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Introduction: After the era of genome-wide association studies (GWAS), thousands of genetic variants have been identified to exhibit main effects on human phenotypes. The next critical issue would be to explore the interplay between genes, the so-called "gene-gene interactions" (GxG) or epistasis. An exhaustive search for all single-nucleotide polymorphism (SNP) pairs is not recommended because this will induce a harsh penalty of multiple testing. Limiting the search of epistasis on SNPs reported by previous GWAS may miss essential interactions between SNPs without significant marginal effects. Moreover, most methods are computationally intensive and can be challenging to implement genome-wide. Methods: I here searched for GxG through variance quantitative trait loci (vQTLs) of 29 continuous Taiwan Biobank (TWB) phenotypes. A discovery cohort of 86,536 and a replication cohort of 25,460 TWB individuals were analyzed, respectively. Results: A total of 18 nearly independent vQTLs with linkage disequilibrium measure r 2 < 0.01 were identified and replicated from nine phenotypes. 15 significant GxG were found with p-values <1.1E-5 (in the discovery cohort) and false discovery rates <2% (in the replication cohort). Among these 15 GxG, 11 were detected for blood traits including red blood cells, hemoglobin, and hematocrit; 2 for total bilirubin; 1 for fasting glucose; and 1 for total cholesterol (TCHO). All GxG were observed for gene pairs on the same chromosome, except for the APOA5 (chromosome 11)-TOMM40 (chromosome 19) interaction for TCHO. Discussion: This study provided a computationally feasible way to search for GxG genome-wide and applied this approach to 29 phenotypes.

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Sensitivity to changes in the stimulus level at one or at both ears and to changes in the interaural level difference (ILD) between the two ears has been studied widely. Several different definitions of threshold and, for one of them, two different ways of averaging single-listener thresholds have been used (i.e., arithmetically and geometrically), but it is unclear which definition and which way of averaging is most suitable. Here, we addressed this issue by examining which of the differently defined thresholds yielded the highest degree of homoscedasticity (homogeneity of the variance). We also examined how closely the differently defined thresholds followed the normal distribution. We measured thresholds from a large number of human listeners as a function of stimulus duration in six experimental conditions, using an adaptive two-alternative forced-choice paradigm. Thresholds defined as the logarithm of the ratio of the intensities or amplitudes of the target and the reference stimulus (i.e., as the difference in their levels or ILDs; the most commonly used definition) were clearly heteroscedastic. Log-transformation of these latter thresholds, as sometimes performed, did not result in homoscedasticity. Thresholds defined as the logarithm of the Weber fraction for stimulus intensity and thresholds defined as the logarithm of the Weber fraction for stimulus amplitude (the most rarely used definition) were consistent with homoscedasticity, but the latter were closer to the ideal case. Thresholds defined as the logarithm of the Weber fraction for stimulus amplitude also followed the normal distribution most closely. The discrimination thresholds should therefore be expressed as the logarithm of the Weber fraction for stimulus amplitude and be averaged arithmetically across listeners. Other implications are discussed, and the obtained differences between the thresholds in different conditions are compared to the literature.

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The failures of reproducibility in psychology (or other social sciences) can be investigated by tracing their logical chains, from statistical hypothesis to their conclusion. This research starts with the normality hypothesis, the homoscedasticity hypothesis, and the robust hypothesis and uses the R language to simulate and analyze the original data of 100 studies in Estimating the Reproducibility of Psychological Science to explore the influence of the premise hypothesis on statistical methods on the reproducibility of psychological research. The results indicated the following: (1) the answer to the question about psychological studies being repeatable or not relates to the fields to which the subjects belonged, (2) not all the psychological variables meet the normal distribution hypothesis, (3) the t-test is a more robust tool for psychological research than the Analysis of Variance (ANOVA), and (4) the robustness of ANOVA is independent of the normality and variance congruence of the analyzed data. This study made us realize that the repeatable study factors in psychology are more complex than we expected them to be.

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Several assumptions such as normality, linear relationship, and homoscedasticity are frequently required in parametric statistical analysis methods. Data collected from the clinical situation or experiments often violate these assumptions. Variable transformation provides an opportunity to make data available for parametric statistical analysis without statistical errors. The purpose of variable transformation to enable parametric statistical analysis and its final goal is a perfect interpretation of the result with transformed variables. Variable transformation usually changes the original characteristics and nature of units of variables. Back-transformation is crucial for the interpretation of the estimated results. This article introduces general concepts about variable transformation, mainly focused on logarithmic transformation. Back-transformation and other important considerations are also described herein.

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SAS and other popular statistical packages provide support for survey data with sampling weights. For example, PROC MEANS and PROC LOGISTIC in SAS have their counterparts PROC SURVEYMEANS and PROC SURVEYLOGISTIC to facilitate analysis of data from complex survey studies. On the other hand, PROC MEANS and many other classic SAS procedures also provide an option for including weights and yield identical point estimates, but different standard errors (SEs), as their corresponding survey procedures. This paper takes an in-depth look at different types of weights and provides guidance on use of different SAS procedures.

