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PubMed2002

On sample size calculation based on odds ratio in clinical trials.

Sample size calculation formulas for testing equality, noninferiority, superiority, and equivalence based on odds ratio were derived under both parallel and one-arm crossover designs. An example concerning the study of odds ratio between a test compound (treatment) and a standard therapy (control) for prevention of relapse in subjects with schizophrenia and schizoaffective disorder is presented to illustrate the derived formulas for sample size calculation for various hypotheses under both a parallel design and a crossover design. Simulations were performed to assess the adequacy of the sample size calculation formulas. Simulation results were given at the end of the paper.

Algorithms↗

PubMed2006

The confidence interval of allelic odds ratios under the Hardy-Weinberg disequilibrium.

In single nucleotide polymorphism (SNP) data analysis, the allelic odds ratio and its confidence interval (CI) are usually used to evaluate the association between disease and alleles at each SNP. The usual formula for calculating the CI of the allelic odds ratio based on the Hardy-Weinberg equilibrium (HWE) may, however, lead to errors beyond the control assured by the nominal confidence level if HWE is not true. We therefore present a generalized formula for CI that does not assume HWE. CIs calculated by this generalized formula are likely to be wider than those by the usual method if the Hardy-Weinberg disequilibrium (HWD) is toward a relative deficiency of the heterozygotes (fixation index greater than 0), whereas they are likely to be narrower if HWD is toward a relative excess of the heterozygotes (fixation index less than 0). A simulation experiment to examine the influence of the generalization was performed for the case where 2% of SNPs had a fixation index greater than 0. The result revealed that the generalized method slightly decreased the mean number of falsely detected SNPs.

Alleles↗

PubMed1988

Sample size requirements for studies estimating odds ratios or relative risks.

This paper presents formulae for determining the number of subjects necessary, in either a case-control or a cohort study, to estimate the odds ratio or relative risk, respectively, to within a selected percentage (epsilon) of the true population value with some specified probability. This approach differs somewhat from previous comparable work that estimated the log odds ratio within a stated fixed distance rather than as a percentage of the actual odds ratio. Comparable development for relative risk has not previously appeared in the literature. These formulae provide guidelines for determination of study size that does not depend on hypothesis testing considerations.

Epidemiologic Methods↗

PubMed1992

The Scottish Heart Health Study. Dietary intake by food frequency questionnaire and odds ratios for coronary heart disease risk. I. The macronutrients.

Identification of the risk of coronary heart disease (CHD) from nutrients in the diet is of importance to both primary and secondary disease prevention. This paper reports the mean intakes and odds ratios for the macronutrients in groups of CHD-diagnosed, -undiagnosed and CHD-free men and women, aged 40-59 years, who participated in the Scottish Heart Health Study (n = 10,359). Diet was assessed by food frequency questionnaire and odds ratios were determined relative to the lowest quintile and adjusted for the classical CHD risk factors (+/- social class). Six per cent of the study population were CHD-diagnosed and 14.5% were identified as possible cases of undiagnosed CHD. The results suggest that change in diet as a result of diagnosis does occur, and is more pronounced in men. The effect is to give odds ratios, for diagnosed CHD, opposite to those which may be expected on the basis of current knowledge of nutrition and CHD risk. According to the intake data from the undiagnosed group, a relatively low energy intake, a high percentage of energy from protein and a moderate percentage of energy from alcohol diet are favourable factors with respect to CHD risk for men. For women, only alcohol significantly altered risk of undiagnosed CHD, and surprisingly, no measure of dietary fat showed a modifying effect on risk of undiagnosed CHD for men or for women. The implications, and influence of measurement error and variance on these results are discussed.

Adult↗

PubMedDate not supplied

[Translation of the English term odds ratio as oportunidad relativa].

In the present work we argue for the translation of the English term odds ratio, a term of formal anti-natural esthetics for the Spanish-speaking and with added phonetic difficulties, for oportunidad relativa. These words respect the English abbreviation OR facilitating the expression of consistent formulations which may be directly translated, as well as communication between users, since the linguistic confusion due to the present abundance of terms used in Spanish, is reduced to one. Our justifications are mainly syntactic and semantic and reflect reasonable comparability between the terms odds ratio and oportunidad relativa. Reviews of some of the most prestigious dictionaries of the English and the Spanish languages lend additional support to our proposition.

