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PubMed2003

Simple approaches to assess the possible impact of missing outcome information on estimates of risk ratios, odds ratios, and risk differences.

Often in clinical trials, the primary outcome is binary and the impact of an intervention is summarized using risk ratios (RRs), odds ratios (ORs), or risk differences (RDs). It is typical that in such studies, the binary outcome variable is not observed for some study participants. When there is missing data, it is well known that analyses based on those participants with complete data can be biased unless it can be assumed that the probability of a missing outcome is unrelated to the value of the missing binary outcome (i.e., missing at random). Unfortunately, this assumption cannot be assessed with the data since the missing outcomes, by definition, are not observed. One approach to this problem is to perform a sensitivity analysis to see the degree to which conclusions based only on the complete data would be affected given various degrees of departure from the missing at random assumption. In this paper we provide researchers formulae for doing such a sensitivity analysis. We quantify the departure from the missing at random assumption with a parameter we call the "response probability ratio" (RPR). This is the ratio between the probability of a nonmissing outcome among those with one value of the binary outcome and the probability of a nonmissing outcome among those with the other value of the outcome. Then we provide simple formulae for the estimation of the RRs, ORs, and RDs given any specific values of the RPRs. In addition to being useful for sensitivity analyses, these formulae provide some insight into the conditions that are necessary for bias to occur. In particular, it can be seen that, under certain plausible assumptions, OR estimates based on participants with complete data will be asymptotically unbiased, even if the probability of missing outcome depends on both the treatment and the outcome.

Bias↗
PubMed2006

The (relative) risks of using odds ratios.

Odds ratios are commonly presented in the medical literature, including dermatology journals. Even when used appropriately, odds ratios are often difficult to interpret. This article illustrates this problem using an example from the recent dermatology literature. It then reviews the definitions of odds and odds ratio, as well as how odds and odds ratio relate to probability and relative risk. The divergence of odds ratios from relative risks when events are common (occurring in > or =10% of a sample) is explained. Methods to convert odds ratios to relative risks (and the reasons why conversion should be considered) are discussed.

Data Interpretation, Statistical↗
PubMed1997

Relationship between prevalence rate ratios and odds ratios in cross-sectional studies.

BACKGROUND: Cross-sectional data are frequently encountered in epidemiology and published results are predominantly presented in terms of prevalence odds ratios (POR). A recent debate suggested a switch from POR, which is easily obtained via logistic regression analysis available in many statistical packages, to prevalence rate ratios (PRR). We thought it useful to explore the mathematical relationship between PRR and POR and to evaluate the degree of divergence of the two measures as a function of the prevalence of disease and exposure. METHODS: With the use of some algebra and the common definitions of prevalence of the disease (Pr(D)), prevalence of the exposure (Pr(E)), PRR, and POR in a 2 x 2 table, we have identified a useful formula that represents the mathematical relationship between these four quantities. Plots of POR versus PRR for selected values of Pr(D) and Pr(E) are reported. RESULTS: Mathematically speaking the general relationship takes the form of a second order curve which can change curvature and/or rotate around the point POR = PRR = 1 according to the values of Pr(D) and Pr(E), with POR being always further from the null value than is PRR. The discrepancies are much more influenced by variations in Pr(D) than in Pr(E). CONCLUSIONS: We think that the choice between POR or PRR in a cross-sectional study ought to be based on epidemiological grounds and not on the availability of software tools. The paper offers a formula and some-examples for a better understanding of the relationship between PRR and POR as a function of the prevalence of the disease and the prevalence of the exposure.

Cross-Sectional Studies↗
PubMed2002

Advanced statistics: up with odds ratios! A case for odds ratios when outcomes are common.

Treatment comparisons from clinical studies involving dichotomous outcomes are often summarized using risk ratios. Risk ratios are typically used because the underlying statistical model is often consistent with the underlying biological mechanism of the treatment and they are easily interpretable. The use of odds ratios to summarize treatment effects has been discouraged, especially in studies in which outcomes are common, largely because odds ratios differ from risk ratios and are frequently interpreted incorrectly as risk ratios. In this article, the author contends that risk ratios can be easily misinterpreted and that, in many cases, odds ratios should be preferred, especially in studies in which outcomes are common.

Humans↗
PubMed1998

On the use of the ratio or the odds ratio of cure rates in therapeutic equivalence clinical trials with binary endpoints.

We discuss in this paper some issues related to the use of the ratio or the odds ratio of cure rates in therapeutic equivalence clinical trials with binary endpoints. Some two one-sided tests procedures are proposed and their fixed sample performances evaluated by Monte Carlo simulations. Sample size formulas are derived for most of these procedures. The consequences of applying acceptance limits proposed for pharmacokinetic responses in bioequivalence studies to clinical endpoints in therapeutic equivalence clinical trials are also described.

Algorithms↗
PubMedDate not supplied

[Razón de posibilidades: a proposed translation of the term odds ratio].

