Degree Of Freedom Test Research Articles

A comparison of methods for multiple degree of freedom testing in repeated measures RNA-sequencing experiments

BackgroundAs the cost of RNA-sequencing decreases, complex study designs, including paired, longitudinal, and other correlated designs, become increasingly feasible. These studies often include multiple hypotheses and thus multiple degree of freedom tests, or tests that evaluate multiple hypotheses jointly, are often useful for filtering the gene list to a set of interesting features for further exploration while controlling the false discovery rate. Though there are several methods which have been proposed for analyzing correlated RNA-sequencing data, there has been little research evaluating and comparing the performance of multiple degree of freedom tests across methods.MethodsWe evaluated 11 different methods for modelling correlated RNA-sequencing data by performing a simulation study to compare the false discovery rate, power, and model convergence rate across several hypothesis tests and sample size scenarios. We also applied each method to a real longitudinal RNA-sequencing dataset.ResultsLinear mixed modelling using transformed data had the best false discovery rate control while maintaining relatively high power. However, this method had high model non-convergence, particularly at small sample sizes. No method had high power at the lowest sample size. We found a mix of conservative and anti-conservative behavior across the other methods, which was influenced by the sample size and the hypothesis being evaluated. The patterns observed in the simulation study were largely replicated in the analysis of a longitudinal study including data from intensive care unit patients experiencing cardiogenic or septic shock.ConclusionsMultiple degree of freedom testing is a valuable tool in longitudinal and other correlated RNA-sequencing experiments. Of the methods that we investigated, linear mixed modelling had the best overall combination of power and false discovery rate control. Other methods may also be appropriate in some scenarios.

Abstract P111: A Mendelian Randomization Study of Alcohol Intake and Ischemic Stroke in a Han Chinese Population

Introduction: Observational studies have reported inconsistent relationships between alcohol intake and ischemic stroke risk. The ALDH2 gene encodes an enzyme critical for alcohol metabolism and can serve as an unconfounded proxy for alcohol intake. The current study examined the association between the ALDH2 gene and ischemic stroke among 11,753 Chinese participants. Hypothesis: This study hypothesized that carriers of the ALDH2 variant tend to drink less alcohol and thus have lower risk for ischemic stroke. Methods: The discovery stage included 999 ischemic stroke cases and 1,001 controls with no history of atherosclerotic disease. The ALDH2 gene was sequenced using the SOLiD 4hq platform. Variants with minor allele count (MAC) >10 were each tested for association with stroke using logistic regression models. Interactions between alcohol intake and ALDH2 variants were also tested. Aggregate analysis of rare variants (MAC <20) used the sequence kernel association test. Variants with P<1х10 -4 were replicated among 4,724 ischemic stroke cases and 5,029 controls from the China Stroke Project. Results: An interaction of alcohol drinking with the ALDH2 rs671 variant, which encodes an inactive aldehyde dehydrogenase isozyme that limits tolerability to alcohol, on ischemic stroke risk was identified using the 2 degree of freedom test (P=2.77х10 -5 , 3.66х10 -11 , and 1.01х10 -15 in discovery, replication and joint analyses, respectively). Among drinkers, each copy of the variant allele conferred decreased odds of ischemic stroke, with odds ratios (95% CI) of 0.38 (0.25, 0.60), 0.79 (0.69, 0.91), and 0.74 (0.65, 0.85) in discovery, replication and joint analyses, respectively. While no association between the variant allele and stroke was observed among non-drinkers in the discovery stage [odds ratio (95% CI): 1.00 (0.82, 1.23)], the protective relation persisted among non-drinkers in the replication and joint analyses [odds ratios (95% confidence interval): 0.77 (0.71, 0.84) and 0.80 (0.74, 0.87), respectively]. This inconsistency may have resulted from disparate frequencies of former drinkers included in the non-drinking groups. No additional variants were identified. Conclusions: This large-scale genomic study implicates increased alcohol intake as an etiologically relevant risk factor for ischemic stroke.

