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PubMed1999

Interval estimation of the common odds ratio from k(2 x 2) tables under cluster sampling.

We propose a simple correction factor for the variance of the logarithm of the common odds ratio estimated by the method of Mantel and Haenszel from a series of (2 x 2) tables when data are cluster correlated. The adjustment is applied to the variance estimators proposed by Hauck and by Robins, Breslow and Greenland for the log of the Mantel-Haenszel common odds ratio, and its performance is evaluated in a simulation study. The key features of the proposed adjustment are: (i) it has closed-form; (ii) it can accommodate covariates defined at the cluster-specific level, the site-specific level, or both; and (iii) it does not require the user to specify a particular correlation structure for the response data. The correction derives from Liang and Zeger's generalized estimating equations (GEE) technique for logistic regression modelling. Via simulation, we examine empirical versus nominal coverage probabilities for interval estimation of the common odds ratio using adjusted and unadjusted variance estimates, and we present ratios of observed to estimated variances. Results are compared to those obtained from the fully iterated GEE analysis. The characteristics of the simulation study mimic scenarios common in the periodontal research setting, with small numbers of subjects (N = 25, 50), moderate numbers of sites per cluster (m = 4, 16, 32), and modest intracluster correlation levels (rho = 0.0, 0.1, 0.2, 0.3). Results show that adjusted confidence intervals (applied to the Hauck or the Robins, Breslow, Greenland variance estimate) provide coverage probabilities close to the nominal level for the Mantel--Haenszel common odds ratio over a variety of cluster sizes and levels of correlation.

Computer Simulation↗

PubMed1991

Residual plots for log odds ratio regression models.

This article describes graphical diagnostic methods for log odds ratio regression models. To study the effects of an additional covariate on log odds ratio regression analysis, three types of residual plots based on weighted least squares (WLS) are discussed: (i) added variable plot (partial regression plot), (ii) partial residual plot, and (iii) augmented partial residual plot. These plots provide diagnostic procedures for identifying heterogeneity of error variances, outliers, or nonlinearity of the model. They are especially useful for clarifying whether including a covariate as a linear term is appropriate, or whether quadratic or other nonlinear transformations are preferable. A well-known data set for case-control studies is analyzed to illustrate the residual plots.

Age Factors↗

PubMed1998

What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes.

Logistic regression is used frequently in cohort studies and clinical trials. When the incidence of an outcome of interest is common in the study population (>10%), the adjusted odds ratio derived from the logistic regression can no longer approximate the risk ratio. The more frequent the outcome, the more the odds ratio overestimates the risk ratio when it is more than 1 or underestimates it when it is less than 1. We propose a simple method to approximate a risk ratio from the adjusted odds ratio and derive an estimate of an association or treatment effect that better represents the true relative risk.

Cohort Studies↗

PubMed2006

Odds ratio based multifactor-dimensionality reduction method for detecting gene-gene interactions.

MOTIVATION: The identification and characterization of genes that increase the susceptibility to common complex multifactorial diseases is a challenging task in genetic association studies. The multifactor dimensionality reduction (MDR) method has been proposed and implemented by Ritchie et al. (2001) to identify the combinations of multilocus genotypes and discrete environmental factors that are associated with a particular disease. However, the original MDR method classifies the combination of multilocus genotypes into high-risk and low-risk groups in an ad hoc manner based on a simple comparison of the ratios of the number of cases and controls. Hence, the MDR approach is prone to false positive and negative errors when the ratio of the number of cases and controls in a combination of genotypes is similar to that in the entire data, or when both the number of cases and controls is small. Hence, we propose the odds ratio based multifactor dimensionality reduction (OR MDR) method that uses the odds ratio as a new quantitative measure of disease risk. RESULTS: While the original MDR method provides a simple binary measure of risk, the OR MDR method provides not only the odds ratio as a quantitative measure of risk but also the ordering of the multilocus combinations from the highest risk to lowest risk groups. Furthermore, the OR MDR method provides a confidence interval for the odds ratio for each multilocus combination, which is extremely informative in judging its importance as a risk factor. The proposed OR MDR method is illustrated using the dataset obtained from the CDC Chronic Fatigue Syndrome Research Group. AVAILABILITY: The program written in R is available.

Fatigue Syndrome, Chronic↗

PubMed2004

Serum osteoprotegerin (OPG) and the A163G polymorphism in the OPG promoter region are related to peripheral measures of bone mass and fracture odds ratios.