Odds Ratio↗

PubMed2002

Predictors of positive health in disability pensioners: a population-based questionnaire study using Positive Odds Ratio.

BACKGROUND: Determinants of ill-health have been studied far more than determinants of good and improving health. Health promotion measures are important even among individuals with chronic diseases. The aim of this study was to find predictors of positive subjective health among disability pensioners (DPs) with musculoskeletal disorders. METHODS: Two questionnaire surveys were performed among 352 DPs with musculoskeletal disorders. Two groups were defined: DPs with positive health and negative health, respectively. In consequence with the health perspective in this study the conception Positive Odds Ratio was defined and used in the logistic regression analyses instead of the commonly used odds ratio. RESULTS: Positive health was associated with age > or = 55 years, not being an immigrant, not having fibromyalgia as the main diagnosis for granting an early retirement, no regular use of analgesics, a high ADL capacity, a positive subjective health preceding the study period, and good quality of life. CONCLUSION: Positive odds ratio is a concept well adapted to theories of health promotion. It can be used in relation to positive outcomes instead of risks. Suggested health promotion and secondary prevention efforts among individuals with musculoskeletal disorders are 1) to avoid a disability pension for individuals <55 years of age; if necessary, to make sure rehabilitation actions continue, 2) to increase efforts to support immigrants to adjust to circumstances connected to ill-health and retirement, 3) to pay special attention to individuals with fibromyalgia and other general pain disorders, and 4) to strengthen ADL activities to support an independent active life among disability pensioners.

Activities of Daily Living↗

PubMedDate not supplied

Small sample estimation of log odds ratios from logistic regression and fourfold tables.

Schaefer has proposed a method to correct the maximum likelihood logistic regression coefficients for bias in small samples. We show here that this reduces, in the special case of a single dichotomous regression variable, to an earlier result of Haldane, for the estimation of a single log odds ratio. This paper reviews various estimators for the log odds ratio in a fourfold table, and compares the properties of two by complete enumeration in sets of tables with small sample sizes. The first of these, also due to Haldane, is based on the addition of 1/2 to each cell of the table; the second is where 1/2 is added to all cells of the table only if a zero frequency arises. We evaluate the bias and mean squared error of both of these estimators in sets of tables with various sample sizes and odds ratios. Haldane's estimator usually has lower bias and MSE, and so we do not in general recommend the practice of adding 1/2 only as necessary. Exceptions might occur if one has good a priori estimates of the outcome probabilities in the two samples under comparison.

Regression Analysis↗

PubMed2004

The reporting odds ratio and its advantages over the proportional reporting ratio.

PURPOSE: The proportional reporting ratio (PRR) is the proportion of spontaneous reports for a given drug that are linked to a specific adverse outcome, divided by the corresponding proportion for all or several other drugs. The PRR is similar to the proportional mortality ratio (PMR), an old epidemiologic measure calculated from death registries and constructed in similar fashion to the PRR. The PMR has important deficiencies, however, which the PRR shares. Miettinen and Wang demonstrated that the PMR could be improved by reformulating it as an odds ratio and applying the principles of a case-control study to the measure. In this paper, we review the problem with the PRR and show how the corresponding odds ratio represents an improvement over the PRR. METHODS: The method used is discussion and illustration by way of a hypothetical example. RESULTS: The PRR does not estimate relative risk. If, however, a spontaneous report database is viewed as source data for a case-control study, the reporting odds ratio (ROR) can be used to estimate relative risk. Treating the data as source data for a case-control study allows for further reduction of bias by the judicious choice of controls. CONCLUSIONS: Calculating the ROR in spontaneous report databases offers advantages over the PRR. It allows for estimation of the relative risk, and focuses attention on which people or reports should be included or excluded from the control series, permitting more deliberate elimination of biases. It also highlights the inherent weaknesses in spontaneous report data, which become more evident in light of the usual principles of control selection in case-control studies.

Adverse Drug Reaction Reporting Systems↗

PubMed1995

Performance of odds ratios obtained with a job-exposure matrix and individual exposure assessment with special reference to misclassification errors.