Abstract WP251: A Mendelian Randomization Study of Alcohol Intake and Ischemic Stroke in a Han Chinese Population

Introduction: Observational studies have reported inconsistent relationships between alcohol intake and ischemic stroke risk. The ALDH2 gene encodes an enzyme critical for alcohol metabolism and can serve as an unconfounded proxy for alcohol intake. The current study examined the association between the ALDH2 gene and ischemic stroke among 11,753 Chinese participants. Methods: The discovery stage included 999 ischemic stroke cases and 1,001 controls with no history of atherosclerotic disease. The ALDH2 gene was sequenced using the SOLiD 4hq platform. Variants with minor allele count (MAC) >10 were each tested for association with stroke using logistic regression models. Interactions between alcohol intake and ALDH2 variants were also tested. Aggregate analysis of rare variants (MAC <20) used the sequence kernel association test. Variants with P<1х10 -4 were replicated among 4,724 ischemic stroke cases and 5,029 controls from the China Stroke Project. Results: An interaction of alcohol drinking with the ALDH2 rs671 variant, which encodes an inactive aldehyde dehydrogenase isozyme that limits tolerability to alcohol, on ischemic stroke risk was identified using the 2 degree of freedom test (P=2.77х10 -5 , 3.66х10 -11 , and 1.01х10 -15 in discovery, replication and joint analyses, respectively). Among drinkers, each copy of the variant allele conferred decreased odds of ischemic stroke, with odds ratios (95% CI) of 0.38 (0.25, 0.60), 0.79 (0.69, 0.91), and 0.74 (0.65, 0.85) in discovery, replication and joint analyses, respectively. While no association between the variant allele and stroke was observed among non-drinkers in the discovery stage [odds ratio (95% CI): 1.00 (0.82, 1.23)], the protective relation persisted among non-drinkers in the replication and joint analyses [odds ratios (95% confidence interval): 0.77 (0.71, 0.84) and 0.80 (0.74, 0.87), respectively]. This inconsistency may have resulted from disparate frequencies of former drinkers included in the non-drinking groups. No additional variants were identified. Conclusions: This large scale genomic study implicates increased alcohol intake as an etiologically relevant risk factor for ischemic stroke.

Calculating Power to Detect Maternal and Offspring Genetic Effects in Genetic Association Studies.

Offspring outcomes are a function of maternal genetics operating on the intrauterine and postnatal environment, offspring genetics and environmental factors. Partitioning genetic effects into maternal and offspring components requires genotyped mother-offspring pairs or genotyped individuals with phenotypic information on themselves and their offspring. We performed asymptotic power calculations and data simulations to estimate power to detect maternal and offspring genetic effects under a range of different study designs and models. We also developed the "Maternal and offspring Genetic effects Power Calculator" (M-GPC), an online utility which allows users to estimate the power to detect maternal and offspring genetic effects in their own studies. We find that approximately 50,000 genotyped mother-offspring pairs will be required to detect realistically sized maternal or offspring genetic effects (> 0.1% variance explained) with appreciable power (power > 90%, α = 5 × 10-8, two degree of freedom test), whereas greater than 10,000 pairs will be required to determine whether known genetic loci have maternal and/or offspring genetic effects (power > 78%, α = 0.05). The structural equation modelling framework espoused in this manuscript provides a natural method of combining different data structures including those present in large scale biobanks in order to maximize power to detect maternal and offspring genetic effects. We conclude that the sample sizes required to detect maternal or offspring genetic effects that explain realistic proportions of the trait variance with appreciable power are achievable and within the range of current research consortia.

Genome-wide interaction with the insulin secretion locus MTNR1B reveals CMIP as a novel type 2 diabetes susceptibility gene in African Americans.