The purpose of this study is to investigate the association of serum osteoprotegerin (OPG) and the A163G polymorphism in the OPG promoter with peripheral measures of bone mass and with odds ratios for wrist and hip fracture in a case-control study of postmenopausal Danish women. The study included 66 women with lower forearm fracture, 41 women with hip fracture, and 206 age-matched controls. All had broadband ultrasound attenuation (BUA) and speed of sound (SOS) measured at the heel as well as bone mineral density (BMD) measured by DXA at the distal forearm. S-OPG was measured by ELISA. The A163G genotypes were determined by PCR-RFLP analysis. S-OPG levels correlated positively with age ( r = 0.45; P << 0.0001) and negatively with distal forearm BMD ( r = -0.31; P << 0.0001), heel BUA ( r = -0.23; P << 0.0001), and heel SOS ( r = -0.22; P << 0.0001). Comparing the highest quartile of S-OPG to the lowest, the odds ratio for osteoporotic fracture was 2.5 (95% CI, 1.3-4.7; P = 0.006). The G allele of the A163G was associated with significantly lower t-scores of both lower forearm BMD, heel BUA, and heel SOS as well as being significantly more frequent in the fracture patients compared to the controls. Patients with a combination of the highest quartile of S-OPG and presence of the G allele ( n = 23) had a significantly elevated fracture odds ratio, 4.0 (95% CI, 1.7-9.9). A significant negative association between S-OPG with peripheral measures of bone mass and with increased fracture odds ratios was found. Furthermore, the A163G mutation in the OPG promoter had a significant influence on bone mass and fracture status independently of S-OPG level.

Bone Density↗

PubMed2000

The generalization of the odds ratio, risk ratio and risk difference to r x k tables.

Familiar measures of association for 2 x 2 tables are the odds ratio, the risk ratio and the risk difference. Analagous measures of outcome-exposure association are desirable when there are several degrees of severity of both exposure and disease outcome. One such measure (alpha), which we label the general odds ratio (OR(G)), was proposed by Agresti. Convenient methods are given for calculation of both standard error and 95 per cent confidence intervals for OR(G). Other approaches to generalizing the odds ratio entail fitting statistical models which might not fit the data, and cannot handle some zero frequencies. We propose a generalization of the risk ratio (RR(G)) following the statistical approaches of Agresti, Goodman and Kruskal. A method of calculating the standard error and 95 per cent confidence interval for RR(G) is provided. A known statistic, Somers' d, fulfils the characteristics necessary for a generalized risk difference (RD(G)). These measures have straightforward interpretations, are easily computed, are at least as precise as other methods and do not require fitting statistical models to the data. We also examine the pooling of such measures as in, for example, meta-analysis.

Anti-Ulcer Agents↗

PubMed1989

Behavior of the exposure odds ratio in a case-control study when the hazard function is not constant over time.

In case-control studies of adverse drug effects there is rarely much evidence to support the assumption that the hazard function among users is constant during therapy. Nonetheless, this assumption is often implicitly made. We will use both clinical reasoning and a simple model to show how non-constancy of the hazard function affects odds ratio interpretation. When the hazard function is non-constant and there is more than one temporal pattern of drug usage, the odds ratio will estimate a weighted mean of incidence ratios with weights dependent on the corresponding fractions of person-time. If the duration-specific incidence ratios differ widely, the odds ratio will depend not only on the drug but also on its usage pattern in the study population. This may explain some of the large regional odds ratio variation for dipyrone-related agranulocytosis in the International Agranulocytosis and Aplastic Anemia Study (JAMA 1986; 256: 1749-1757.

Agranulocytosis↗

PubMed1995

Comparison of speed of sound ultrasound with single photon absorptiometry for determining fracture odds ratios.

The purpose of this study was to compare the ability of ultrasound velocity measurement with that of single photon absorptiometry to determine the odds of history of fracture since age 40, for a population-based study. To do this we computed odds ratios and 95% confidence intervals for 809 women and 502 men, aged 50 years and older, who are participants in the prospective phase of the Saunders County Bone Quality Study. These participants received both the ultrasound and single photon absorptiometry bone measurements at the initiation of the study. In addition, a history of all fractures that had occurred to participants since age 40 was obtained. The two bone assessment methods were compared by examining the magnitude of the odds ratios, to determine which produces the highest estimate of the probability of odds of fracture, and by examining widths of the respective confidence intervals to show which estimate of odds ratio is the most precise. Ultrasound velocity estimates a higher probability of odds of both low-trauma fractures and all fractures than distal radius and ulna bone mineral content, but lower than bone mineral density at the same sites for both women and men. However, the ultrasound measure is more precise than bone mineral density, but less precise than bone mineral content. We conclude that ultrasound velocity is as good as single photon absorptiometry in estimating odds of fracture.

