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PubMed2006

Measuring additive interaction using odds ratios.

Interaction measured on the additive scale has been argued to be better correlated with biologic interaction than when measured on the multiplicative scale. Measures of interaction on the additive scale have been developed using risk ratios. However, in studies that use odds ratios as the sole measure of effect, the calculation of these measures of additive interaction is usually performed by directly substituting odds ratios for risk ratios. Yet assessing additive interaction based on replacing risk ratios by odds ratios in formulas that were derived using the former may be erroneous. In this paper, we evaluate the extent to which three measures of additive interaction - the interaction contrast ratio (ICR), the attributable proportion due to interaction (AP), and the synergy index (S), estimated using odds ratios versus using risk ratios differ as the incidence of the outcome of interest increases in the source population and/or as the magnitude of interaction increases. Our analysis shows that the difference between the two depends on the measure of interaction used, the type of interaction present, and the baseline incidence of the outcome. Substituting odds ratios for risk ratios, when calculating measures of additive interaction, may result in misleading conclusions. Of the three measures, AP appears to be the most robust to this direct substitution. Formulas that use stratum specific odds and odds ratios to accurately calculate measures of additive interaction are presented.

Journal Article↗
PubMed1981

The effect of response bias on the odds ratio.

The effect of response bias on odds ratio results was determined based on data from a population-based cardiovascular disease survey. The study subjects consisted of 5000 adult residents of a predominantly white, upper-middle class community. Information from 60% of the 1100 non-respondents was obtained by telephone. Consistent patterns of participation associated with risk factors and diseases under study were found. A simple error term was developed to convert the odds ratio for respondents to the odds ratio for the target population using individual cell response rates. This error term demonstrates that the response patterns found tended to minimize the error in odds ratio calculations for respondents. Only by obtaining relevant information on non-respondents can investigators accurately estimate response bias and its effects on the odds ratio.

Adult↗
PubMed2004

Estimation of cumulative odds ratios.

PURPOSE: Standard estimation of ordered odds ratios requires the constraint that the etiologic effects of exposure are homogenous across thresholds of the ordered response. We present a method to relax this often-unrealistic constraint. METHODS: The kernel of the proposed method is the expansion of observed data into "person-thresholds." Using standard statistical software, for each subject we create a separate record for each response threshold and then apply binary logistic regression to estimate generalized cumulative odds ratios for one or more exposures. RESULTS: Two examples demonstrate that the proposed method provides increased flexibility in assessing the etiologic effects of exposures. A Monte Carlo simulation study supports the proposed approach by suggesting the estimated cumulative odds ratios are unbiased with proper confidence interval coverage attained by use of generalized estimating equations. CONCLUSION: The proposed method provides simple estimates of ordered odds ratios that allow the etiologic effects of exposure to vary across levels of the ordered response.

Diabetic Retinopathy↗
PubMed2003

Use of odds ratios on anaesthesia related studies.

In line with other medical journals, odds ratios are increasingly being reported in anaesthesia literature. The frequency of the use of odds ratio and how well it relates to the relative risk when it is interpreted as relative risk remains unknown. We investigated the use of odds ratio, and its relationship to relative risk and the incidence of outcome in this study. We identified 60 meta-analyses and 87 original articles that reported odds ratios. While relative risk could have been reported in 79% of the studies, only a small proportion (3%) of these studies have estimated and reported the relative risk in addition to the odds ratio. There is a significant bias if odds ratio is interpreted as relative risk, especially so when the incidence of outcome is high. While odds ratio is a valid measure of treatment effect in its own right, anaesthetists and investigators should be careful not to interpret odds ratio as equivalent to relative risk.

Anesthesia↗
PubMed1993

What does the odds ratio estimate in a case-control study?