Although type 2 diabetes (T2D) results from metabolic defects in insulin secretion and insulin sensitivity, most of the genetic risk loci identified to date relates to insulin secretion. We reported that T2D loci influencing insulin sensitivity may be identified through interactions with insulin secretion loci, thereby leading to T2D. Here, we hypothesize that joint testing of variant main effects and interaction effects with an insulin secretion locus increases power to identify genetic interactions leading to T2D. We tested this hypothesis with an intronic MTNR1B SNP, rs10830963, which is associated with acute insulin response to glucose, a dynamic measure of insulin secretion. rs10830963 was tested for interaction and joint (main + interaction) effects with genome-wide data in African Americans (2,452 cases and 3,772 controls) from five cohorts. Genome-wide genotype data (Affymetrix Human Genome 6.0 array) was imputed to a 1000 Genomes Project reference panel. T2D risk was modeled using logistic regression with rs10830963 dosage, age, sex, and principal component as predictors. Joint effects were captured using the Kraft two degrees of freedom test. Genome-wide significant (P<5×10-8 ) interaction with MTNR1B and joint effects were detected for CMIP intronic SNP rs17197883 (Pinteraction =1.43×10-8 ; Pjoint =4.70×10-8 ). CMIP variants have been nominally associated with T2D, fasting glucose, and adiponectin in individuals of East Asian ancestry, with high-density lipoprotein, and with waist-to-hip ratio adjusted for body mass index in Europeans. These data support the hypothesis that additional genetic factors contributing to T2D risk, including insulin sensitivity loci, can be identified through interactions with insulin secretion loci.

Common variants associated with changes in levels of circulating free fatty acids after administration of glucose-insulin-potassium (GIK) therapy in the IMMEDIATE trial.

Glucose-insulin-potassium (GIK) therapy may promote a shift from oxygen-wasteful free fatty acid (FFA) metabolism to glycolysis, potentially reducing myocardial damage during ischemia. Genetic variation associated with FFA response to GIK was investigated in an IMMEDIATE (Immediate Myocardial Metabolic Enhancement During Initial Assessment and Treatment in Emergency care) sub-study (n=117). In patients with confirmed acute coronary syndromes, associations between 132 634 variants and 12-h circulating FFA response were assessed. Between initial and 6-h measurements, three LINGO2 variants were associated with increased levels of total FFA (P-value for 2 degree of freedom test, P2df ⩽5.51 × 10-7). Lead LINGO2 single-nucleotide polymorphism, rs12003487, was nominally associated with reduced 30-day ejection fraction (P2df=0.03). Several LINGO2 signals were linked to alterations in epigenetic profile and gene expression levels. Between 6 and 12 h, rs7017336 nearest to IMPA1/FABP12 showed an association with decreased saturated FFAs (P2df=5.47 × 10-7). Nearest to DUSP26, rs7464104 was associated with a decrease in unsaturated FFAs (P2df=5.51 × 10-7). Genetic variation may modify FFA response to GIK, potentially conferring less beneficial outcomes.

A Note on Linear and Second Order SignificanceTesting in Nonlinear Models

A modified ANOVA setting is used to develop a one degree of freedom test for intrinsic curvature effect. The approach provides clear cutoffs for the measurement of intrinsic curvature effect. It is shown that the significance of the correction factor itself and its usefulness in correcting a global test based on linear approximation are distinct elements. They depend on the local frame of reference provided by the model-data combination and null hypothesis considered.

Chi8: a GPU program for detecting significant interacting SNPs with the Chi-square 8-df test.

BackgroundDetermining interacting SNPs in genome-wide association studies is computationally expensive yet of considerable interest in genomics. Findings We present a program Chi8 that calculates the Chi-square 8 degree of freedom test between all pairs of SNPs in a brute force manner on a Graphics Processing Unit. We analyze each of the seven WTCCC genome-wide association studies that have about 5000 total case and controls and 400,000 SNPs in an average of 9.6 h on a single GPU. We also study the power, false positives, and area under curve of our program on simulated data and provide a comparison to the GBOOST program. Our program source code is freely available from http://www.cs.njit.edu/usman/Chi8.Electronic supplementary materialThe online version of this article (doi:10.1186/s13104-015-1392-5) contains supplementary material, which is available to authorized users.