In English, odds ratio is a basic epidemiological measure approximating the relative risk. Odds ratio has been translated into Spanish in several ways, which has produced great terminological confusion. On the other hand, the English word odds is often used in epidemiology or statistics English textbooks, alone or as part of other expressions, but always keeping a definite mathematical meaning, which calls for a similarly definite term in Spanish. We discuss several translations of odds ratio found in the literature and propose the Spanish word "posibilidades" as a translation of odds and "razón de posibilidades" as a translation of odds ratio.

Odds Ratio↗
PubMed1985

Conditions for confounding of the risk ratio and of the odds ratio.

There are disagreements in the literature about the criteria to be used to ascertain whether or not a measure of association is confounded. The authors postulate the general principle that a crude unconfounded measure of association is structured as a weighted average of the stratum-specific values of the measure. They examine the relationships between stratum-specific measures of association, crude overall measures, and weighted averages of stratum-specific measures, and indicate how these relationships may be used to define criteria for the assessment of confounding in cohort studies in which the exposure, disease, and stratification variables are classified dichotomously. The criteria presented differ for the risk ratio and for the disease-odds ratio. In other words, one can reach different conclusions about the confounding effect of a given extraneous variable, depending on which measure of association is chosen. This view differs from that of Miettinen and Cook (Confounding: essence and detection. Am J Epidemiol 1981;114:593-603) who postulated one set of criteria for the assessment of confounding, which was applicable to both measures of association. These different approaches may lead to different conclusions about the presence or absence of confounding.

Epidemiology↗
PubMed2001

An odd measure of risk: use and misuse of the odds ratio.

OBJECTIVE: To determine how often the odds ratio, as used in clinical research of obstetrics and gynecology, differs substantially from the risk ratio estimate and to assess whether the difference in these measures leads to misinterpretation of research results. METHODS: Articles from 1998 through 1999 in Obstetrics & Gynecology and the American Journal of Obstetrics and Gynecology were searched for the term "odds ratio." The key odds ratio in each article was identified, and, when possible, an estimated risk ratio was calculated. The odds ratios and the estimated risk ratios were compared quantitatively and graphically. RESULTS: Of 151 studies using odds ratios, 107 were suitable to estimate a risk ratio. The difference between the odds ratio and the estimated risk ratio was greater than 20% in 47 (44%) of these articles. An odds ratio appears to magnify an effect compared with a risk ratio. In 39 (26%) articles the odds ratio was interpreted as a risk ratio without explicit justification. CONCLUSION: The odds ratio is frequently used, and often misinterpreted, in the current literature of obstetrics and gynecology.

Data Interpretation, Statistical↗
PubMed2003

Concordance odds ratios and approximate rate ratios in longitudinal twin studies.

Odds ratios derived from probandwise concordance rates are usually interpreted as increased risks in twins. Though the odds ratios in case-control studies have been shown to reflect rate ratios, few studies focused on such relationships in twin studies. The authors derived an approximate formula for the ratios of person-time incidence rates after the random assignment of twins into index twins and co-twins, i.e., incidence rate ratios. The resulting rate ratio was estimated as the product of the concordance odds ratio and a term that reflect the follow-up duration and the average time to occurrence of disease. Odds ratios coincide with rate ratios when the average time to occurrence of disease is half the duration of follow-up, although in studies spanning several decades these two measures might be different. The authors illustrated that when the incidence rate is not constant over the follow-up period as in longitudinal twin studies, the conventional odds ratio should not be used as an estimator of rate ratio.

Case-Control Studies↗
PubMed1994

Publication probability of a study on odds ratio value circumstantial evidence for publication bias in medical study areas.

A summarized odds ratio, calculated from odds ratios of published studies in a meta-analysis, may be overestimated because of publication bias. A method has been developed estimating indirectly the summarized odds ratio of all studies in a given research area, including not only those published but also unpublished. In the present study, a publication probability according to odds ratio value was obtained from the probability density function of all the studies, and a histogram of those published. A publication probability, according to odds ratio value, enables us to infer the quantitative relationship between publication probability and odds ratio. A notable nonpublication of studies whose odds ratios were close to unity was shown from examples of studies on the relationship between passive smoking and lung cancer, whereas nonpublication of studies whose summarized odds ratio was located far from unity was not detected from examples of studies on the relationship between cryptorchidism and testicular cancer. In both study areas, however, the differences between the summarized odds ratios, either with or without the hypothetical unpublished studies, were not large. The small difference, however, should not be ignored, when the study area is recognized as a social problem.

Cryptorchidism↗
PubMedDate not supplied

Understanding the odds ratio and the relative risk.

Both the odds ratio and the relative risk compare the relative likelihood of an event occurring between two groups. The relative risk is easier to interpret and is consistent with general intuition. Some designs, however, allow only for the calculation of the odds ration. Covariate adjustment is easier for an odds ratio. Finally, the odds ratio avoids ambiguity by being invariant to lthe labeling of the outcome measure. The Table summarizes the advantages and disadvantages of the odds ratio and relative risk. Whe reading research that summarizes data using odds ratios, or relative risks, be aware of the limitations of booth of these measures.

Odds Ratio↗