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Correlation and prediction: interpreting the significance of r.

Given the growing popularity of cephalometric programs for the personal computer, it is once again necessary for the specialty to confront the problem of prediction accuracy. The strength of the relationships upon which a prediction scheme is based is often assessed by means of the coefficient of linear correlation, r. Although it is common to judge the practical significance of a relationship by squaring the correlation coefficient, the present paper argues that the index of forecasting efficiency, the percentage reduction in error, is not only the more appropriate index, but also one that is easy to infer directly from r.

Cephalometry↗

Philosophical conjectures and their refutation.

Sir Karl Popper is well known for explicating science in falsificationist terms, for which his degree of corroboration formalism, C(h,e,b), has become little more than a symbol. For example, de Queiroz and Poe in this issue argue that C(h,e,b) reduces to a single relative (conditional) probability, p(e,hb), the likelihood of evidence e, given both hypothesis h and background knowledge b, and in reaching that conclusion, without stating or expressing it, they render Popper a verificationist. The contradiction they impose is easily explained--de Queiroz and Poe fail to take account of the fact that Popper derived C(h,e,b) from absolute (logical) probability and severity of test, S(e,h,b), where critical evidence, p(e,b), is fundamental. Thus, de Queiroz and Poe's conjecture that p(e,hb) = C(h,e,b) is refuted. Falsificationism, not verificationism, remains a fair description of the parsimony method of inference used in phylogenetic systematics, not withstanding de Queiroz and Poe's mistaken understanding that "statistical" probability justifies that method. Although de Queiroz and Poe assert that maximum likelihood has the power "to explain data", they do not successfully demonstrate how causal explanation is achieved or what it is that is being explained. This is not surprising, bearing in mind that what is assumed about character evolution in the accompanying likelihood model M cannot then be explained by the results of a maximum likelihood analysis.

Likelihood Functions↗

Seasonality of birth and conception to teenagers in Texas.

We study the births to teenagers during the years 1964-2000 and analyze separately the three main racial/ethnic groups in Texas (White, Hispanic, and African American), as well as married and unmarried teens during the years 1994-2000. By using traditional statistical methods of analysis and a filter based on the multiresolution wavelet analysis, we draw inferences about the times of the year when adolescent females of different racial/ethnic and marital groups have the highest probability for pregnancy ending in live birth. Multiple factors influencing teen pregnancy are identified and associated with temporal features of social, cultural, educational, and familial processes. In particular, we detect links between unmarried teen conception times and school terms, and weekly birth patterns associated with scheduled c-sections that differ according to racial/ethnic groups.

Adolescent↗

GRNContext: an interactive web platform for contextualized gene regulatory networks visualization across human cancers.

SUMMARY: While current Gene Regulatory Network (GRN) databases provide comprehensive reference maps of potential interactions between transcription factors and target genes, they do not specify which regulatory interactions are active within specific biological contexts. This limitation is particularly critical in cancer, where transcriptional programs are inherently tissue-specific. To address this gap, we developed GRNContext, an interactive web platform designed for the visualization, exploration, and comparative analysis of gene regulatory networks contextualized across 33 cancer types from The Cancer Genome Atlas (TCGA). Our approach uses the TFLink human reference GRN as a starting point and integrates TCGA transcriptomic profiles to infer cancer-specific regulatory activity. Regulatory relevance was assessed using complementary machine learning and statistical methods, which were unified into a consensus score to prioritize and filter the most relevant candidate regulators for each target gene. By providing both curated context-specific GRNs and a user-friendly platform, GRNContext constitutes a comprehensive and accessible resource that supports mechanistic investigations, hypothesis generation, and translational research focused on transcriptional regulation in cancer. AVAILABILITY AND IMPLEMENTATION: GRNContext is supported by all major browsers and freely available on the web at https://apps.cienciavida.org/grncontext. It is implemented as a client-server web application featuring a FastAPI backend and a React frontend utilizing Cytoscape.js for interactive network visualization, all containerized via Docker for cross-platform compatibility.

Humans↗

BGX: a fully Bayesian integrated approach to the analysis of Affymetrix GeneChip data.

We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common statistically coherent framework, allowing all components and thus associated errors to be considered simultaneously. Secondly, inference is based on the full posterior distribution of gene expression indices and derived quantities, such as fold changes or ranks, rather than on single point estimates. Measures of uncertainty on these quantities are thus available. The models presented represent the first building block for integrated Bayesian Analysis of Affymetrix GeneChip data: the models take into account additive as well as multiplicative error, gene expression levels are estimated using perfect match and a fraction of mismatch probes and are modeled on the log scale. Background correction is incorporated by modeling true signal and cross-hybridization explicitly, and a need for further normalization is considerably reduced by allowing for array-specific distributions of nonspecific hybridization. When replicate arrays are available for a condition, posterior distributions of condition-specific gene expression indices are estimated directly, by a simultaneous consideration of replicate probe sets, avoiding averaging over estimates obtained from individual replicate arrays. The performance of the Bayesian model is compared to that of standard available point estimate methods on subsets of the well known GeneLogic and Affymetrix spike-in data. The Bayesian model is found to perform well and the integrated procedure presented appears to hold considerable promise for further development.