Perception of Burden and Stigma by Caretaker of Schizophrenia and Bipolar Disorder: a Comparative Study

Background burden of care can be conceptualized into two distinct components (objective and subjective). Objective burden of care is meant to indicate its effects on the household such as taking care of daily tasks, whereas subjective burden indicates the extent to which the caregivers perceived the burden of care. Aim of the present study was to assess level of burden and stigma on caretaker of schizophrenia and bipolar patients. Method researcher took N=80 samples from the population of schizophrenia and bipolar disorder. Researcher used ‘t’ test, ‘f’ test, correlation test, degree of freedom test to analyzed the data. Results researcher found that caretaker perceived higher stigma and burden, there will be no significant difference in education level. Twenty two (50.0 %) caretaker of schizophrenia perceived moderate to severe burden comparatively 9 (25.0 %) BMD (bipolar manic disorder) perceived moderate to severe burden. Researcher concluded that caretaker of schizophrenia and bipolar both perceived burden and stigma.

The power of approximate degrees of freedom tests in heteroscedastic factorial designs.

Several viable approaches have been proposed for conducting factorial analysis when the homogeneous variances assumption is violated. Although robust type I error control and excellent power performance are desirable properties of a test procedure for making statistical inferences, the corresponding power calculations must also be considered to extend its applicability in planning research studies. This article presents the power functions of two approximate degrees of freedom tests within the context of two-way factorial designs. Both theoretical examination and empirical investigation are performed to demonstrate the underlying features of the two approaches. Simulation results showed that the suggested procedures provide remarkably good approximations over a wide range of model configurations. In view of the overall accuracy, the power functions are recommended for enhancing the usefulness of the associated test procedures. To facilitate the adoption of the suggested methodology in factorial research designs, computer code is presented for implementing the described power calculations.

Quantitative analysis of urban sprawl in Tripoli using Pearson's Chi-Square statistics and urban expansion intensity index

Urban expansion is a spatial phenomenon that reflects the increased level of importance of metropolises. The remotely sensed data and GIS have been widely used to study and analyze the process of urban expansions and their patterns. The capital of Libya (Tripoli) was selected to perform this study and to examine its urban growth patterns. Four satellite imageries of the study area in different dates (1984, 1996, 2002 and 2010) were used to conduct this research. The main goal of this work is identification and analyzes the urban sprawl of Tripoli metropolitan area. Urban expansion intensity index (UEII) and degree of freedom test were used to analyze and assess urban expansions in the area of study. The results show that Tripoli has sprawled urban expansion patterns; high urban expansion intensity index; and its urban development had high degree of freedom according to its urban expansion history during the time period (1984-2010). However, the novel proposed hypothesis used for zones division resulted in very good insight understanding of urban expansion direction and the effect of the distance from central business of district (CBD).

Considerations to Calculate Expected Genotypic Frequencies and Formal Statistical Testing of Hardy-Weinberg Assumptions for nonpseudoautosomal X chromosome SNPs

HWE is a popular concept from population genetics that provides the investigator with an expectation regarding how genotypes are distributed in a given population. Although relying on a set of assumptions, HWE has been proven useful for genetic studies and, among its several applications, has been used as a quality control metric in GWAS. In this correspondence, the calculation to obtain expected genotypic frequencies of non-pseudoautosomal X chromosome SNPs (assuming HWE holds) by weighting within-sex expected genotypic frequencies by the prevalence of the respective sex in the sample is shown. It is also described that, under the assumption that each sex represents 50% of the sample, a one degree of freedom test can be derived. The calculation is simple and intuitive and, therefore, straightforward to incorporate in routine quality control analyses. This correspondence fills an existing gap in GWAS and may contribute to future investigations.

Germline single-nucleotide polymorphisms (SNPs) associated with response of urothelial carcinoma (UC) to platinum-based therapy: The role of the host.

