kg m-2) adults (n = 23; 61% African Americans [AF], 39% Caucasian) 42.0 ± 9.8 years with hypertension (139.8 ± 10.4/84.6 ± 6.2 mmHg) completed three random experiments: bouts of vigorous and moderate intensity cycling and control. Subjects wore an ambulatory BP monitor for 19 h. We performed deep-targeted exon sequencing using the Illumina TruSeq Custom Amplicon kit. Variant genotypes were coded as number of minor alleles (#MA) and selected for further statistical analysis based upon Bonferonni or Benjamini-Yekutieli multiple testing corrected p-values under time adjusted linear models for 19 hourly BP measurements per subject. After vigorous intensity over 19 h among ACE, AGTR1, CYP11B2, and ADD1 variants passing multiple testing thresholds, as the #MA increased, systolic (SBP) and/or diastolic BP decreased 12 mmHg (P = 4.5E-05) to 30 mmHg (P = 6.4E-04) among AF only. In contrast, after moderate intensity over 19 h among ACE and CYP11B2 variants passing multiple testing thresholds, as the #MA increased, SBP increased 21 mmHg (P = 8.0E-04) to 22 mmHg (P = 8.2E-04) among AF only. In this replication study, ACE, AGTR1, CYP11B2, and ADD1 variants exhibited associations with PEH after vigorous, but not moderate intensity exercise among AF only. Renal variants should be explored further with a multi-level "omics" approach for associations with PEH among a large, ethnically diverse sample of adults with hypertension.

Mismatch between asthma symptoms and spirometry: implications for managing asthma in children.

OBJECTIVES: To examine the concordance between spirometry and asthma symptoms in assessing asthma severity and beginning therapy by the general pediatrician. STUDY DESIGN: Between 2008 and 2012, spirometry testing was satisfactorily performed in 894 children (ages 5-19 years) whose asthma severity had been determined by their pediatrician using asthma guideline-based clinical criteria. Spirometry-determined asthma severity using national asthma guidelines and clinician-determined asthma severity were compared for concordance using weighted Kappa coefficients. RESULTS: Thirty percent of participants had clinically determined intermittent asthma; 32%, 33%, and 5% had mild, moderate, and severe, persistent asthma, respectively. Increasing disease severity was associated with decreases in the forced expiratory volume in 1 second/forced vital capacity (FVC) ratio (P < .001), the forced expiratory volume in 1 second/FVC% predicted (P < .0001), and the FVC% predicted (P < .01). In 319 children (36%), clinically determined asthma severity was lower than spirometry-determined severity. Concordance was 0.16 (95% CI 0.10, 0.23), and when adjusted for bias and prevalence, was 0.20 (95% CI 0.17, 0.23). When accounting for age, sex, exposure to smoke, and insurance type, only spirometry-determined asthma severity was a significant predictor of agreement (P < .0001), with worse agreement as spirometry-determined severity increased. CONCLUSIONS: Concordance between spirometry and asthma symptoms in determining asthma severity is low even when guideline-based clinical assessment tools are used. Because appropriate therapy reduces asthma morbidity and is guided by disease severity, results from spirometry testing could better guide pediatricians in determining appropriate therapy for their patients with asthma.

A-clustering: a novel method for the detection of co-regulated methylation regions, and regions associated with exposure.

MOTIVATION: DNA methylation is a heritable modifiable chemical process that affects gene transcription and is associated with other molecular markers (e.g. gene expression) and biomarkers (e.g. cancer or other diseases). Current technology measures methylation in hundred of thousands, or millions of CpG sites throughout the genome. It is evident that neighboring CpG sites are often highly correlated with each other, and current literature suggests that clusters of adjacent CpG sites are co-regulated. RESULTS: We develop the Adjacent Site Clustering (A-clustering) algorithm to detect sets of neighboring CpG sites that are correlated with each other. To detect methylation regions associated with exposure, we propose an analysis pipeline for high-dimensional methylation data in which CpG sites within regions identified by A-clustering are modeled as multivariate responses to environmental exposure using a generalized estimating equation approach that assumes exposure equally affects all sites in the cluster. We develop a correlation preserving simulation scheme, and study the proposed methodology via simulations. We study the clusters detected by the algorithm on high dimensional dataset of peripheral blood methylation of pesticide applicators. AVAILABILITY: We provide the R package Aclust that efficiently implements the A-clustering and the analysis pipeline, and produces analysis reports. The package is found on http://www.hsph.harvard.edu/tamar-sofer/packages/ CONTACT: tsofer@hsph.harvard.edu

Genome-wide association analysis for multiple continuous secondary phenotypes.

