Statistical Association Measures Research Articles

Detecting Causal Nonlinear Exposure-Response Relations in Epidemiological Data

The possibility of hormesis in individual dose-response relations undermines traditional epidemiological criteria and tests for causal relations between exposure and response variables. Non-monotonic exposure-response relations in a large population may lack aggregate consistency, strength, biological gradient, and other hallmarks of traditional causal relations. For example, a u-shaped or n-shaped curve may exhibit zero correlation between dose and response. Thus, possible hormesis requires new ways to detect potentially causal exposure-response relations. This paper introduces information-theoretic criteria for identifying potential causality in epidemiological data that may contain nonmonotonic or threshold dose-response nonlinearities. Roughly, exposure variable X is a potential cause of response variable Y if and only if: (a) X is INFORMATIVE about Y (i.e., the mutual information between X and Y, I(X; Y), measured in bits, is positive. This provides the required generalization of statistical association measures for monotonic relations); (b) UNCONFOUNDED: X provides information about Y that cannot be removed by conditioning on other variables. (c) PREDICTIVE: Past values of X are informative about future values of Y, even after conditioning on past values of Y; (d) CAUSAL ORDERING: Y is conditionally independent of the parents of X, given X. These criteria yield practical algorithms for detecting potential causation in cohort, case-control, and time series data sets. We illustrate them by identifying potential causes of campylobacteriosis, a foodborne bacterial infectious diarrheal illness, in a recent case-control data set. In contrast to previous analyses, our information-theoretic approach identifies a hitherto unnoticed, highly statistically significant, hormetic (U-shaped) relation between recent fast food consumption and women's risk of campylobacteriosis. We also discuss the application of the new information-theoretic criteria in resolving ambiguities and apparent contradictions due to confounding and information redundancy or overlap among variables in epidemiological data sets.

To BIS or Not to BIS? That Is the Question

T his editorial accompanies two papers (1,2) on the use of the Bispectral Index (BIS) as a sedation index in children. Before discussing the salient elements and findings of these papers, it is instructive to consider what processed electroencephalogram (EEG) monitors actually measure. As an analogy, consider the dark days before the introduction of pulse oximetry into clinical practice, when clinicians generally used something that might approximate to a four-point scale (pink/slightly blue/ dark blue/black) to assess oxygenation. The introduction of pulse oximetry gave a continuous measure of oxygen saturation as a percentage of saturated hemoglobin and quickly became the gold standard for measuring oxygenation, despite the lack of prospective randomized trial evidence of improved outcomes (3). Similarly, we have multiple discontinuous clinical scales for describing sedation levels in adults, including the Observer’s Assessment of Alertness and Sedation (OAAS) and the Ramsay scales. The purpose of processed EEG monitors is to provide a continuous measure that encompasses the full range of sedation levels measured by the discontinuous scales. Pulse oximetry measures a physiological parameter that most physicians can readily understand (oxygen saturation). In contrast, processed EEG monitors calculate a mathematical abstraction of the electroencephalogram, a concept less familiar and less accessible to the practicing clinician. BIS was derived by empirically estimating the EEG parameters that best predicted OAAS measurements in a large patient and volunteer database of subjects receiving hypnotics and opioids. As a continuous measure that correlates to OAAS measures obtained from subjects receiving hypnotic drugs, BIS may be described as a “probability of state” measure, reflecting the complex nature of consciousness (4). Being derived from the OAAS, BIS should be expected to correlate well with the OAAS. The correlation would probably be less strong with other rating scales, such as the Ramsay scale, the modified maintenance of wakefulness test (MMWT) scale used in pediatrics, or the University of Michigan sedation scale (UMSS). These latter scales were not part of the database used to develop the BIS monitor, and the original database was entirely constructed from adult EEG data. Normal pediatric EEG differs markedly from adult EEG, displaying more variation than adult EEG (5,6). This may make processed EEG parameters less reliable in children. In general, the electrical activity of the brain changes during growth and development, warranting age-specific considerations and cautious interpretation of EEG data in the pediatric population. Despite such theoretical concerns, studies suggest that the performance of BIS in pediatric patients older than 6 months of age may be similar to that of adults (7–9). In younger infants, brain maturation and development may render processed EEG measures unreliable. However, McDermott et al. (8) still found a significant correlation between BIS and the UMSS in patients younger than 6 months of age in a small group of patients. In this issue of Anesthesia & Analgesia, Malviya et al. (1) report on the observed relationship between BIS and two observational measures, the UMSS and MMWT, in children 1 month to 17 years conceptual age. In lieu of clinical guidelines that call for delineation of sedation states, the investigators were particularly interested in the ability of different measures to discriminate conscious from deep sedation. Data from 39 patients were included, comprising repeated measurements (about 8 per individual on average) of sedation indices after unspecified procedures that required sedation/analgesia or general anesthesia. The authors report good correlation between UMSS and BIS ( 0.73), indicating reasonable concordance between these discontinuous and continuous scales. This supports the validity of BIS as a pediatric sedation monitor and complements similar reports by this group (10) and others (8). MMWT scores, by contrast, correlated weakly (0.36) with BIS, in contrast to earlier Dr. Peter S. Sebel is a paid consultant to Aspect Medical Systems. Accepted for publication November 16, 2005. Address correspondence and reprint requests to Peter S. Sebel, MB BS, PhD, MBA, Department of Anesthesiology, Emory University School of Medicine, 49 Jesse Hill Jr. Drive, SE, Atlanta, GA 30303. Address e-mail to peter_sebel@emoryhealthcare.org.

