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Concept: Bonferroni correction


Over the past ten years, unconventional gas and oil drilling (UGOD) has markedly expanded in the United States. Despite substantial increases in well drilling, the health consequences of UGOD toxicant exposure remain unclear. This study examines an association between wells and healthcare use by zip code from 2007 to 2011 in Pennsylvania. Inpatient discharge databases from the Pennsylvania Healthcare Cost Containment Council were correlated with active wells by zip code in three counties in Pennsylvania. For overall inpatient prevalence rates and 25 specific medical categories, the association of inpatient prevalence rates with number of wells per zip code and, separately, with wells per km2 (separated into quantiles and defined as well density) were estimated using fixed-effects Poisson models. To account for multiple comparisons, a Bonferroni correction with associations of p<0.00096 was considered statistically significant. Cardiology inpatient prevalence rates were significantly associated with number of wells per zip code (p<0.00096) and wells per km2 (p<0.00096) while neurology inpatient prevalence rates were significantly associated with wells per km2 (p<0.00096). Furthermore, evidence also supported an association between well density and inpatient prevalence rates for the medical categories of dermatology, neurology, oncology, and urology. These data suggest that UGOD wells, which dramatically increased in the past decade, were associated with increased inpatient prevalence rates within specific medical categories in Pennsylvania. Further studies are necessary to address healthcare costs of UGOD and determine whether specific toxicants or combinations are associated with organ-specific responses.

Concepts: Medicine, Statistics, Petroleum, Statistical significance, The Association, Multiple comparisons, Natural gas, Bonferroni correction


Growing interest in personalised medicine and targeted therapies is leading to an increase in the importance of subgroup analyses. If it is planned to view treatment comparisons in both a predefined subgroup and the full population as co-primary analyses, it is important that the statistical analysis controls the familywise type I error rate. Spiessens and Debois (Cont. Clin. Trials, 2010, 31, 647-656) recently proposed an approach specific for this setting, which incorporates an assumption about the correlation based on the known sizes of the different groups, and showed that this is more powerful than generic multiple comparisons procedures such as the Bonferroni correction. If recruitment is slow relative to the length of time taken to observe the outcome, it may be efficient to conduct an interim analysis. In this paper, we propose a new method for an adaptive clinical trial with co-primary analyses in a predefined subgroup and the full population based on the conditional error function principle. The methodology is generic in that we assume test statistics can be taken to be normally distributed rather than making any specific distributional assumptions about individual patient data. In a simulation study, we demonstrate that the new method is more powerful than previously suggested analysis strategies. Furthermore, we show how the method can be extended to situations when the selection is not based on the final but on an early outcome. We use a case study in a targeted therapy in oncology to illustrate the use of the proposed methodology with non-normal outcomes. Copyright © 2012 John Wiley & Sons, Ltd.

Concepts: Scientific method, Clinical trial, Statistics, Evaluation methods, Normal distribution, Multiple comparisons, Bonferroni correction, Familywise error rate


In comparing multiple treatments, 2 error rates that have been studied extensively are the familywise and false discovery rates. Different methods are used to control each of these rates. Yet, it is rare to find studies that compare the same methods on both of these rates, and also on the per-family error rate, the expected number of false rejections. Although the per-family error rate and the familywise error rate are similar in most applications when the latter is controlled at a conventional low level (e.g., .05), the 2 measures can diverge considerably with methods that control the false discovery rate at that same level. Furthermore, we shall consider both rejections of true hypotheses (Type I errors) and rejections of false hypotheses where the observed outcomes are in the incorrect direction (Type III errors). We point out that power estimates based on the number of correct rejections do not consider the pattern of those rejections, which is important in interpreting the total outcome. The present study introduces measures of interpretability based on the pattern of separation of treatments into nonoverlapping sets and compares methods on these measures. In general, range-based (configural) methods are more likely to obtain interpretable patterns based on treatment separation than individual p-value-based measures. Recommendations for practice based on these results are given in the article. Although the article is complex, these recommendations can be understood without the necessity for detailed perusal of the supporting material. (PsycINFO Database Record © 2013 APA, all rights reserved).