The use of the term 'odds ratio' in reporting the findings of case-control studies is technically correct, but is often misleading. The meaning of the odds ratio estimates obtained in a case-control study differs according to whether controls are selected from person-time at risk (the study base), persons at risk (the base-population at risk at the beginning of follow-up), or survivors (the population at risk at the end of follow-up). These three methods of control selection correspond to estimating the rate ratio, risk ratio, or the odds ratio respectively, by means of calculating the odds ratio in the subjects actually studied. None of these estimation procedures depends on any rare disease assumption. Where the rare disease assumption is relevant is whether the effect which is estimated (e.g. the odds ratio) is approximately equal to some other effect measure of interest (e.g. the risk ratio or rate ratio) in the underlying study base. To avoid confusion on this issue, authors should be encouraged to not only specify the manner in which controls have been selected (e.g. by density sampling) but also the corresponding effect measure which is being estimated (e.g. the rate ratio) by the 'odds ratio' which is obtained in a case-control analysis.

Case-Control Studies↗
PubMed2005

Distributional interaction: Interpretational problems when using incidence odds ratios to assess interaction.

It is well known that the incidence odds ratio approximates the risk ratio when the disease of interest is rare, but increasingly overestimates the risk ratio as the disease becomes more common. However when assessing interaction, incidence odds ratios may not approximate risk ratios even when the disease is rare. We use the term "distributional interaction" to refer to interaction that appears when using incidence odds ratios that does not appear, or appears to a lesser degree, when using risk ratios. The interpretational problems that arise from this discrepancy can have important implications in epidemiologic research. Therefore, quantification of the relationship between the interaction odds ratio and the interaction risk ratio is warranted. In this paper, we provide a formula to quantify the differences between incidence odds ratios and risk ratios when they are used to estimate effect modification on a multiplicative scale. Using this formula, we examine the conditions under which these two estimates diverge. Furthermore, we expand this discussion to the implications of using incidence odds ratios to assess effect modification on an additive scale. Finally, we illustrate how distributional interaction arises and the problems that it causes using an example from the literature. Whenever the risk of the outcome variable is non-negligible, distributional interaction is possible. This is true even when the disease is rare (e.g., disease risk is less than 5%). Therefore, when assessing interaction on either an additive or multiplicative scale, caution should be taken in interpreting interaction estimates based on incidence odds ratios.

Journal Article↗
PubMed1992

Estimating a summarized odds ratio whilst eliminating publication bias in meta-analysis.

Publication bias is a recognized phenomenon, i.e. studies with statistically significant results are more likely to be published than those finding no difference between the groups studied. Summarized odds ratio calculated from odds ratios of published studies in a meta-analysis may be overestimated because of publication bias. This is a significant problem in research areas involving weak associations between causes and results. The magnitude of publication bias in a given research area cannot be determined directly. The present study enables us to calculate the summarized odds ratio of hypothetical unpublished studies from odds ratios of published studies indirectly, employing a moment method by assuming the natural logarithm value of the odds ratio to be distributed normally. We can then estimate summarized odds ratio in all studies, which include not only those published but also those unpublished. When these studies are homogeneous in quality and their odds ratios homogeneous in quantity, the method can eliminate publication bias.

Bias↗
PubMed1995

To use or not to use the odds ratio in epidemiologic analyses?

This paper argues that the use of the odds ratio parameter in epidemiology needs to be considered with a view to the specific study design and the types of exposure and disease data at hand. Frequently, the odds ratio measure is being used instead of the risk ratio or the incidence-proportion ratio in cohort studies or as an estimate for the incidence-density ratio in case-referent studies. Therefore, the analyses of epidemiologic data have produced biased estimates and the presentation of results has been misleading. However, the odds ratio can be relinquished as an effect measure for these study designs; and, the application of the case-base sampling approach permits the incidence ratio and difference measures to be estimated without any untenable assumptions. For the Poisson regression, the odds ratio is not a parameter of interest; only the risk or rate ratio and difference are relevant. For the conditional logistic regression in matched case-referent studies, the odds ratio remains useful, but only when it is interpreted as an estimate of the incidence-density ratio. Thus the odds ratio should, in general, give way to the incidence ratio and difference as the measures of choice for exposure effect in epidemiology.

Data Interpretation, Statistical↗
PubMed1992

Effect of nondifferential misclassification on estimates of odds ratios with multiple levels of exposure.

