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.     

Likelihood ratios,sensitivity, and specificity values can be back-calculated when the odds ratios are known

ObjectiveTo provide a solution for calculating the true-positive, false-positive, false-negative, and true-negative results from studies where only the odds ratios (ORs), number of patients with the finding, and number of patients with the target condition are given.ResultsThe quadratic formula shown here allows investigators conducting systematic reviews to back-calculate the sensitivity, specificity, and likelihood ratios (LRs) from the OR. A spreadsheet that requires only the OR, and the row and column total from the 2 × 2 table enables the back-calculation of the individual true positives, false positives, false negatives, and true negatives. Solutions are also available for the special situations when the OR = 1 or the OR is nonestimable because of zero false positives or false negatives.ConclusionsA simple spreadsheet enables those conducting systematic reviews of diagnostic tests to include studies that report only the OR. This approach should enrich the number of studies retained in meta-analyses of diagnostic tests where the desire is to create summary sensitivity, specificity, or LRs.     

Adjusted odds ratios under nondifferential misclassification: application to prostate cancer

The high prevalence of unsuspected prostate cancer among middle-aged and elderly men is unique among cancers. With their uncertain natural history, unsuspected prostate cancer cases may be misclassified into control groups in which they can obscure the identification of prostate cancer risk factors in case-control studies. Assuming that the exposure experience of diagnosed and of unsuspected prostate cancers is the same (nondifferential misclassification), case-control odds ratios are biased toward the null, which may provide a rationale for reexamining findings in negative case-control studies of prostate cancer. This article reviews the evidence supporting a high prevalence of prostate cancer and describes formulae that can be used to adjust for misclassification bias in completed case-control studies and to estimate required sample sizes in proposed studies.     

Estimation of conditional and marginal odds ratios using the prognostic score

Introduced by Hansen in 2008, the prognostic score (PGS) has been presented as ‘the prognostic analogue of the propensity score’ (PPS). PPS‐based methods are intended to estimate marginal effects. Most previous studies evaluated the performance of existing PGS‐based methods (adjustment, stratification and matching using the PGS) in situations in which the theoretical conditional and marginal effects are equal (i.e., collapsible situations). To support the use of PGS framework as an alternative to the PPS framework, applied researchers must have reliable information about the type of treatment effect estimated by each method. We propose four new PGS‐based methods, each developed to estimate a specific type of treatment effect. We evaluated the ability of existing and new PGS‐based methods to estimate the conditional treatment effect (CTE), the (marginal) average treatment effect on the whole population (ATE), and the (marginal) average treatment effect on the treated population (ATT), when the odds ratio (a non‐collapsible estimator) is the measure of interest. The performance of PGS‐based methods was assessed by Monte Carlo simulations and compared with PPS‐based methods and multivariate regression analysis. Existing PGS‐based methods did not allow for estimating the ATE and showed unacceptable performance when the proportion of exposed subjects was large. When estimating marginal effects, PPS‐based methods were too conservative, whereas the new PGS‐based methods performed better with low prevalence of exposure, and had coverages closer to the nominal value. When estimating CTE, the new PGS‐based methods performed as well as traditional multivariate regression. Copyright © 2016 John Wiley & Sons, Ltd.     

Down with odds ratios: risk ratios in cohort studies and randomised clinical trials

Various effect measures are available for quantifying the relationship between an intervention or a risk factor and an outcome, such as the risk ratio and the odds ratio. Odds ratios are intended for use in case-control studies in which they are an appropriate measure for estimating the relative risk; however, this measure is also often presented in cohort studies and in randomized clinical trials. When used for cohort studies and randomized clinical trials, the odds ratio is often incorrectly interpreted as the risk ratio; the odds ratio then provides an overestimation of the risk ratio, especially when the outcome is frequent. The use of logistic regression to adjust for confounding is one of the reasons that odds ratios are presented. For cohort studies and randomized clinical trials, however, there are methods to estimate adjusted risk ratios; these include the Mantel-Haenszel method, log-binomial regression, Poisson regression with robust standard error, and 'doubling of cases' method with robust standard error. To avoid misinterpretation of odds ratios, risk ratios should be calculated in cohort studies and randomized clinical trials.     

Fluctuations in odds ratios due to variance differences in case-control studies

If small effects of exposure on disease outcome are to be appropriately assessed, it is necessary to consider all potential sources of the fluctuation of relative odds. The authors consider the impact of differential variance in case and control exposure reports on the magnitude of the observed relative odds. With equal dispersion of case and control exposure, a difference in mean exposure generally produces a dose-response increase in relative odds. The combination of equal mean and unequal dispersion of case and control exposure produces a curvilinear pattern of relative odds. Greater mean exposure and dispersion of exposure among cases produce odds ratios lower than those that would be observed if dispersion among cases and controls were equal. Conversely, less dispersion among cases than among controls produces higher relative odds estimates. Differential error as a source of differential dispersion constitutes a potentially important source of bias.     

Case-mix adjusted odds ratios as an alternative way to compare hospital performances

The purpose of this study was to compare two different methods to describe C-section variability among hospital units: case-mix adjusted ORs and case-mix adjusted rates.About 41,755 deliveries without previous C-section occurred in 60 hospitals in 2001 were analysed. Logistic regression was used to produce both adjusted rates and ORs by maternity unit. The two methods showed similar rankings, however ORs estimates were more precise and proved to be a useful tool to describe C-section variability across hospitals.The revised version was published online in July 2005 with corrections in the title.     

