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PubMed2001

An asymptotically unbiased estimator of exposed versus non-exposed odds ratio from reported dose-response data.

Summary effect measures in meta-analysis of published epidemiological cohort or case control studies are often based on odds ratios reported for several exposure levels with varying arrangements and number of levels across primary studies. Usually only two-way contingency tables together with exposure specific adjusted odds ratios and corresponding standard errors are presented in articles. An asymptotically unbiased estimate of exposed versus non-exposed adjusted odds ratio from reported dose-response data is proposed. This estimate is based on the weighted sum of the exposure specific odds ratios, with the prevalences of the control group as weights. Large sample variance is derived accounting for the dependency between exposure specific adjusted odds ratios. The exposed versus non-exposed adjusted odds ratio could then be used in systematic reviewing.

Case-Control Studies↗

PubMed1990

Kappa and attenuation of the odds ratio.

This paper explores the relation between reliability and validity for binary variables. An equation is first derived for expressing the kappa coefficient of reliability as a function of true prevalence, sensitivity, specificity, and the degree of correlation of errors within true positives and within true negatives. It is then shown that under certain circumstances kappa is closely related to an index of the validity of the odds ratio as a means for quantifying an association between an imperfectly classified binary factor and membership in two subpopulations. This index is defined as the ratio of the observed odds ratio minus one to the true odds ratio minus one. Numerical results indicate that, when error rates are high, kappa can be of smaller magnitude than this index of validity. When the value of kappa reflects substantial correlation of errors, however, the value of kappa typically exceeds that of the index of validity. Correlated errors among the true negatives are found to affect the correspondence between kappa and the index of validity rather differently than do correlated errors among the true positives. Although kappa often exceeds the index of validity, use of kappa to correct the odds ratio for attenuation owing to nondifferential misclassification generally leads to undercorrection rather than overcorrection. Consequently, the relation between kappa and the index of the validity of the odds ratio may have practical value for reducing bias in the estimation of exposure-disease associations in epidemiologic research.

Case-Control Studies↗

PubMed1991

The effect on the stratum-specific odds ratios of nondifferential misclassification of a dichotomous covariate.

Precise measurement of confounding or effect modifying variables is seldom possible. Nondifferential misclassification of such a variable can introduce bias in the odds ratios within the strata of the confounding variable. For two strata, the effect on the odds ratios is dependent on separate measures of the degree of nondifferential misclassification of the confounding variable. The authors investigate the bias in the stratum-specific odds ratios from nondifferential misclassification of a confounder in a case-control study, and show how estimates of the true stratum-specific odds ratios can be derived. For one stratum, the degree of bias introduced in the odds ratio is dependent only on the sensitivity of the measure of the confounding variable while only the specificity of this measure determines the bias introduced in the other stratum-specific odds ratio. The results are applied to a case-control study of fenoterol prescription and asthma death.

Bias↗

PubMed2003

Np.OR: an S-Plus function for pointwise nonparametric estimation of odds-ratios of continuous predictors.

Calculating odds ratios (OR) and corresponding confidence intervals (CI) for exposures that have been measured using a continuous scale, presents important limitations in the traditional practice of epidemiology. Our objective is to describe an S-Plus function, that we called np.OR, that allows the computation of the pointwise estimates of the ORs as well as their corresponding CIs of continuous predictors introduced nonlinearly in a generalised model. The function can also be generalised to compute the pointwise estimates of categorical predictors that were introduced nonlinearly. To illustrate usage of the program we analyse the relationship between ambient temperature and total mortality in Barcelona for the period 1991-1995, while controlling for observed and unobserved confounders.

Confidence Intervals↗

PubMed1991

A consequence of omitted covariates when estimating odds ratios.

In the epidemiologic literature, one finds three criteria for confounding, which we will call the classical (marginal), operational (change-in-estimate) and conditional criteria. We define mavericks to be covariates that satisfy the operational criterion, but not the classical criterion. We present what is known about the problems of mavericks for estimating odds ratios and clarify the interpretation of odds ratios. Key results are: (1) omitting mavericks biases odds ratios towards 1; (2) omitting mavericks cannot artificially introduce an effect in contrast to omitting classical confounders; (3) the operational criterion for confounding corresponds to the conditional criterion when estimating odds ratios, but for relative risks, there are no mavericks (i.e. the classical and operational criterion correspond); and (4) the interpretation of odds ratios obtained from standard methods is that of comparing proportions, not of individual risk.

Confounding Factors, Epidemiologic↗

PubMed1996

Mantel-Haenszel-type inference for cumulative odds ratios with a stratified ordinal response.