OBJECTIVES: Individual assessment of exposure by experts and the use of a job-exposure matrix are the two main methods of evaluating past occupational exposures in community-based case-referent studies. The objective of this study was to compare the performance of the estimations of the odds ratio in the two methods. This paper focuses on job-exposure matrices whose entries consist of proportions of persons exposed. METHODS: Simulations were used to compare the variances of the estimations of the odds ratios obtained with the two methods and to study the consequences with respect to bias and the precision of the odds ratios estimated for misclassifications of exposure produced by either the experts or the matrix. RESULTS: When there was no misclassification, the results showed that the precision obtained with the job-exposure matrix was about three times less than that achieved by experts in a large range of practical situations. However, when potential errors of exposure assessment were taken into account, the simulations suggested that the test of the hypothesis OR = 1 against the alternative OR not equal to 1 when exposure was assessed with an unbiased job-exposure matrix had a statistical power close to that obtained when exposure was assessed by an expert with high sensibility and specificity. CONCLUSIONS: The evaluation of exposure with an unbiased job-exposure matrix in studies of the association between exposure and disease had a statistical power close to that expected in practice with a good expert in the large range of practical situations which were investigated.

Bias↗

PubMed1999

On logit confidence intervals for the odds ratio with small samples.

Unless the true association is very strong, simple large-sample confidence intervals for the odds ratio based on the delta method perform well even for small samples. Such intervals include the Woolf logit interval and the related Gart interval based on adding .5 before computing the log odds ratio estimate and its standard error. The Gart interval smooths the observed counts toward the model of equiprobability, but one obtains better coverage probabilities by smoothing toward the independence model and by extending the interval in the appropriate direction when a cell count is zero.

Biometry↗

PubMed1990

Sample size requirements for interval estimation of the odds ratio.

Sample sizes are calculated for unmatched case-control (or cohort) studies where the goal is interval estimation of the odds ratio. The procedure used gives the smallest sample size for which a 100(1-alpha)% confidence interval for the log odds ratio will not exceed a specified width with specified probability (1-gamma). Tables of sample sizes for various choices of parameter values are presented. Considerable disagreement is found with a published method which has as its basis expected cell counts.

Case-Control Studies↗

PubMed1999

Design of validation studies for estimating the odds ratio of exposure-disease relationships when exposure is misclassified.

We compared several validation study designs for estimating the odds ratio of disease with misclassified exposure. We assumed that the outcome and misclassified binary covariate are available and that the error-free binary covariate is measured in a subsample, the validation sample. We considered designs in which the total size of the validation sample is fixed and the probability of selection into the validation sample may depend on outcome and misclassified covariate values. Design comparisons were conducted for rare and common disease scenarios, where the optimal design is the one that minimizes the variance of the maximum likelihood estimator of the true log odds ratio relating the outcome to the exposure of interest. Misclassification rates were assumed to be independent of the outcome. We used a sensitivity analysis to assess the effect of misspecifying the misclassification rates. Under the scenarios considered, our results suggested that a balanced design, which allocates equal numbers of validation subjects into each of the four outcome/mismeasured covariate categories, is preferable for its simplicity and good performance. A user-friendly Fortran program is available from the second author, which calculates the optimal sampling fractions for all designs considered and the efficiencies of these designs relative to the optimal hybrid design for any scenario of interest.

Biometry↗

PubMed1993

Comparison of three methods of estimating odds ratios from a job exposure matrix in occupational case-control studies.

A job exposure matrix consists of jobs on one axis and substances on the other, with the matrix elements describing the likelihood of an individual's exposure to a substance in a given job. This can be used in case-control studies to infer exposures of subjects whose jobs are known. The simplest form of job exposure matrix contains binary entries, but it is also possible to envisage continuous variables describing the probability of exposure in the job (probabilistic matrix). In such a case, the user has various options for transforming and analyzing the data, including the following: 1) transform to binary variables and analyze as conventional binary exposure variables; 2) leave as continuous variables and analyze using logistic regression; 3) leave as continuous variables and analyze using a linear model. Simulations were carried out to compare the ability of the three methods to estimate odds ratios under 36 experimental conditions. The linear model produced unbiased estimates, the logistic model produced somewhat biased estimates at high odds ratios, and the transformation to a binary variable produced systematically low estimates in most experimental circumstances. With the linear and logistic models, the odds ratio estimators had similar precision when the bias of the latter was not too great. The authors conclude that the linear model permits optimal use of a probabilistic matrix in an epidemiologic study and hope that these results will encourage the development of job exposure matrices containing probabilities rather than dichotomies.