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Background: Precision medicine is the Holy Grail of interventions that are tailored to a patient's individual characteristics. However, conventional clinical trials are designed to find differences in averages, and interpreting these differences depends on untestable assumptions. Although only an ideal, a constant effect of treatment would facilitate individual management. A direct consequence of a constant effect is that the variance of the outcome measure would be the same in the treated and control arms. We reviewed the literature to explore the similarity of these variances as a foundation for examining whether and how often precision medicine is definitively required. Methods: We reviewed parallel clinical trials with numerical primary endpoints published in 2004, 2007, 2010 and 2013. We collected the baseline and final standard deviations of the main outcome measure. We assessed homoscedasticity by comparing the variance of the primary endpoint between arms through the outcome variance ratio (treated to control group). Results: The review provided 208 articles with enough information to conduct the analysis. One out of five studies (n = 40, 19.2%) had statistically different variances between groups, implying a non-constant-effect. The adjusted point estimate of the mean outcome variance ratio (treated to control group) is 0.89 (95% CI 0.81 to 0.97). Conclusions: The mean variance ratio is significantly lower than 1 and the lower variance was found more often in the intervention group than in the control group, suggesting it is more usual for treated patients to be stable. This observed reduction in variance might also imply that there could be a subgroup of less ill patients who derive no benefit from treatment. This would require further study as to whether the treatment effect outweighs the side effects as well as the economic costs. We have shown that there are ways to analyze the apparently unobservable constant effect.

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We have discussed many statistical tests and tools in this series of commentaries, and while we have mentioned the underlying assumptions of the tests, we have not explored them in detail. We stop to look at some of the assumptions of the t-test and linear regression, justify and explain them, mention what can go wrong when the assumptions are not met, and suggest some solutions in this case.

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The comparison of two measurement systems is important in medical and other contexts. A common goal is to decide if a new measurement system agrees suitably with an existing one, and hence whether the two can be used interchangeably. Various methods for assessing interchangeability are available, the most popular being the limits of agreement approach due to Bland and Altman. In this article, we review the challenges of this technique and propose a model-based framework for comparing measurement systems that overcomes those challenges. The proposal is based on a simple metric, the probability of agreement, and a corresponding plot which can be used to summarize the agreement between two measurement systems. We also make recommendations for a study design that facilitates accurate and precise estimation of the probability of agreement.

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The existing literature addressing Religion and Spirituality supports the idea that attending church is positively associated with health outcomes. However, within this literature there has been an impoverished effort to determine whether the Religiously Unaffiliated will report these positive relationships. Using representative data from Ontario (N = 3620), the relationships between Religious/Spiritual variables (Attendance, Prayer/Meditation, and Religiosity) and health outcomes (Happiness, Self-Rated Health, and Satisfaction with Life) were assessed. Results focused on three recurring trends: the Religiously Unaffiliated experienced attending church less positively than Christians; when compared at the highest level of Attendance, the Religiously Unaffiliated were less healthy than Christians; and when only considering the Religiously Unaffiliated, Religious/Spiritual variables were not significant and positive predictors of health outcomes. The discussion focused on the need to delineate between how Christians and the Religiously Unaffiliated experience Religious/Spiritual variables, and the need to stop over-generalizing the positive relationship between Religious/Spiritual variables and health.

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The relationship between atheism and health is poorly understood within the Religion/Spirituality-health literature. While the extant literature promotes the idea that Attendance, Prayer, and Religiosity are connected to positive health outcomes, these relationships have not been established when controlling for whether a person is an atheist. Data from the 2008-2012 American General Social Survey (n = 3210) were used to investigate this relationship. Results indicated that atheists experienced Religiosity more negatively than non-atheists. Additionally, results demonstrated that non-belief in God was not related to better or worse perceived global health, suggesting that belief in God is not inherently linked to better reported health.

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Group-based trajectory models had a rapid development in the analysis of longitudinal data in clinical research. In these models, the assumption of homoscedasticity of the residuals is frequently made but this assumption is not always met. We developed here an easy-to-perform graphical method to assess the assumption of homoscedasticity of the residuals to apply especially in group-based trajectory models. The method is based on drawing an envelope to visualize the local dispersion of the residuals around each typical trajectory. Its efficiency is demonstrated using data on CD4 lymphocyte counts in patients with human immunodeficiency virus put on antiretroviral therapy. Four distinct distributions that take into account increasing parts of the variability of the observed data are presented. Significant differences in group structures and trajectory patterns were found according to the chosen distribution. These differences might have large impacts on the final trajectories and their characteristics; thus on potential medical decisions. With a single glance, the graphical criteria allow the choice of the distribution that best capture data variability and help dealing with a potential heteroscedasticity problem.