Absorptiometry, Photon↗

PubMed1989

A comparison of tests of homogeneity of odds ratios in K 2 x 2 tables.

We conducted a simulation study to determine the performance of nine procedures for testing the homogeneity of odds ratios in K 2 x 2 contingency tables. We recommend Tarone's approximate score test, based on the Mantel-Haenszel estimator of the common odds ratio, for use in practice. We also recommend a non-iterative statistic developed by Gart and based on the modified Woolf estimator of the common odds ratio for very large samples in balanced or mildly unbalanced designs. We base our recommendation of a statistic on its performance in terms of size and power in comparison with the other statistics considered.

Odds Ratio↗

PubMed1983

Interactive electronic computing of the mortality odds ratio.

An interactive computer program which computes the standardized mortality odds ratio and the standardized proportional mortality ratio has been developed for use in the analysis of occupational mortality studies. The program provides flexibility in the selection of the comparison (unexposed) population, permitting both internal and external comparison, including comparison with the United States general population. Considerable control for potential confounding factors and for differences in information collection procedures can be exercised through careful choice of the comparison population. The user must select the reference cause(s) of death among 55 categories (59 for women). The condition for equivalence of the standardized mortality odds ratio and the standardized mortality ratio will be met when the selected reference cause(s) is unrelated to the exposure. The program reduces the loss of information due to sparse data during stratification by allowing the user to define the length of the age and time intervals. The program is written in Fortran IV and is designed to produce rapid, cost-efficient interactive results on any mainframe computer system.

Adult↗

PubMed1989

A Monte Carlo investigation of homogeneity tests of the odds ratio under various sample size configurations.

Epidemiologic data for case-control studies are often summarized into K 2 x 2 tables. Given a fixed number of cases and controls, the degree of sparseness in the data depends on the number of strata, K. The effect of increasing stratification on size and power of seven tests of homogeneity of the odds ratio is studied using Monte Carlo methods. In all the designs considered here, the numbers of cases and controls per stratum are the same. Considering both size and power in non-sparse-data settings, we recommend the Breslow-Day statistic (1980, Statistical Methods in Cancer Research, 1. The Analysis of Case-Control Studies, p. 142; Lyon: International Agency for Research on Cancer) for general use. In sparse-data settings the T4 statistic of Liang and Self (1985, Biometrika 72, 353-358) performs the best when all tables, regardless of sample size, have odds ratios generated from the same distribution. In sparse-data settings characterized by a large table with an odds ratio of 1 and many small tables with odds ratios greater than 1, the T5 statistic of Liang and Self (1985) performs the best. One of the most important results of this study is the generally low power for all homogeneity tests especially when the data are sparse.

Computer Simulation↗

PubMed1992

The Scottish Heart Health Study. Dietary intake by food frequency questionnaire and odds ratios for coronary heart disease risk. II. The antioxidant vitamins and fibre.

High serum antioxidant vitamins are increasingly being associated with reduced risk of coronary heart disease (CHD). Previous studies have not addressed the relationship between dietary antioxidant vitamins and risk of CHD although diet is a key factor which modifies blood antioxidant vitamin levels. In prospective studies, high-fibre diets have also been associated with reduced CHD incidence. In this analysis CHD-diagnosed, -undiagnosed and non-CHD controls were selected from 10,359 men and women aged 40-59 who participated in a cross-sectional study of CHD risk factors. Diet was assessed by food frequency questionnaire, odds ratios were adjusted for the classical CHD risk factors (+/- social class) and calculated relative to the first quintile for each vitamin and total fibre. The antioxidant vitamins were further combined in a principal component analysis and the odds ratios for undiagnosed and diagnosed CHD were again calculated. For undiagnosed CHD, risk was significantly lower in the highest quintiles of beta-carotene, fibre and vitamin C, E and A for men, but only lower for fibre in women. Opposite trends were observed in the odds ratios for vitamin C and E and fibre for male-diagnosed CHD which possibly indicates changes in diet as a result of diagnosis. Principal component analysis showed significantly reduced risk of undiagnosed CHD in the top three quintiles for men (odds ratios 0.66, 0.67 and 0.64; P less than 0.05 in each case). A similar trend occurred for women but was non-significant. The results suggest that high dietary intake of the antioxidant vitamins may reduce risk of CHD, particularly in men, and that fibre may be equally cardio-protective in both sexes.