This article proposes a Mantel-Haenszel-type estimator of an assumed common cumulative odds ratio in a proportional odds model for an ordinal response with several 2 x c contingency tables. It is useful, for instance, for comparing two treatments on an ordinal response for data from several centers when the data are highly sparse. The estimator has behavior similar to the Mantel-Haenszel estimator of a common odds ratio for several 2 x 2 tables. It is consistent under the ordinary asymptotic framework in which the number of tables is fixed and, unlike the maximum likelihood (ML) estimator, also under sparse asymptotics in which the number of tables grows with the sample size. Simulations reveal a considerable difference between it and the ML estimator when each table has few observations. Efficiency comparisons suggest that little efficiency loss occurs compared to the ML estimator when the data are not sparse. Tests and estimators are presented for detecting and handling heterogeneity in the odds ratios, and generalizations are available for stratified r x c contingency tables.

Asthma↗

PubMed2006

Conditional relative odds ratio and comparison of accuracy of diagnostic tests based on 2 x 2 tables.

In order to evaluate the accuracy of diagnostic tests based on 2 x 2 tables, a number of indices were used, some of which are occasionally used inappropriately. This paper demonstrates the characteristics and problems with those indices, and introduces several methods to compare the accuracy of two diagnostic tests. The author summarizes existing indices based on 2 x 2 tables, agreement rate, kappa (kappa), and odds ratio, and reviews their characteristics to find better indices by which to compare two diagnostic tests using hypothetical examples. Because only the odds ratio is not affected by prevalence, the relative odds ratio is the most appropriate index for comparing diagnostic accuracy. In order to decrease selection bias, giving the two tests to the same individuals is preferred. However, no standard method has been established to obtain the standard error of relative odds ratios. In this case, using the newly proposed conditional relative odds ratio (CROR), based on McNemar's odds ratio, the standard error is available. The CROR is a less biased index when the two tests were given to the same individuals, and it is also preferable in light of its ethical and economic advantages. However, a large base population is required for the two tests to be highly accurate and produce few discordant results.

Data Interpretation, Statistical↗

PubMed1987

Prevalence rates and odds ratios of shoulder-neck diseases in different occupational groups.

The aim of the present study was to evaluate the association and impact of occupational exposure and diseases of the shoulder and neck. Prevalence rates, odds ratios, aetiological fractions, and their confidence intervals were computed for pooled and non-pooled data of previous published reports. By comparison with office workers and farmers, dentists had an increased odds ratio for cervical spondylosis (two studies) and for shoulder joint osteoarthrosis. Meat carriers, miners, and "heavy workers" also had significantly higher rates of cervical spondylosis compared with referents. Compared with iron foundry workers, civil servants had a significant odds ratio (4.8) of cervical disc disease and a 0.79 aetiological fraction. Whether this was due to exposure or healthy worker effect was not clear. In four occupational groups with high shoulder-neck load an odds ratio of 4.0 was found for thoracic outlet syndrome with an aetiological fraction of 0.75. Rotator cuff tendinitis in occupational groups with work at shoulder level (two studies) showed an odds ratio of 11 and an aetiological fraction of 0.91. Keyboard operators had an odds ratio of 3.0 for tension neck syndrome (five studies). Unfortunately, owing to the scanty description of the work task, the exposure could be analysed only by job title. Examination of published reports shows clearly that certain job titles are associated with shoulder-neck disorders. High rates and aetiological fractions for rotator cuff tendinitis and tension neck syndrome suggest that preventive measures could be effective. Although job descriptions are brief, the associations noted suggest that highly repetitive shoulder muscle contractions, static contractions, and work at shoulder level are hazardous exposure factors. In reports of cross sectional studies of occupational shoulder-neck disorders presentation of age, exposure, and effect distribution may help for future meta-analysis.

Adult↗

PubMed2002

On the potential of measurement error to induce differential bias on odds ratio estimates: an example from radon epidemiology.

It is well established that odds ratios estimated by logistic regression are subject to bias if exposure is measured with error. The dependence of this bias on exposure parameter values, particularly for multiplicative measurement error, and its implications in epidemiology are not, however, as fully acknowledged. We have been motivated by a German West case-control study on lung cancer and residential radon, where restriction to a subgroup exhibiting larger mean and variance of exposure than the entire group has shown higher odds ratio estimates as compared to the full analysis. By means of correction formulae and simulations, we show that bias from additive classical type error depends on the exposure variance, not on the exposure mean, and that bias from multiplicative classical type error depends on the geometric standard deviation (in other words on the coefficient of variation of exposure), but not on the geometric mean of exposure. Bias from additive or multiplicative Berkson type error is independent of exposure distribution parameters. This indicates that there is a potential of differential bias between groups where these parameters vary. Such groups are commonly compared in epidemiology: for example when the results of subgroup analyses are contrasted or meta-analyses are performed. For the German West radon study, we show that the difference of measurement error bias between the subgroup and the entire group exhibits the same direction but not the same dimension as the observed results. Regarding meta-analysis of five European radon studies, we find that a study such as this German study will necessarily result in smaller odds ratio estimates than other studies due to the smaller exposure variance and coefficient of variation of exposure. Therefore, disregard of measurement error can not only lead to biased estimates, but also to inconsistent results and wrongly concluded effect differences between groups.