Bayes Theorem↗

Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies.

We describe extensions to the method of Pritchard et al. for inferring population structure from multilocus genotype data. Most importantly, we develop methods that allow for linkage between loci. The new model accounts for the correlations between linked loci that arise in admixed populations ("admixture linkage disequilibium"). This modification has several advantages, allowing (1) detection of admixture events farther back into the past, (2) inference of the population of origin of chromosomal regions, and (3) more accurate estimates of statistical uncertainty when linked loci are used. It is also of potential use for admixture mapping. In addition, we describe a new prior model for the allele frequencies within each population, which allows identification of subtle population subdivisions that were not detectable using the existing method. We present results applying the new methods to study admixture in African-Americans, recombination in Helicobacter pylori, and drift in populations of Drosophila melanogaster. The methods are implemented in a program, structure, version 2.0, which is available at http://pritch.bsd.uchicago.edu.

Algorithms↗

Potential dangers in the customary methods of conducting meta-analyses. Recombinant versus urinary follicle stimulating hormone.

The customary method of combining success rates in meta-analyses may often result in serious biases, leading to erroneous inferences. This arises because of an inadmissible pooling of frequencies from heterogeneous sources. The fundamental statistical principle, that the magnitude of an 'effect' should always be tested against the variation in that effect over the sample, may not therefore be satisfied. A simple, but rigorous, alternative method is described.

Bias↗

Assessing, accommodating, and interpreting the influences of heterogeneity.

Heterogeneity, ranging from measurement error to variation among individuals or regions, influences all levels of data collected for risk assessment. In its role as a nemesis, heterogeneity can reduce the precision of estimates, change the shape of a population model, or reduce the generalizability of study results. In many contexts, however, heterogeneity is the primary object of inference. Indeed, some degree of heterogeneity in excess of a baseline amount associated with a statistical model is necessary in order to identify important determinants of response. This report outlines the causes and influences of heterogeneity, develops statistical methods used to estimate and account for it, discusses interpretations of heterogeneity, and shows how it should influence study design. Examples from dose-response modeling, identification of sensitive individuals, assessment of small area variations and meta analysis provide applied contexts.

Animals↗

Application of log-linear model in inference on karyotypic evolution in chronic myelocytic leukemia.

Relationships among additional chromosome abnormalities in chronic myelocytic leukemia (CML) with translocation 9;22 [Philadelphia chromosome (Ph1)-positive CML] were analyzed by log-linear models on 709 karyotypes reported in the literature. Additional abnormalities, such as the gain of chromosome 8 (+8), gain of Philadelphia chromosome (+Ph1), isochromosome of the long arm (q) of chromosome 17 [i(17q)], and the gain of chromosome 19 (+19), were frequently observed. A four-way 2 x 2 x 2 x 2 contingency table was considered with respect to the appearance of these four abnormalities, then the hierarchical log-linear models having at least four main effects were fitted to the observed contingency table. Akaike's information criteria of the models reflected the fitness of the model very well. Parameter estimates of the interaction terms indicated that the combinations of two abnormalities, '+8 and +19', '+Ph1 and +19', and '+8 and i(17q)' were positively associated, while '+Ph1 and i(17q)', and '+19 and i(17q)' were negatively associated. Based on the results of the data analysis, an inference was made on the route of karyotypic evolution in Ph1-positive CML; it statistically supports the hypothesis presented by Heim and Mitelman.

Aneuploidy↗

Current fertility: a first glimpse from the 1983 National Demographic Survey.

This paper highlights initial findings from the 1983 National Demographic Surveys (NDS) based on a 25% sub-sample of the survey respondents. The discussion focuses on measures of current fertility as well as on selected fertility "predictors" for the 3 major island groups -- Luzon, Visay, and Mindanao. Owing to the restrictive nature of the data set, no statistical tests are performed to measure the influence on fertility of these explanatory variables. Instead, inferences are drawn from a descriptive analysis of the patterns exhibited. Findings point to a continuation of fertility decline as evidenced by the estimated crude birthrate of 33.6 births/1000.

Asia↗

The success of restorative dentistry?