236 Background: Platinum-based therapy improves outcome in neoadjuvant and metastatic UC. Since cell-line and human subject studies in other cancers show germline associations with platinum response, we hypothesized that germline variation also identifies genes that determine UC response to platinum-based therapy. Methods: Saliva or blood was prospectively collected from 651 UC patients (pts) diagnosed between 1984 and 2010. SNPs (n=80) were selected based on previously reported associations with UC and/or platinum response and genotyped using Sequenom MassArray iPLEX system. Samples and SNPs were filtered for genotyping rate (&lt;0.8), minor allele frequency (&lt;0.05) and departures from Hardy-Weinberg equilibrium (&lt;1E-03). Clinical data were ascertained and linked with the genomic data in an anonymized manner. This analysis focused on 199 pts who received cisplatin or carboplatin and were eligible for response assessment (RES=partial response or complete response, n=90). Associations between SNPs and RES were tested using one and two degree of freedom tests. Results: Sixty-nine pts received neoadjuvant therapy (RES=54%), 126 chemo-naive pts received first-line metastatic treatment (RES=37%) and 4 received systemic treatment after prior chemoradiotherapy (RES=25%). We expected 4 associations due to chance alone at p &lt; 0.05. However, on univariate analysis using a 2 degree of freedom test, 9 SNPs were associated (p &lt; 0.05) with RES. Individual odds ratios (ORs) ranged from 0.32 to 3.29 with p-values ranging from 0.006 to 0.05. In analysis of rs9344 (CCND1) in all treated pts, 75/148 (51%) responded with AG/GG compared to 12/44 (27%) with AA [p=0.005312, OR 2.74 (CI 1.34, 5.92)]. In neoadjuvant pts treated with cisplatin, rs9344 analysis showed 29/48 (60%) responses in AG/GG pts compared to 5/17 (29%) with AA [p=0.026, OR 3.66 (CI 1.16, 13.1)]. Conclusions: We identified associations between 9 SNPs and response of UC to platinum-based therapy that are biologically and clinically relevant. A larger study will be required to independently validate these findings. Additional investigation of associations with time to metastasis and overall survival is ongoing. [Table: see text]

Association of polymorphisms in the klotho gene with severity of non-diabetic ESRD in African Americans

Non-diabetic forms of nephropathy commonly lead to end-stage renal disease (non-DM ESRD). Previous studies have demonstrated that African Americans are more susceptible to non-DM ESRD compared to other ethnic groups, and this risk has a strong genetic component. A genome-wide scan for ESRD in African American families enriched for non-DM ESRD showed evidence for linkage in chromosome 13q33.3, and a candidate gene in this region, klotho, was selected for a detailed analysis in a follow-up case-control association study. Thirty-four single-nucleotide polymorphisms (SNPs) in the klotho gene were genotyped in 317 unrelated African American non-DM ESRD cases and 354 non-nephropathy controls, including 12 SNPs identified by re-sequencing a region around exon 4. Two SNPs demonstrated modest admixture-adjusted evidence of association with non-DM ESRD, rs650439 (P = 0.013, recessive model) and rs643780 (P = 0.017, recessive model), while rs17643698 approached significance (P = 0.0953, two degrees of freedom test). Eight of the most significant SNPs were tested for replication in a second case-control collection (557 African American non-DM ESRD cases and 187 controls), and there was no evidence of association in replicate cases and controls; nor when the samples were combined for a total of 874 non-DM cases and 541 controls. Cox proportional hazards models were computed to test for association between polymorphisms in klotho and age at onset of ESRD. A three-SNP haplotype, rs526906, rs525014 and rs571118 (T/T/A), was associated with age of onset of ESRD [P = 0.007, recessive model; hazard ratio (HR) = 0.70]. Subjects homozygous for this haplotype had a mean 4 years later onset of ESRD, suggesting a slower disease progression. HapMap subjects homozygous for this haplotype had increased expression of klotho, further supporting a protective role of this variant in ESRD. We conclude that three SNPs in intron 1 of the klotho gene are associated with delayed age at onset of non-DM ESRD in African Americans.

Generalizing Terwilliger's likelihood approach: a new score statistic to test for genetic association

Background:In this paper, we propose a one degree of freedom test for association between a candidate gene and a binary trait. This method is a generalization of Terwilliger's likelihood ratio statistic and is especially powerful for the situation of one associated haplotype. As an alternative to the likelihood ratio statistic, we derive a score statistic, which has a tractable expression. For haplotype analysis, we assume that phase is known.Results:By means of a simulation study, we compare the performance of the score statistic to Pearson's chi-square statistic and the likelihood ratio statistic proposed by Terwilliger. We illustrate the method on three candidate genes studied in the Leiden Thrombophilia Study.Conclusion:We conclude that the statistic follows a chi square distribution under the null hypothesis and that the score statistic is more powerful than Terwilliger's likelihood ratio statistic when the associated haplotype has frequency between 0.1 and 0.4 and has a small impact on the studied disorder. With regard to Pearson's chi-square statistic, the score statistic has more power when the associated haplotype has frequency above 0.2 and the number of variants is above five.