Concepts: Multiple comparisons, All rights reserved, Expected value, Bonferroni correction, Hypothesis testing, Familywise error rate, Closed testing procedure, False discovery rate


Purpose To evaluate the diagnostic yield of recommended chest computed tomography (CT) prompted by abnormalities detected on outpatient chest radiographic images. Materials and Methods This HIPAA-compliant study had institutional review board approval; informed consent was waived. Reports of all outpatient chest radiographic examinations performed at a large academic center during 2008 (n = 29 138) were queried to identify studies that included a recommendation for a chest CT imaging. The radiology information system was queried for these patients to determine if a chest CT examination was obtained within 1 year of the index radiographic examination that contained the recommendation. For chest CT examinations obtained within 1 year of the index chest radiographic examination and that met inclusion criteria, chest CT images were reviewed to determine if there was an abnormality that corresponded to the chest radiographic finding that prompted the recommendation. All corresponding abnormalities were categorized as clinically relevant or not clinically relevant, based on whether further work-up or treatment was warranted. Groups were compared by using t test and Fisher exact test with a Bonferroni correction applied for multiple comparisons. Results There were 4.5% (1316 of 29138 [95% confidence interval { CI confidence interval }: 4.3%, 4.8%]) of outpatient chest radiographic examinations that contained a recommendation for chest CT examination, and increasing patient age (P < .001) and positive smoking history (P = .001) were associated with increased likelihood of a recommendation for chest CT examination. Of patients within this subset who met inclusion criteria, 65.4% (691 of 1057 [95% CI confidence interval : 62.4%, 68.2%) underwent a chest CT examination within the year after the index chest radiographic examination. Clinically relevant corresponding abnormalities were present on chest CT images in 41.4% (286 of 691 [95% CI confidence interval : 37.7%, 45.2%]) of cases, nonclinically relevant corresponding abnormalities in 20.6% (142 of 691 [95% CI confidence interval : 17.6%, 23.8%]) of cases, and no corresponding abnormalities in 38.1% (263 of 691 [95% CI confidence interval : 34.4%, 41.8%]) of cases. Newly diagnosed, biopsy-proven malignancies were detected in 8.1% (56 of 691 [95% CI confidence interval : 6.2%, 10.4%]) of cases. Conclusion A radiologist recommendation for chest CT to evaluate an abnormal finding on an outpatient chest radiographic examination has a high yield of clinically relevant findings. © RSNA, 2014.

Concepts: Medical imaging, Interval finite element, Radiology, Multiple comparisons, Fisher's exact test, Bonferroni correction


Recent studies suggested that forkhead box class O3 (FOXO3) functions as a key regulator for the insulin/insulin-like growth factor-1signaling pathway that influence aging and longevity. This study aimed to comprehensively elucidate the association of common genetic variants in FOXO3 with human longevity in a Chinese population. Eighteen single-nucleotide polymorphisms (SNPs) in FOXO3 were successfully genotyped in 616 unrelated long-lived individuals and 846 younger controls. No nominally significant effects were found. However, when stratifying by gender, four SNPs (rs10499051, rs7762395, rs4946933 and rs3800230) previously reported to be associated with longevity and one novel SNP (rs4945815) showed significant association with male longevity (P-values: 0.007-0.032), but all SNPs were not associated with female longevity. Correspondingly, males carrying the G-G-T-G haplotype of rs10499051, rs7762395, rs4945815 and rs3800230 tended to have longer lifespan than those carrying the most common haplotype A-G-C-T (odds ratio = 2.36, 95% confidence interval = 1.20-4.63, P = 0.013). However, none of the associated SNPs and haplotype remained significant after Bonferroni correction. In conclusion, our findings revealed that the FOXO3 variants we tested in our population of Chinese men and women were associated with longevity in men only. None of these associations passed Bonferroni correction. Bonferroni correction is very stringent for association studies. We therefore believe the effects of these nominally significant variants on human longevity will be confirmed by future studies.

Concepts: Bioinformatics, Male, Female, Single-nucleotide polymorphism, Genetic genealogy, Population genetics, Genetic association, Bonferroni correction


The consensus approach to genome-wide association studies (GWAS) has been to assign equal prior probability of association to all sequence variants tested. However, some sequence variants, such as loss-of-function and missense variants, are more likely than others to affect protein function and are therefore more likely to be causative. Using data from whole-genome sequencing of 2,636 Icelanders and the association results for 96 quantitative and 123 binary phenotypes, we estimated the enrichment of association signals by sequence annotation. We propose a weighted Bonferroni adjustment that controls for the family-wise error rate (FWER), using as weights the enrichment of sequence annotations among association signals. We show that this weighted adjustment increases the power to detect association over the standard Bonferroni correction. We use the enrichment of associations by sequence annotation we have estimated in Iceland to derive significance thresholds for other populations with different numbers and combinations of sequence variants.