There is increasing interest in the joint analysis of multiple phenotypes in genome-wide association studies (GWASs), especially for the analysis of multiple secondary phenotypes in case-control studies and in detecting pleiotropic effects. Multiple phenotypes often measure the same underlying trait. By taking advantage of similarity across phenotypes, one could potentially gain statistical power in association analysis. Because continuous phenotypes are likely to be measured on different scales, we propose a scaled marginal model for testing and estimating the common effect of single-nucleotide polymorphism (SNP) on multiple secondary phenotypes in case-control studies. This approach improves power in comparison to individual phenotype analysis and traditional multivariate analysis when phenotypes are positively correlated and measure an underlying trait in the same direction (after transformation) by borrowing strength across outcomes with a one degree of freedom (1-DF) test and jointly estimating outcome-specific scales along with the SNP and covariate effects. To account for case-control ascertainment bias for the analysis of multiple secondary phenotypes, we propose weighted estimating equations for fitting scaled marginal models. This weighted estimating equation approach is robust to departures from normality of continuous multiple phenotypes and the misspecification of within-individual correlation among multiple phenotypes. Statistical power improves when the within-individual correlation is correctly specified. We perform simulation studies to show the proposed 1-DF common effect test outperforms several alternative methods. We apply the proposed method to investigate SNP associations with smoking behavior measured with multiple secondary smoking phenotypes in a lung cancer case-control GWAS and identify several SNPs of biological interest.

SNP set association analysis for familial data.

Genome-wide association studies (GWAS) are a popular approach for identifying common genetic variants and epistatic effects associated with a disease phenotype. The traditional statistical analysis of such GWAS attempts to assess the association between each individual single-nucleotide polymorphism (SNP) and the observed phenotype. Recently, kernel machine-based tests for association between a SNP set (e.g., SNPs in a gene) and the disease phenotype have been proposed as a useful alternative to the traditional individual-SNP approach, and allow for flexible modeling of the potentially complicated joint SNP effects in a SNP set while adjusting for covariates. We extend the kernel machine framework to accommodate related subjects from multiple independent families, and provide a score-based variance component test for assessing the association of a given SNP set with a continuous phenotype, while adjusting for additional covariates and accounting for within-family correlation. We illustrate the proposed method using simulation studies and an application to genetic data from the Genetic Epidemiology Network of Arteriopathy (GENOA) study.

Estimating the arm-wise false discovery rate in array comparative genomic hybridization experiments.

Array Comparative Genomic Hybridization (aCGH) is an array-based technology which provides simultaneous spot assays of relative genetic abundance (RGA) levels at multiple sites across the genome. These spot assays are spatially correlated with respect to genomic location and, as a result, the univariate tests conducted using data generated from these spot assays are also spatially correlated. In the context of multiple hypothesis testing, this spatial correlation complicates the question of how best to define a 'discovery' and consequently, how best to estimate the false discovery rate (FDR) corresponding to a given rejection region. One can quantify the number of discoveries as the total number of spots for which the spot-based univariate test statistic falls within a given rejection region. Under this spot-based method, separate but correlated discoveries are identified. We show via a simulation study that the method of Benjamini and Hochberg (1995) can provide a reasonable estimate of the spot-wise FDR, but these results require that the simulated spot assays are categorized as true or false discoveries in a particular way. However, laboratory researchers may actually be interested in estimating a 'regional' FDR, rather than a 'local' spot-wise FDR. We describe an example of such circumstances, and present a method for estimating the (chromosome) arm-wise False Discovery Rate. In this framework, one can quantify the number of discoveries as the total number of chromosome arms for which at least one spot-based test statistic falls into a given rejection region. Defining the discoveries in this way, both the biological and testing objectives coincide. We provide results from a series of simulations which involved the analysis of preferentially re-sampled spot assay values from a real aCGH dataset.