Air Pollutants, Radioactive↗

PubMed2000

Use of conditional and marginal odds-ratios for analysing familial aggregation of binary data.

We propose a method for measuring familial aggregation of binary outcomes that incorporates unconditional, i.e., marginal, odds-ratios, for measuring association between outcomes within generations while using conditional odds-ratios to measure association between generations. This method may be used together with marginal odds-ratio models to explore the strength of association between individuals within a generation while accounting for the outcomes of predecessors. Interpretation of resulting odds-ratios is straightforward and a number of features of the method are discussed. An example, using smoking status data from Busselton Health Study families, is used to illustrate our approach.

Bias↗

PubMed2005

Reduction of sampling bias of odds ratios for vertebral fractures using propensity scores.

INTRODUCTION: Assessment of the predictive power of a newly introduced diagnostic technique with regard to fracture risk is frequently limited by the enormous costs and long time periods required for prospective studies. A preliminary estimate of predictive power usually relies on cross-sectional case-control studies in which bone measurements of normal and fractured subjects are compared. The measured discriminatory power is taken as an estimate of predictive power. Because of possible sample selection bias, study participants may have different bone mineral density (BMD) values, and fractured patients may have fractures of different severity levels. The same diagnostic techniques for the measured discriminatory power, expressed as odds ratios, will differ among studies with different patient and control populations. METHODS: In this paper, we propose a weighted logistic regression approach to adjust the odds ratio in order to reduce the effect of sampling bias. The weight is derived from age, deformity severity, BMD, and the interactions of these, using the propensity score theory and reference population data. RESULTS: Simulation examples using data from the Osteoporosis and Ultrasound Study (OPUS) demonstrate that such a procedure can effectively reduce the estimation bias of odds ratios introduced by sampling differences, such as for dual x-ray absorptiometry (DXA) scans of the spine and hip as well as various quantitative ultrasound techniques. The derived estimated odds ratios are substantially less biased, and the corresponding 95% confidence intervals contain the true odds ratios from the population data. CONCLUSIONS: We conclude that a statistical correction procedure based on propensity scores and weighted logistic regression can effectively reduce the effect of sampling bias on the odds ratios calculated from cross-sectional case-control studies. For a new diagnostic technique, hip BMD and deformity severity information are necessary and likely sufficient to derive the propensity scores required to adjust the measured standardized odds ratios.

Adult↗

PubMed2004

Odds ratios for a continuous outcome variable without dichotomizing.

The loss of information from dichotomizing a continuous outcome is well documented in the literature. One advantage of dichotomizing is that it allows estimation of odds ratio parameters through a logistic regression analysis. The objective of this paper is to develop a new estimator of the same odds ratio parameters through regression analysis on the original continuous outcome without the inherent loss of information caused by dichotomizing. Through a mathematical, asymptotic development the relative sample sizes required to attain a specified power when testing the odds ratio parameter are compared for the dichotomizing procedure and the proposed approach. The comparison highlights the substantial sample size savings attained by the proposed approach, particularly for large values of the odds ratio parameter and for small proportions of dichotomized successes or failures. In a Monte Carlo simulation the variances and absolute biases of the two odds ratio estimators and the length of their respective confidence intervals again demonstrate the improvement attained by the proposed approach. In addition, coverage probabilities of the confidence intervals of the proposed approach converge quickly to the nominal levels. The cost savings due to the reduction in required sample size when using this method make it a very attractive study design and analysis tool for medical researchers.

Adult↗

PubMed2004

Limitations of the odds ratio in gauging the performance of a diagnostic, prognostic, or screening marker.

A marker strongly associated with outcome (or disease) is often assumed to be effective for classifying persons according to their current or future outcome. However, for this assumption to be true, the associated odds ratio must be of a magnitude rarely seen in epidemiologic studies. In this paper, an illustration of the relation between odds ratios and receiver operating characteristic curves shows, for example, that a marker with an odds ratio of as high as 3 is in fact a very poor classification tool. If a marker identifies 10% of controls as positive (false positives) and has an odds ratio of 3, then it will correctly identify only 25% of cases as positive (true positives). The authors illustrate that a single measure of association such as an odds ratio does not meaningfully describe a marker's ability to classify subjects. Appropriate statistical methods for assessing and reporting the classification power of a marker are described. In addition, the serious pitfalls of using more traditional methods based on parameters in logistic regression models are illustrated.