Direct statistical evidence of the value of routine, periodic dental examination and treatment is lacking and inferences can only be drawn from surveys of population samples and groups of people. Except perhaps in areas of exceptionally favourable dentist: population ratios the restorative philosophy makes too high a demand on scarce professional resources for it to answer the treatment needs of populations. However, it was originally developed to benefit individual patients who sought dental care and the evidence at present suggests that it may postpone the loss of teeth. It is hypothesized that the restorative philosophy is palliative rather than remedial.

Adolescent↗

The effectiveness of orofacial myofunctional therapy in improving dental occlusion.

The most significant findings of this study definitively establish the beneficial effects of orofacial myofunctional therapy on improving dental occlusion, decreasing dental open bite, and decreasing dental overjet. The results reported are actually quite conservative because of the method of measuring. Measuring and recording every tooth unquestionably dilutes the results which would have been achieved if only the anterior teeth had been used in the calculations. Some may question the small millimeter change as being significant. The change is reflective of the overall relative value change of incorporating all teeth within the dental arches and not limiting the analysis to only the anterior teeth. The secondary findings of the study confirm that age is not necessarily a factor in predicting success of a therapy program. Further, this study indicates that improvement of open bite and overjet can result from OMT without prior or concurrent orthodontic intervention. Orofacial myofunctional therapy, from a public health standpoint, is a classic form of primary prevention to improve the overall health and well-being of the individual. The end result of OMT therapeutic programs is the establishment of new neuromuscular patterns, correction of functional and resting postures, correction of chewing/swallowing/feeding patterns and elimination of deleterious behaviors. Stabilization and maintenance of therapeutic goals become part of the lifelong learning and change process. Orofacial myofunctional therapy utilizes knowledge and skills acquired through multidisciplinary education and training. Licensed professionals, from dental hygiene, dentistry, speech pathology, medicine, nursing, and other allied health professions with advanced education and training in orofacial myofunctional therapy have demonstrated expertise in providing collaborative, integrated, and interdisciplinary primary care. Reference to earlier research works and anecdotal reports of ineffectiveness unfortunately perpetuate and reinforce the dichotomous quandary of form and function. Instead, recognition of the interrelationship of form and function, as conjoint fundamental processes, would encourage more pro-active patient referrals for orofacial myofunctional therapy services. This would allow the specialty area of orofacial myology to further validate the effectiveness of OMT on tooth movement in a positive, collaborative, and beneficial manner. Acknowledging the small sample size in this study may encourage other clinicians to conduct future research in this area. Additional research is needed on the physiologic adaptive capacity of the orofacial environment. Developmental aspects of orofacial and jaw neurophysiology, especially in children, are scant in the literature. Treatment recommendations for specific dental malocclusions are based on many factors. Each malocclusion classification presents opportunity for OMT research. A major research dilemma for the practicing clinician is the moral and ethical responsibility of providing treatment when dysfunction is diagnosed. Designing a study and identifying a "control group" is difficult due to the unethical aspect of knowingly withholding therapy when the benefits are statistically proven and available. A study design using the sample as its own control can infer and demonstrate validity. The next logical test is replication of this study to determine the level of reliability. This issue of the I.J.O.M. addresses the effectiveness of orofacial myology treatment in improving speech articulation, eliminating digit sucking, and improving dental occlusion. It is time the professions of dental hygiene, dentistry, medicine, and speech pathology move forward and acknowledge current substantive research and literature that supports the philosophies of prevention, early interception (intervention), and corrective treatment. The dark ages of disbelief only remain dark as long as we forget to turn on the light. (ABSTRACT TRU

Adolescent↗

APACHE II and SAPS II are poorly calibrated in a Hong Kong intensive care unit.

This study seeks to determine if the Acute Physiology and Chronic Health Evaluation II (APACHE II) and the new Simplified Acute Physiology Score (SAPS II) model predictions are well calibrated in our adult Intensive Care Unit (ICU) patient population. 1064 successive ICU discharges were enrolled with 222 deaths at hospital discharge. APACHE II predicted 287.44 deaths, thus giving an APACHE II standardised mortality ratio (SMR) of 0.77 (95% confidence interval +/- 0.07). SAPS II predicted 269.59 deaths, giving a SAPS II SMR of 0.82 (95% confidence interval +/- 0.07). The Hosmer-Lemeshow goodness-of-fit C statistic was 43.96 for APACHE II and 49.06 for SAPS II (P < 0.001 for both, inferring significant departures from the null hypotheses of good calibration). The area under the Receiver Operating Characteristic plot for SAPS II risk of death was 0.87 (95% confidence interval +/- 0.028) while that for APACHE II risk of death was 0.88 (95% confidence interval +/- 0.026). Although the APACHE II and SAPS II models provide good discriminatory performance this study finds the APACHE II and SAPS II models to be poorly calibrated in that they over-predict mortality in our ICU population.