Nondifferential misclassification of exposure status with a dichotomous exposure will produce biased estimates of odds ratios such that the misclassified odds ratio is always biased toward the null value. However, when an exposure classification has more than two levels, empirical data indicate that the direction of bias is less predictable. Analysis of an algebraic model of multi-level exposure misclassification reveals that all odds ratios based on the misclassified data are constrained between the nonmisclassified odds ratio for the most extreme category and the inverse of this value. This implies that the misclassified odds ratio for the most extreme exposure level will be biased toward the null but that odds ratios for intermediate levels of exposure could be biased away from the null value. Further, the amount of bias depends not only on the misclassification rates but also on the distribution of subjects across exposure levels. If it is assumed that misclassification is likely to occur only between adjacent categories, the range of possible misclassified odds ratios is reduced but is still sufficient to permit serious distortion of an exposure-response relation. In general, biases away from the null occur only for intermediate levels of exposure. Reversal of an exposure-response relation is more likely to occur when misclassification rates are high (especially between nonadjacent levels) and when the number of exposure levels is low.

Bias↗
PubMed1998

Per capita gross national product and summarized odds ratio for epidemiologic studies on the relationship between passive smoking and lung cancer.

The summarized odds ratios of epidemiologic studies on the relationship between exposure to environmental tobacco smoke (ETS) and lung cancer by country were recalculated, using the odds ratio values in a 1992 report entitled, "Respiratory Health Effects of Passive Smoking: Lung Cancer and Other Disorders" by the US Environmental Protection Agency. The relationship between the summarized odds ratio and per capita gross national product (GNP) in 1964 was studied by the country. The graphic relationship between the summarized odds ratio (ordinate) and GNP (abscissa) showed an upward convex curve. The summarized odds ratios of a developing country (China) and developed countries (USA, Western Europe) in 1964 indicated a very weak association, while those of other countries (Greece, Hong Kong, and Japan) were slightly greater than unity (1.0). This means that ETS in the developing and developed countries in 1964 hardly affected lung cancer, whereas that in the other areas affected lung cancer somewhat. Socioeconomic status in developed countries is far better than that in developing countries, and factors related to socioeconomic status may affect the summarized odds ratio. It is recognized that cancer is diagnosed clinically some years after cancer risk factors appear. If the socioeconomic status involves some risk factors which affect lung cancer, the relationship between the summarized odds ratio and the GNP may be significant. Therefore, we can forecast that the summarized odds ratio of Japan will decrease to close to unity and that that of China will increase in the future because of economic growth, making it possible for the Chinese Government to adopt a policy to reduce the influence of ETS on health.

Air Pollutants↗
PubMed2001

Application of nonparametric models for calculating odds ratios and their confidence intervals for continuous exposures.

Calculating odds ratios and corresponding confidence intervals for exposures that have been measured using a continuous scale presents important limitations in the traditional practice of analytical epidemiology. Approximations based on linear models require making arbitrary assumptions about the shape of the relation curve or about its breakpoints. Categorical analyses generally have low statistical efficiency, and cutpoints for the categories are in most cases arbitrary and/or opportunistic. The use of logistic generalized additive models to calculate odds ratios does not require these assumptions and allows great flexibility and adequate statistical efficiency. Based on the asymptotic normality of the logarithm of the odds ratio, the authors propose the use of an approximate analytical expression for the corresponding covariance matrix, which will allow the construction of confidence intervals for odds ratios that can be interpreted as in the classical parametric context. The authors illustrate this procedure by examining the relation between glycemia and risk of postoperative infection, using data obtained from a cohort study of patients undergoing surgery in Santiago, Spain (January 1996--March 1997). The authors found that glycemia values below 75 mg/dl and above 130 mg/dl were associated with increased risk of postoperative infection.

Blood Glucose↗
PubMed1999

Statistical methods in epidemiology. III. The odds ratio as an approximation to the relative risk.

PURPOSE: This paper introduces readers to case-control studies and how to analyse them. Specifically, the odds ratio statistic is discussed. The importance of the odds ratio in epidemiology is that it is used as an approximation to the true relative risk. METHOD: Data are presented in the form of 2 x 2 contingency tables, and a method for calculating the odds ratio is presented. An extension to 2 x k tables (where k > 2) is given, as is a graphical method for plotting odds ratios. Confidence intervals based on the Normal approximation are introduced. RESULTS: Some properties of the odds ratio statistic are illustrated by taking examples from the author's own teaching experiences. CONCLUSION: As long as the odds ratio is not used uncritically as an estimate of the relative risk, it remains an attractive statistic for epidemiologists to calculate.