Propensity score model overfitting led to inflated variance of estimated odds ratios

ObjectiveSimulation studies suggest that the ratio of the number of events to the number of estimated parameters in a logistic regression model should be not less than 10 or 20 to 1 to achieve reliable effect estimates. Applications of propensity score approaches for confounding control in practice, however, do often not consider these recommendations.Study Design and SettingWe conducted extensive Monte Carlo and plasmode simulation studies to investigate the impact of propensity score model overfitting on the performance in estimating conditional and marginal odds ratios using different established propensity score inference approaches. We assessed estimate accuracy and precision as well as associated type I error and type II error rates in testing the null hypothesis of no exposure effect.ResultsFor all inference approaches considered, our simulation study revealed considerably inflated standard errors of effect estimates when using overfitted propensity score models. Overfitting did not considerably affect type I error rates for most inference approaches. However, because of residual confounding, estimation performance and type I error probabilities were unsatisfactory when using propensity score quintile adjustment.ConclusionOverfitting of propensity score models should be avoided to obtain reliable estimates of treatment or exposure effects in individual studies.     

An approach for modelling multiple correlated outcomes in a network of interventions using odds ratios

A multivariate meta‐analysis of two or more correlated outcomes is expected to improve precision compared with a series of independent, univariate meta‐analyses especially when there are studies reporting some but not all outcomes. Multivariate meta‐analysis requires estimates of the within‐study correlations, which are seldom available. Existing methods for analysing multiple outcomes simultaneously are limited to pairwise treatment comparisons. We propose a model for a joint, simultaneous synthesis of multiple dichotomous outcomes in a network of interventions and introduce a simple way to elicit expert opinion for the within‐study correlations by utilizing a set of conditional probability parameters. We implement our multiple‐outcomes network meta‐analysis model within a Bayesian framework, which allows incorporation of expert information. As an example, we analyse two correlated dichotomous outcomes, response to the treatment and dropout rate, in a network of pharmacological interventions for acute mania. The produced estimates have narrower confidence intervals compared with the simple network meta‐analysis. We conclude that the proposed model and the suggested prior elicitation method for correlations constitute a useful framework for performing network meta‐analysis for multiple outcomes. Copyright © 2014 John Wiley & Sons, Ltd.     

Testing for qualitative interaction using ratios of treatment differences

Testing for or against a qualitative interaction is relevant in randomized clinical trials that use a common primary factor treatment and have a secondary factor, such as the centre, region, subgroup, gender or biomarker. Interaction contrasts are formulated for ratios of differences between the levels of the primary treatment factor. Simultaneous confidence intervals allow for interpreting the magnitude and the relevance of the qualitative interaction. The proposed method is demonstrated by means of a multi‐centre clinical trial, using the R package mratios. Copyright © 2013 John Wiley & Sons, Ltd.     

Unbiased estimation of odds ratios: combining genomewide association scans with replication studies

Odds ratios or other effect sizes estimated from genome scans are upwardly biased, because only the top‐ranking associations are reported, and moreover only if they reach a defined level of significance. No unbiased estimate exists based on data selected in this fashion, but replication studies are routinely performed that allow unbiased estimation of the effect sizes. Estimation based on replication data alone is inefficient in the sense that the initial scan could, in principle, contribute information on the effect size. We propose an unbiased estimator combining information from both the initial scan and the replication study, which is more efficient than that based just on the replication. Specifically, we adjust the standard combined estimate to allow for selection by rank and significance in the initial scan. Our approach explicitly allows for multiple associations arising from a scan, and is robust to mis‐specification of a significance threshold. We require replication data to be available but argue that, in most applications, estimates of effect sizes are only useful when associations have been replicated. We illustrate our approach on some recently completed scans and explore its efficiency by simulation. Genet. Epidemiol. 33:406–418, 2009. © 2009 Wiley‐Liss, Inc.     

A conditional synergy index to assess biological interaction

In genetic studies of complex diseases, a crucial task is to identify and quantify gene–gene interactions which are often defined as deviance from genetic additive effects. This statistical definition, however, does not need to reflect the biological interactions of genes. We propose a new method to detect gene–gene interactions. This new approach exploits the concept of synergy and antagonism that is appropriate to capture biological relationships. The conditional synergy index (CSI) describes the extent of interaction on the penetrance scale. We develop the CSI for two-locus disease models and cohort data. The index assumes genotypes to be dichotomized into risk-genotypes (exposed) and non-risk-genotypes (unexposed) but it does not assume the loci to be in linkage equilibrium. We investigate the performance of the CSI and compare it to classical epidemiological interaction measures like Rothman’s synergy index (S) and the attributable proportion due to interaction (AP). In addition, the performance of an estimator of this new parameter is illustrated in a practical example.     

Studies reporting ROC curves of diagnostic and prediction data can be incorporated into meta-analyses using corresponding odds ratios

OBJECTIVE: To develop an approach by which studies describing the accuracy of diagnostic tests or clinical predictions can be combined in a meta-analysis, even though studies may report their results using different summary measures. STUDY DESIGN: A method is proposed to allow algebraic and numerical conversion of values of the Receiver Operating Characteristic Area Under the Curve (AUC) summary statistic into corresponding odds ratios (OR). A similar conversion is demonstrated for the standard errors (SEs) of these summary statistics. RESULTS: The conversion of the AUC values into OR values was achieved using a logit-threshold model. The delta method was used to convert the associated SEs. An example concerning predictions of mortality in the intensive care unit illustrates the calculations. CONCLUSION: This paper provides an accessible method that permits the meta-analyst to overcome some of the difficulties implied by incomplete and inconsistent reporting of research studies in this area. It allows all studies to be included on the same metric, which in turn more easily permits exploration of issues such as heterogeneity. The method can readily be used for meta-analyses of diagnostic or screening tests, or for prediction data.