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n−1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.

Genetic model testing and statistical power in population‐based association studies of quantitative traits

The optimal method for considering different genetic models in association studies is not clear. We compared analytical strategies that use different genetic models to analyze genotype-phenotype information from association studies of quantitative traits in unrelated individuals. We created simulated datasets where the minor alleles are causal with an additive, dominant, or recessive mode of inheritance over a range of allele frequencies. We then computed power to detect these causal alleles using one or a combination of statistical models in a standard regression framework, including corrections for the multiple testing incurred by analyzing multiple models. Our results show that, as expected, maximal power is achieved when we test a single genetic model that matches the actual underlying mode of inheritance of the causal allele. When the inheritance pattern of the causal allele is unknown, the co-dominant model, a single two degrees of freedom test, has good overall performance in any of the three simple modes of inheritance simulated. Alternatively, it is slightly more powerful to analyze all three genetic models together (additive, dominant, and recessive), but only if the significance thresholds used to correct for analyzing multiple models are appropriately determined (such as by permutation). Finally, a commonly employed approach, testing the additive model alone, performs poorly for recessive causal alleles when the minor allele frequency is not close to 50%. Our observations were confirmed by analyzing an existing genetic association dataset in which we detect the effect of a KCNJ11 variant on insulinogenic index in unrelated non-diabetic individuals.

Augmented HIV vaccine trial design for estimating reduction in infectiousness and protective efficacy.

It is important to design HIV vaccine trials to estimate the efficacy of a vaccine in reducing infectiousness in addition to the protective efficacy. Currently planned phase III HIV vaccine field trials in which at-risk individuals are randomized and followed over time do not permit estimation or testing of the vaccine's effect on reducing infectiousness of vaccinees who become infected. We suggest an augmentation of these field trials that recruits steady sexual partners of the primary participants into the trial as far as they are willing to participate. This study design would allow estimation of the efficacy of the vaccine on reducing infectiousness as well as the protective efficacy. We compare the classical design that does not include partners to two different types of augmented design. In the first type of augmentation, called the non-randomized partner design, the steady sexual partners are not randomized to vaccine or placebo. In the second type of augmentation, called the randomized partner design, the steady sexual partners are also randomized to vaccine or placebo. We present a probability model based on infection status at the end of the trial that provides maximum likelihood estimates of the protective efficacy of the vaccine, VES, and the efficacy of the vaccine on reducing infectiousness, VEI. Wald statistics are used for one degree of freedom tests on VES and VEI. With the augmented design, a likelihood ratio test is used to test whether the vaccine has any effect at all. The randomized partner design has more power and provides narrower confidence intervals than does the non-randomized partner design.

The correlation effects on service control point response time

AbstractAs the centralized database for the integration across multiple wireless tiers and wireline access, traffic design considerations for SCP performance measurement are of great important in the personal communications era. By neglecting the effect of disk access time, the SCP response time R includes the SCP processing time P and signalling link delay L only. A bivariate normal distribution has been proposed for modelling (P, L) such that some statistical estimations of L given P can be conveniently obtained in different combination of SCP processing load and link utilization. Further, the correlation effects of (P, L| P=p) on R are investigated. After a Tukey one degree of freedom test with one observation of μL|P=p per treatment (n=1) under different normalized processing times and correlations, the two‐factor ANOVA model becomes an interaction model without pure error effects due to the computed F* values being significantly greater than the critical F (0.95; 1, 11). Besides, rejection threshold criteria of SCP response time with minimum loss rate (0.01 per cent) of messages are proposed to ensure a good service quality of SCP.

Approximate degrees of freedom tests: A unified perspective on testing for mean equality.

Approximate degrees of freedom tests: A unified perspective on testing for mean equality.