Using small random samples for the manual evaluation of statistical association measures

In this paper, we describe the empirical evaluation of statistical association measures for the extraction of lexical collocations from text corpora. We argue that the results of an evaluation experiment cannot easily be generalized to a different setting. Consequently, such experiments have to be carried out under conditions that are as similar as possible to the intended use of the measures. Finally, we show how an evaluation strategy based on random samples can reduce the amount of manual annotation work significantly, making it possible to perform many more evaluation experiments under specific conditions.

Evaluation of statistical association measures for the automatic signal generation in pharmacovigilance

Pharmacovigilance aims at detecting the adverse effects of marketed drugs. It is generally based on the spontaneous reporting of events thought to be the adverse effects of drugs. Spontaneous Reporting Systems (SRSs) supply huge databases that pharmacovigilance experts cannot exhaustively exploit without data mining tools. Data mining methods; i.e., statistical association measures in conjunction with signal generation criteria, have been proposed in the literature but there is no consensus regarding their applicability and efficiency, especially since such methods are difficult to evaluate on the basis of actual data. The objective of this paper is to evaluate association measures on simulated datasets obtained with SRS modeling. We compared association measures using the percentage of false positive signals among a given number of the most highly ranked drug-event combinations according to the values of the association measures. By considering 150 drugs and 100 adverse events, these percentages of false positives, among the 500 most highly ranked drug-event couples, vary from 1.1% to 53.4% (averages over 1000 simulated datasets). As the measures led to very different results, we could identify which measures appeared to be the most relevant for pharmacovigilance.

Violence exposure in home and community: Influence on posttraumatic stress symptoms in Army recruits*

AbstractThis study assessed the levels and types of violence exposure, levels of posttraumatic stress symptoms, and the relationship among exposure to violence, posttraumatic stress symptoms, and early discharge in U.S. Army recruits at Basic Combat Training (BCT). The study applied a modified ABCX model of family stress adaptation developed by McCubbin, Thompson, and McCubbin (1996). A sample of 779 BCT recruits were surveyed before training began. At the end of training, data was collected on those recruits who had been discharged before completion of training. Statistical measures of association were used to assess the relationship between the variables. Results supported all three of the hypotheses tested. Significant positive relationships were found between violence exposure and trauma symptoms, as well as levels of trauma symptoms and odds of early discharge. Patterns of association were found between types of exposure to community versus home violence and specific symptom clusters of traumatic stress. © 2004 Wiley Periodicals, Inc. J Comm Psychol 32: 527–541, 2004.