APACHE↗

Enumerating and ranking discrete motifs.

Discrete motifs that discriminate functional classes of proteins are useful for classifying new sequences, capturing structural constraints, and identifying protein subclasses. Despite the fact that the space of such motifs can grow exponentially with sequence length and number, we show that in practice it usually does not, and we describe a technique that infers motifs from aligned protein sequences by exhaustively searching this space. Our method generates sequence motifs over a wide range of recall and precision, and chooses a representative motif based on a score that we derive from both statistical and information-theoretic frameworks. Finally, we show that the selected motifs perform well in practice, classifying unseen sequences with extremely high precision, and infer protein subclasses that correspond to known biochemical classes.

Algorithms↗

Determining the composition and microstructure of ethylene-propylene copolymers by pyrolysis-gas chromatography.

The average composition and detailed microstructure of copolymers of ethylene and propylene have been studied by pyrolysis-gas chromatography (Py-GC), using a statistical modeling approach to analyze the data. The trimer distribution obtained from Py-GC is used to infer monomer arrangement information, which is quantified in terms of a number-average sequence length for each monomer. These values are used to define the microstructure and to calculate the average composition. Compared with other available techniques, Py-GC provides a simple, quick and reliable approach to study the microstructure and composition of polyolefin copolymers. Details of this Py-GC method are discussed, including an examination of its advantages and disadvantages, and a summary of the qualitative and quantitative analysis aspects of this approach is presented. The combination of a statistical modeling approach with Py-GC to study copolymer composition and microstructure allows one to investigate the complex problem of monomer arrangement in copolymers using a widely available analytical technique. We expect that with further advances in separation technology, especially two-dimensional gas chromatography (GC x GC), research of this type will be become increasingly accurate and reproducible in the near future.

Alkenes↗

Some sources of error and their effect on Census statistics.

Often the reliability of survey data is examined only in relationship to sampling variances, excluding many other potential sources of error. If the sampling variance dominates the mean-square error, then few mistakes result by considering sampling variance only; however, if sampling variance is only a small part of the mean-square error, serious mistakes in inference could be made. The Bureau of the Census has developed a model describing the joint effect of sampling and nonsampling errors on census statistics. This article shows how a study of the components of error may lead to methods of improving the accuracy and reliability of survey data.

Demography↗

On the covariance between parameter estimates in models of twin data.

We study the covariance between estimates of additive genetic variance and either dominance genetic variance or common environmental variance in likelihood-based twin analyses. The central tools used in these investigations are the asymptotic covariances of variance component estimates, which we present for several commonly used twin models. We first illustrate the use of the asymptotic covariance terms for determining the optimal ratio of monozygotic to dizygotic group sample sizes for a twin study. We then focus attention on the asymptotic correlations between estimates of additive genetic variance, and either dominance genetic variance or common environmental variance, and their use in understanding when parameters are efficiently estimable from twin data. The results of this investigation are confirmed by simulation studies, and highlight inherent limitations of the twin model, in the sense that having only twin data limits the ability to detect individual variance components. Finally, remarks on possible alternative statistical methods are given, and results are presented to illustrate the improvements in efficiency that are possible with additional family data. In particular, the results provide insight into the limitations of inference from twin data.

Analysis of Variance↗

Endocrine-disrupting chemical-induced gene networks confer coronary heart disease risk revealed by causal inference and single-cell analyses.

BACKGROUND: Endocrine-disrupting chemicals (EDCs) are linked to coronary heart disease (CHD), but underlying mechanisms remain unclear. We aimed to identify EDC-related genes and evaluate their causal roles in CHD. METHODS: We curated EDC-related genes from a compound-gene interaction database and integrated them with CHD genome-wide association study (GWAS) summary statistics and tissue-specific expression quantitative trait loci (eQTL) data. Two-sample Mendelian randomization (MR) and Bayesian colocalization were applied to infer causality. Functional enrichment, single-cell RNA sequencing of human coronary arteries, and EDC-gene networks were further analyzed. RESULTS: After FDR correction, 39 genes were significantly associated with CHD risk via MR. Four genes-ZNF827, FCHO1, IPO9 (protective), and RPL13 (risk-increasing)-showed strong colocalization (PPH4&#x202f;>&#x202f;0.9). Pathway and single-cell analyses of coronary artery tissue indicated that vascular and immune pathways mediate these effects. An interaction network highlighted associations between specific EDCs and candidate genes implicated in CHD susceptibility. CONCLUSION: This integrative genomic study provides evidence that EDCs influence CHD susceptibility through distinct gene networks, revealing potential mechanisms and molecular targets for prevention and therapy.

Humans↗