Case-Control Studies↗

PubMed1991

Exploring the order of odds ratios using the bootstrap.

We show the use of the bootstrap resampling method to examine further the order of a series of odds ratios. Specifically, the bootstrap provides a method for estimating the probabilities that one would find in subsequent independent samples from the same population the observed odds ratio rankings. To illustrate this use of the bootstrap, we modelled the responses of 77 white male physicians to an ethical dilemma involving hypothetical patients. Would the physician report positive HIV status to the health department or would he maintain patient confidentiality? To see if a patient's sex, race, or sexual preference would influence the physicians' decisions, each physician received one of eight randomly selected descriptions of a hypothetical patient. To evaluate the initial order of the patient categories, we constructed 1000 bootstrap samples. Black heterosexual males ranked first or second in 92.2 per cent of the bootstrap samples; black homosexual males ranked first, second or third in 88.6 per cent; and white homosexual females ranked sixth or seventh in 82.9 per cent. Thus we would expect to observe these rankings of the categories in a high percentage of subsequent independent samples.

Black or African American↗

PubMed1991

Estimating standardized risk differences from odds ratios.

Holland (1989, Biometrics 45, 1009-1016) gave simple formulas for an "adjusted" risk difference based on the Mantel-Haenszel odds ratio estimator and its variance. This "adjusted" risk difference is, in general, inconsistent, but Holland's variance formula is an immediate corollary of a more general formula by Greenland (1987, Journal of Chronic Diseases 40, 1087-1094). We show how, under a large-stratum limiting model, one can derive consistent estimators of standardized risk differences from any consistent odds ratio estimator. We also show how one can derive nonparametric standardized estimators under a sparse-data limiting model.

Biometry↗

PubMed2001

Unbiased confidence intervals for the odds ratio of two independent binomial samples with application to case-control data.

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.

Case-Control Studies↗

PubMedDate not supplied

Estimating odds ratios adjusting for misclassification in Alzheimer's disease risk factor assessment.

Epidemiological studies of Alzheimer's disease and dementia are often two-phase studies including a screening phase and a clinical assessment phase. It is common to interview a relative of the subject at each of these phases to obtain information about the subject's exposure to risk factors. This can result in a misclassification error when assessing risk factors, as the two responses of the relative often differ. This is especially a problem for risk factors involving life-style and family history which cannot be confirmed using the subject's medical records. A naive analysis using data from each phase separately would give two different estimates of the odds ratio; both estimates could be biased. In this paper, we extend the estimation methods adjusting for misclassification developed by Liu and Liang to data collected through two-phase sampling. We first use a latent class analysis and the EM algorithm to estimate the misclassification parameters. We then derive the maximum pseudo-likelihood estimators, conditional on the misclassification parameters, to estimate the odds ratios accounting for the complex sampling study design. We propose to use the jack-knife estimator for estimation of the variances. We apply the above method to data collected in the Indianapolis-Ibadan Dementia Study to estimate the odds ratio for smoking adjusting for misclassification error.

Black or African American↗

PubMed2005

Method for indirectly estimating gene-environment effect modification and power given only genotype frequency and odds ratio of environmental exposure.

Both genes and environment are important determinants of disease. In this paper we model gene-environment effect modification on the odds ratio scale OR(GEID) and show how to indirectly estimate the effect and 95% confidence intervals (CI) for the simple case of no main genetic and environmental effects [i.e., OR(GE/D) = OR(GE/D) = 1]. A statistic is presented to test the null hypothesis OR(GE/D) = 1 and to calculate corresponding power, given the odds ratio for environmental exposure OR(E/D) and population genotype frequency (g). Direct extension of the above model provides a mathematical framework for estimating confidence bounds in more complex cases involving partial genetic and/or environmental effects.

Confidence Intervals↗