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A UPLC-ESI+/--MS/MS method for the simultaneous determination of free (alternariol, alternariol monomethyl ether, altenuene, tenuazonic acid, tentoxin, altertoxin-I) and conjugated (sulfates and glucosides of alternariol and alternariol monomethyl ether) Alternaria toxins in cereals and cereal products (rice, oat flakes and barley) was developed. Optimization of the sample preparation and extraction methodology was achieved through experimental design, using full factorial design for extraction solvent composition optimization and fractional factorial design to identify the critical factors in the sample preparation protocol, which were in turn subjected to optimization. Final extracts were analysed using an Waters Acquity UPLC system coupled to a Quattro Premier XE mass spectrometer equipped with an electrospray interface operated in both positive and negative ionization mode. Chromatographic separation was achieved using an Acquity UPLC HSS T3 column, and the applied gradient elution programme allowed for the simultaneous determination of 10 Alternaria toxins in a one-step chromatographic run with a total run time of only 7min. Subsequently, the method, applying isotopically labelled internal standards ([2H4]-alternariol monomethyl ether and [13C6,15N]-tenuazonic acid), was validated for several parameters such as linearity, apparent recovery, limit of detection, limit of quantification, precision, measurement uncertainty and specificity (in agreement with the criteria mentioned in Commission Regulation No. 401/2006/EC and Commission Decision No. 2002/657/EC). During validation, quality of the bioanalytical data was improved by counteracting the observed heteroscedasticity through the application of weighted least squares linear regression (WLSLR). Finally, 24 commercially available cereal-based foodstuffs were subjected to analysis, revealing the presence of tenuazonic acid in both rice and oat flake samples (

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La técnica de análisis por combustión y detección por infrarrojo no dispersivo (IRND) fue validada para la determinación de materia orgánica en agua, cuantificada como carbono orgánico total (COT). Previamente se optimizó la eliminación del carbono inorgánico (CI) de la muestra con un tiempo óptimo de 1,5 min y una relación ácido de 5%. Se estableció un rango dinámico lineal (RDL) entre 3 y 20 mg/L de COT, en el cual la recta de regresión cumplió con los parámetros que acreditaron su linealidad según el análisis por el método de los mínimos cuadrados, mostrando un coeficiente de correlación de 0,9994. La sensibilidad expresada por la pendiente de la recta de regresión indicó una variación de aproximadamente 5 unidades en la respuesta del detector por cada mg/L de COT. Los límites de detección y cuantificación obtenidos a partir de la recta de regresión fueron 0,517 y 1,722 mg/L de COT, respectivamente. La precisión de la técnica, teniendo como meta un 5% en coeficiente de variación (CV), fue mejor en el agua potable y en concentraciones cercanas a ésta (aprox. 7 mg/L de COT), mientras que las mayores desviaciones se presentaron en concentraciones cercanas a los límites inferior y superior del RDL. Las recuperaciones de concentraciones conocidas sobre muestras reales adicionadas fueron del 85% con baja adición y del 83% con adición alta, valores que sugieren una reevaluación del desempeño de la técnica con respecto a su exactitud, no obstante se alcanzó la meta de recuperación comprendida entre el 70 y el 130%. La técnica así establecida es por tanto apta para el análisis de aguas crudas, potables y residuales y es viable su utilización en el seguimiento a procesos de oxidación avanzada aplicados en el tratamiento de agua para consumo humano.

The technique of combustion analysis and detection by non-dispersive infrared (NDIR) was validated for the determination of organic matter in water, quantified as total organic carbon (TOC). Previously optimized the elimination of inorganic carbon (IC) of the sample with an optimum time sparge of 1.5 min and an acid ratio of 5%. It established a linear dynamic range (LDR) between 3 and 20 mg/L of TOC, in which the regression line that met the parameters credited its linearity as analyzed by the method of least squares, showing a correlation coefficient of 0,9994. The sensitivity expressed by the slope of the regression line indicated a variation of about 5 units in the detector response for each mg/L of TOC. The detection and quantification limits obtained from the regression line were 0.517 and 1.722 mg/L of TOC, respectively. The precision of the technique, aiming at 5% coefficient of variation (CV) was better in the drinking water at concentrations close to it (about 7 mg/L of TOC), whereas larger deviations were presented at concentrations near the lower and upper limits of LDR. The recoveries of known concentrations of actual samples of 85% additions were low addition and 83% with high added values that suggest a reevaluation of the performance of the technique with respect to its accuracy, however the goal was reached between recovery 70 to 130%. The technique is well established thereby capable of analyzing raw water, drinking and waste and feasible to use in monitoring advanced oxidation processes applied in the treatment of drinking water.

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