Concepts: Statistics, Genome-wide association study, The Association, Annotation, Multiple comparisons, Weight, Bonferroni correction, Familywise error rate


Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.

Concepts: Regression analysis, Genetics, Statistical significance, Model organism, Genome-wide association study, Arabidopsis thaliana, Arabidopsis, Bonferroni correction


Anterior cruciate ligament (ACL) rupture is a significant injury in National Football League (NFL) quarterbacks. The purpose of this study was to determine (1) return-to-sport (RTS) rate in NFL quarterbacks following ACL reconstruction, (2) performance upon RTS, and (3) the difference in RTS and performance between players who underwent ACL reconstruction and controls. Thirteen quarterbacks (14 knees) who met inclusion criteria underwent ACL reconstruction while in the NFL. Matched controls were selected from the NFL during the same time span to compare and analyze age, body mass index (BMI), position, performance, and NFL experience. Student t tests were performed for analysis of within- and between-group variables. Bonferroni correction was used in the setting of multiple comparisons. Twelve quarterbacks (13 knees; 92%) were able to RTS in the NFL. Mean player age was 27.2±2.39 years. Mean career length in the NFL following ACL reconstruction was 4.85±2.7 years. Only 1 player needed revision ACL reconstruction. In both cases and controls, player performance was not significantly different from preinjury performance after ACL reconstruction (or index year in controls). There was also no significant performance difference between case and control quarterbacks following ACL reconstruction (or index year in controls). There is a high rate of RTS in the NFL following ACL reconstruction. In-game performance following ACL reconstruction was not significantly different from preinjury or from controls.

Concepts: Body mass index, Knee, Anterior cruciate ligament, Anterior cruciate ligament reconstruction, Cruciate ligament, American football, Bonferroni correction, National Football League


In risk assessment, it is often desired to make inferences on the risk at certain low doses or on the dose(s) at which a specific benchmark risk (BMR) is attained. At times, [Formula: see text] dose levels or BMRs are of interest, and some form of multiplicity adjustment is necessary to ensure a valid [Formula: see text] simultaneous inference. Bonferroni correction is often employed in practice for such purposes. Though relative simple to implement, the Bonferroni strategy can suffer from extreme conservatism (Nitcheva et al., 2005; Al-Saidy et al., 2003). Recently, Kerns (2017) proposed the use of simultaneous hyperbolic and three-segment bands to perform multiple inferences in risk assessment under Abbott-adjusted log-logistic model with the dose level constrained to a given interval. In this paper, we present and compare methods for deriving multiplicity-adjusted upper limits on extra risk and lower bounds on the benchmark dose under Abbott-adjusted log-logistic model. Monte Carlo simulations evaluate the characteristics of the simultaneous limits. An example is given to illustrate the use of the methods.

Concepts: Risk, Monte Carlo, Monte Carlo method, Monte Carlo methods in finance, Logic, Computer simulation, Statistical inference, Bonferroni correction


Early estimation of mortality risk in patients with trauma is essential. In this study, we evaluate the validity of the Emergency Trauma Score (EMTRAS) and Rapid Emergency Medicine Score (REMS) for predicting in-hospital mortality in patients with trauma. Furthermore, we compared the REMS and the EMTRAS with 2 other scoring systems: the Revised Trauma Score (RTS) and Injury Severity score (ISS).We performed a retrospective chart review of 6905 patients with trauma reported between July 2011 and June 2016 at a large national university hospital in South Korea. We analyzed the associations between patient characteristics, treatment course, and injury severity scoring systems (ISS, RTS, EMTRAS, and REMS) with in-hospital mortality. Discriminating power was compared between scoring systems using the areas under the curve (AUC) of receiver operating characteristic (ROC) curves.The overall in-hospital mortality rate was 3.1%. Higher EMTRAS and REMS scores were associated with hospital mortality (P < .001). The ROC curve demonstrated adequate discrimination (AUC = 0.957 for EMTRAS and 0.9 for REMS). After performing AUC analysis followed by Bonferroni correction for multiple comparisons, EMTRAS was significantly superior to REMS and ISS in predicting in-hospital mortality (P < .001), but not significantly different from the RTS (P = .057). The other scoring systems were not significantly different from each other.The EMTRAS and the REMS are simple, accurate predictors of in-hospital mortality in patients with trauma.

Concepts: Cohort study, Hospital, Actuarial science, Scores, Multiple comparisons, Receiver operating characteristic, Injury Severity Score, Bonferroni correction