Confidence Intervals↗
PubMed1995

Odds ratio in the estimation of the significance of occlusal factors in craniomandibular disorders.

The usage of odds ratios for estimating the significance of occlusion is based on the assumption that the aetiological factors are additive and interchangeable in several different composite causes. If the factor studied is a necessary causal factor, odds ratios cannot be used in risk estimation. The present study analysed odds ratios in a sample of children half of whom had undergone an annual prophylactic elimination of occlusal interferences. The sample consisted of 178 children followed up for 5 years from the baseline age of 5 or 10. The distribution of interferences was computed for children with tenderness of the masticatory muscles ('cases'), and for children without ('controls'). Although the increase in the number of children free from interferences was not remarkable, the overall result was statistically significant (P < 0.01). None of the children free from interferences showed muscular tenderness at any of the annual examinations. Therefore, odds ratios could not be calculated in our study sample. It is concluded that estimation by means of odds ratios of the significance of occlusal factors in CMD may be misleading.

Case-Control Studies↗
PubMed1992

Importance of trends in the interpretation of an overall odds ratio in the meta-analysis of clinical trials.

This paper contains a proposition related to the publication of meta-analyses of clinical trials. We consider the situation where the results of a number of trials are summarized by a common or typical odds ratio. We show that stating such an odds ratio as the summary of evidence from a number of trials can be misleading if certain systematic differences between trials exist. In such cases the author should state not just one odds ratio but also its dependence on the relevant characteristics of the trials. In particular, we propose that those reporting a meta-analysis state in advance a (limited) number of variables to be considered for potential interaction with the exposure (risk factor or treatment) of interest. The list might include centre size and the odds in the placebo or control group if such an effect is a priori clinically plausible. The trials should be ordered according to each of these variables and a trend test for the odds ratio should be computed. Apart from a 'genuine' effect, an appreciable interaction could also be indicative of the (multiplicative) odds ratio being an inappropriate measure for the particular meta-analysis. Without any consideration as to the possibility of interaction, the meta-analysis should be considered incomplete. If such an interaction exists, the odds ratio should be stated as a function of the interacting variable, either as a formula or (preferably) in a table stating the odds ratio for a number of different values of the interacting variable, and not as a single summary statistic.

Clinical Trials as Topic↗
PubMed2006

A deficiency of the odds ratio as a measure of effect size.

The odds ratio is probably the most widely used measure of association for binary variables. It has many well-recognized advantages and disadvantages vis-à-vis the risk ratio. We demonstrate that for chained or conditional probabilities, odds ratios can behave paradoxically, by failing to show a reinforcement effect that is expressed very clearly when risk ratios are used.

Adolescent↗
PubMed2007

The performance of different propensity score methods for estimating marginal odds ratios.

The propensity score which is the probability of exposure to a specific treatment conditional on observed variables. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. In the medical literature, propensity score methods are frequently used for estimating odds ratios. The performance of propensity score methods for estimating marginal odds ratios has not been studied. We performed a series of Monte Carlo simulations to assess the performance of propensity score matching, stratifying on the propensity score, and covariate adjustment using the propensity score to estimate marginal odds ratios. We assessed bias, precision, and mean-squared error (MSE) of the propensity score estimators, in addition to the proportion of bias eliminated due to conditioning on the propensity score. When the true marginal odds ratio was one, then matching on the propensity score and covariate adjustment using the propensity score resulted in unbiased estimation of the true treatment effect, whereas stratification on the propensity score resulted in minor bias in estimating the true marginal odds ratio. When the true marginal odds ratio ranged from 2 to 10, then matching on the propensity score resulted in the least bias, with a relative biases ranging from 2.3 to 13.3 per cent. Stratifying on the propensity score resulted in moderate bias, with relative biases ranging from 15.8 to 59.2 per cent. For both methods, relative bias was proportional to the true odds ratio. Finally, matching on the propensity score tended to result in estimators with the lowest MSE.

Bias↗