Nonstationary Time Series, Cointegration, and the Principle of the Common Cause

Elliot Sober ([2001]) forcefully restates his well-known counterexample to Reichenbach's principle of the common cause: bread prices in Britain and sea levels in Venice both rise over time and are, therefore, correlated; yet they are ex hypothesi not causally connected, which violates the principle of the common cause. The counterexample employs nonstationary data-i.e., data with time-dependent population moments. Common measures of statistical association do not generally reflect probabilistic dependence among nonstationary data. I demonstrate the inadequacy of the counterexample and of some previous responses to it, as well as illustrating more appropriate measures of probabilistic dependence in the nonstationary case. 1 A challenge to the principle of the common cause 2 Sober's argument and the attempts to rescue the principle 3 Probabilistic dependence 4 Nonstationary time series 5 Probabilistic dependence in nonstationary time series 6 Do Venetian sea levels and British bread prices violate the principle of the common cause?

Measuring praise and criticism

The evaluative character of a word is called its semantic orientation . Positive semantic orientation indicates praise (e.g., "honest", "intrepid") and negative semantic orientation indicates criticism (e.g., "disturbing", "superfluous"). Semantic orientation varies in both direction (positive or negative) and degree (mild to strong). An automated system for measuring semantic orientation would have application in text classification, text filtering, tracking opinions in online discussions, analysis of survey responses, and automated chat systems ( chatbots ). This article introduces a method for inferring the semantic orientation of a word from its statistical association with a set of positive and negative paradigm words. Two instances of this approach are evaluated, based on two different statistical measures of word association: pointwise mutual information (PMI) and latent semantic analysis (LSA). The method is experimentally tested with 3,596 words (including adjectives, adverbs, nouns, and verbs) that have been manually labeled positive (1,614 words) and negative (1,982 words). The method attains an accuracy of 82.8% on the full test set, but the accuracy rises above 95% when the algorithm is allowed to abstain from classifying mild words.

A corpus-based approach to comparative evaluation of statistical term association measures

Statistical association measures have been widely applied in information retrieval research, usually employing a clustering of documents or terms on the basis of their relationships. Applications of the association measures for term clustering include automatic thesaurus construction and query expansion. This research evaluates the similarity of six association measures by comparing the relationship and behavior they demonstrate in various analyses of a test corpus. Analysis techniques include comparisons of highly ranked term pairs and term clusters, analyses of the correlation among the association measures using Pearson's correlation coefficient and MDS mapping, and an analysis of the impact of a term frequency on the association values by means of z-score. The major findings of the study are as follows: First, the most similar association measures are mutual information and Yule's coefficient of colligation Y, whereas cosine and Jaccard coefficients, as well as χ2 statistic and likelihood ratio, demonstrate quite similar behavior for terms with high frequency. Second, among all the measures, the χ2 statistic is the least affected by the frequency of terms. Third, although cosine and Jaccard coefficients tend to emphasize high frequency terms, mutual information and Yule's Y seem to overestimate rare terms.

A corpus‐based approach to comparative evaluation of statistical term association measures

Statistical association measures have been widely applied in information retrieval research, usually employing a clustering of documents or terms on the basis of their relationships. Applications of the association measures for term clustering include automatic thesaurus construction and query expansion. This research evaluates the similarity of six association measures by comparing the relationship and behavior they demonstrate in various analyses of a test corpus. Analysis techniques include comparisons of highly ranked term pairs and term clusters, analyses of the correlation among the association measures using Pearson's correlation coefficient and MDS mapping, and an analysis of the impact of a term frequency on the association values by means of z-score. The major findings of the study are as follows: First, the most similar association measures are mutual information and Yule's coefficient of colligation Y, whereas cosine and Jaccard coefficients, as well as χ2 statistic and likelihood ratio, demonstrate quite similar behavior for terms with high frequency. Second, among all the measures, the χ2 statistic is the least affected by the frequency of terms. Third, although cosine and Jaccard coefficients tend to emphasize high frequency terms, mutual information and Yule's Y seem to overestimate rare terms.