Biomarkers↗

PubMed1990

Model selection and the estimation of odds ratios in the presence of extraneous factors.

This paper deals with model selection and the estimation of odds ratios from cross-classified frequencies in the presence of extraneous factors. The odds ratio is estimated in different ways dependent on whether the extraneous factor is modelled as an effect modifier, a confounder, or neither. Routinely this choice is based on statistical tests of null hypotheses. By contrast, we propose selection of the model which is estimated to maximize the accuracy of the estimator of the odds ratio, on average. We demonstrate how a non-parametric bootstrap method can be used to carry out the selection, and illustrate the methodology using an example on use of oral contraceptives and myocardial infarction.

Adult↗

PubMed2002

Estimating crude or common odds ratios in case-control studies with informatively missing exposure data.

In case-control studies, the crude odds ratio derived from a 2 x 2 table and the common odds ratio adjusted for stratification variables are staple measures of exposure-disease association. While missing exposure data are encountered in the majority of such studies, formal attempts to deal with them are rare, and a complete-case analysis is the norm. Furthermore, the probability that exposure is missing may depend on true exposure status, so the missing-at-random assumption is often unreasonable. In this paper, the authors present an adjustment to the usual product binomial likelihood to properly account for missing data. Estimation of model parameters without restrictive assumptions requires an additional data collection effort akin to a validation study. Closed-form results are provided to facilitate point and confidence interval estimation of crude and common odds ratios after properly accounting for informatively missing data. Simulations assess performance of the likelihood-based estimates and inferences, and they display the potential for bias in complete-case analyses. An example is presented to illustrate the approach.

Bias↗

PubMed1986

Application of odds ratio regression models for assessing familial aggregation from case-control studies.

A regression model for estimating covariate effects on odds ratios to test for familial aggregation of common disease in first-degree relatives of cases and controls is presented and illustrated by using family data from a study of chronic obstructive pulmonary disease. These estimators are in essence an extension of the Mantel-Haenszel estimator of odds ratio but do not require the assumption of independence among relatives. A robust test statistic for possible effects of covariates such as the matching variables for cases and controls on odds ratio is also presented. In data on 156 adult first-degree relatives of 28 cases with demonstrated airway obstruction and 28 controls matched for age, sex, race, and hospital status, there appeared to be a difference in the odds ratio among families of black and white case-control pairs. However, the small sample size available prevents conclusive interpretation of this observation.

Adult↗

PubMed2006

Understanding the relationship between risks and odds ratios.

BACKGROUND: Many articles provide only odds ratios (OR) and non relative risks (RR) as the effect estimate. For a variety of important reasons, multiple logistic regression used to adjust for confounders routinely provides only the adjusted OR (ORadj). However, from the clinician's perspective, the ORadj is only easily interpretable when it approximates the adjusted RR (RRadj). In general, the relationship between the OR and RR (adjusted or nonadjusted) is dependent on prevalence of disease in the control group (Po) and has always been presented as nonlinear. Therefore, it is difficult for the clinician to convert the OR to RR when reading the published data. A formula was proposed by Zhang and Yu, but the relationship remains nonlinear. OBJECTIVE: To develop a simple method to convert OR to RR without the use of computer. METHODS: Algebraic manipulation. RESULTS: Through algebraic manipulation, we show that although the OR and RR relationship is nonlinear over the range Po, the ratio OR/RR has a linear relationship with Po with a slope of "OR-1": OR/RR=(OR-1)xPo+1. This makes the prediction of RR on the basis of OR more transparent. It is clear that if Po is small, the RR approximates the OR, but only if the OR is also small. Previous problems with confidence intervals noted with the Zhang and Yu formula remain (ie, they are too narrow under some conditions) and the result should be interpreted with this limitation. Relationships between ORadj and risk difference or number needed to treat remain curvilinear, but some overall approximations can be made. CONCLUSION: A simple relationship exists that allows readers to easily convert ORadj to RRadj. Limitations of the approach remain but seem to be less restrictive than the limitations of not converting ORadj to RRadj.

Mathematics↗

PubMed2000

A simple method for converting an odds ratio to effect size for use in meta-analysis.

A systematic review may encompass both odds ratios and mean differences in continuous outcomes. A separate meta-analysis of each type of outcome results in loss of information and may be misleading. It is shown that a ln(odds ratio) can be converted to effect size by dividing by 1.81. The validity of effect size, the estimate of interest divided by the residual standard deviation, depends on comparable variation across studies. If researchers routinely report residual standard deviation, any subsequent review can combine both odds ratios and effect sizes in a single meta-analysis when this is justified.

Animals↗