Some benefits of dichotomization in psychiatric and criminological research

AbstractBackgroundThe product‐moment correlation r is widely used in criminology and psychiatry to measure strength of association. However, most criminological and psychiatric variables contravene its underlying assumptions.AimTo compare statistical measures of association based on dichotomous variables with the use of r.MethodExplanatory variables for delinquency are investigated in the Pittsburgh Youth Study using a sample of 506 boys aged 13–14.ResultsDichotomization does not necessarily cause a decrease in measured strength of associations. Conclusions about the most important explanatory variables for delinquency were not greatly affected by using dichotomous as opposed to continuous variables, by different dichotomization splits, or by using logistic versus OLS multiple regression. Non‐linear relationships, interaction effects and multiple risk factor individuals were easily studied using dichotomous data.ConclusionsDichotomization produces meaningful findings that are easily understandable to a wide audience. Measures of association for dichotomous variables, such as the odds ratio, have many advantages and are often more realistic and meaningful measures of strength of relationship than the product‐moment correlation r. Copyright © 2000 Whurr Publishers Ltd.

Massively parallel processing of spatial statistics

Abstract Statistical measures of spatial association have significant computational requirements when large data sets are analysed. In this paper, a measure of spatial association, G(d), is used to illustrate how a massively parallel computer can be used to address the computational requirements of spatial statistical analysis. The statistical algorithms were implemented using two MasPar MP-1 computers, one with 8192 and the other with 16834 processors, and an MP-2 machine with 4096 processors. The results demonstrate that substantial reductions in processing times can be achieved using massively parallel architectures: when compared to a superscalar workstation, speed-up values in excess of 20 were obtained. The design of parallel programmes, however, requires careful planning since many factors under programmer control affect the efficiency of the resulting computations.

Algebraic learning of statistical associations for language acquisition

Statistical association measures play an important role in many areas of natural language research. An impediment to reliable estimation of such associations is the problem of small-sample statistics, since in any natural corpus there will be many infrequently occurring words.This paper proposes an alternative method for estimating such associations, which circumvents the small-sample issues. The idea is to view sentence/meaning pairs as algebraic equations, rather than as observations of a pattern in some class. Associations are estimated via solving these equations rather than via relative frequency estimates of mutual information. We develop a theoretical foundation for the dual algebraic/statistical nature of associations, proving two uniqueness theorems. We then exploit this theory to provide an algorithmic solution to the estimation problem. This algorithm is experimentally evaluated on 1494 natural languages messages from a rudimentary Data Retrieval experiment. One striking result is that the algebraic algorithm can often provide reliable estimates even for words which occur only once in a corpus.

MacArthur's consumer-resource model

MacArthur's consumer-resource model is reviewed and new ways of understanding it are presented. Statistical measures of association between the utilization functions of different species are developed to show how coexistence conditions can be expressed in simple and understandable ways without the need to introduce strong symmetry assumptions. It is hoped that this new analysis will encourage both the use of the model in its full form without special simplifying assumptions, and the development of competition models of similar biological richness but different basic assumptions.

Reviewing the statistical measures of association for the triple dichotomy

Reviewing the statistical measures of association for the triple dichotomy

Consensual Attitudes and Attitude Structure

Consensual Attitudes and Attitude Structure

Contingency spaces and measures in classical and instrumental conditioning.

The contingency between conditional and unconditional stimuli in classical conditioning paradigms, and between responses and consequences in instrumental conditioning paradigms, is analyzed. The results are represented in two- and three-dimensional spaces in which points correspond to procedures, or procedures and outcomes. Traditional statistical and psychological measures of association are applied to data in classical conditioning. Root mean square contingency, Ø, is proposed as a measure of contingency characterizing classical conditioning effects at asymptote. In instrumental training procedures, traditional measures of association are inappropriate, since one degree of freedom-response probability-is yielded to the subject. Further analysis of instrumental contingencies yields a surprising result. The well established "Matching Law" in free-operant concurrent schedules subsumes the "Probability Matching" finding of mathematical learning theory, and both are equivalent to zero contingency between responses and consequences.