Adult↗

PubMed2002

Odds ratios for hip- and lower forearm fracture using peripheral bone densitometry; a case-control study of postmenopausal women.

BACKGROUND: Dual-energy X-ray absorptiometry (DXA) measured at the lumbar spine and particularly at the hip remain the gold-standard for diagnosing osteoporosis. However, devices for assessing the peripheral skeleton present several advantages in terms of lower price and portability. A major concern when using peripheral densitometry is the poor correlation with the central measurements. The main aim of this study is, therefore, to assess the possibility of expressing ultrasound measurements at the heel and bone mineral density (BMD) measured at the distal forearm as fracture odds ratios rather than an absolute measure of bone mass. METHODS: A total of 76 women with lower forearm fracture, 47 women with hip fracture and 231 age-matched women (controls) were included. All had broadband ultrasound attenuation (BUA) and speed of sound (SOS) measured at the heel using the DTU-one ultrasound scanner as well as BMD measured by dual X-ray absorptiometry on the DTX-200 at the distal forearm. RESULTS: BUA, SOS and BMD at the distal forearm were all significantly lower in fracture patients compared with their respective control groups. The odds ratio for lower forearm fracture was 3.1 (95% CI: 1.8; 5.2) for heel-BUA (T-score cutoff: -2.3), 4.1 (2.3; 7.4) for heel-SOS (-2.1) and 2.2 (1.3; 3.7) for lower forearm BMD (-2.7). The odds ratio for hip fracture was 3.4 (1.5-7.7) for heel-BUA (-2.7), 3.6 (1.6; 8.1) for heel-SOS (-2.6) and 3.2 (1.4; 7.4) for lower forearm BMD (-2.9). CONCLUSION: Peripheral densitometry can discriminate between hip- and lower forearm fracture patients and age-matched controls. Significantly elevated odds ratios for incurring these fractures can be calculated using device- and site specific t-score cutoff values. The results from this case-control study need to be confirmed by prospective cohort studies.

Absorptiometry, Photon↗

PubMedDate not supplied

Antipsychotic medication dispensing and associated odds ratios of death in elderly veterans and war widows, 2001.

OBJECTIVES: To explore the odds ratios (ORs) of death associated with antipsychotic (AP) medications dispensed to elderly subjects. METHOD: Subjects were veterans and war widows 65 years and older dispensed an AP drug in 2001 in NSW or ACT. For all subjects, dispensing records for AP medication, benzodiazepines, lithium, carbamazepine, sodium valproate and antidepressant medication were extracted and combined with age, gender and date of death. A study date was allocated, either the date of death or a random date from 1.5.01 to 31.12.01. Subjects dispensed an AP in 2001, but not dispensed an AP or other psychotropic medication in the 120 days prior to their study date, formed a reference group. Psychotropic dispensing in the 120 days prior to the study date was analysed using nested logistic regression models to produce ORs of death associated with various AP drugs. The ORs for risperidone, olanzapine and pericyazine were compared. Haloperidol ORs were established for those dispensed the drug 0-30 days prior to study date or 31-120 days prior to the study date. RESULTS: The ORs associated with haloperidol, olanzapine, risperidone, pericyazine, thioridazine and chlorpromazine were significant when compared with the reference group. Odds ratios for all three haloperidol periods were significant when compared with olanzapine, risperidone and pericyazine 120 day ORs. Although there was a trend favouring olanzapine when compared with risperidone, the difference in the ORs failed to reach significance (p=0.066). CONCLUSIONS: Haloperidol is associated with significantly higher mortality rates than other AP medication but it is not clear whether this represents drug toxicity or the medical conditions for which it was dispensed. There was no evidence that the conventional AP pericyazine was associated with a higher mortality rate than olanzapine or risperidone.

Aged↗

PubMed1993

Conditional regression analysis of the exposure-disease odds ratio using known probability-of-exposure values.

Conditional inference methods are proposed for the odds ratio between binary exposure and disease variables when only the probability of exposure is known for each study subject. We develop a conditional likelihood approach that removes nuisance parameters and permits inferences to be made about important parameters in log odds ratio regression models. We also discuss a heuristic procedure based on estimating the (unknown) number of truly exposed individuals; this procedure provides a simple framework for interpreting our likelihood-based statistics, and leads to a Mantel-Haenszel-type estimator and a goodness-of-fit test. As an example of the use of this methodology, we present an analysis of some genetic data of Swift et al. (1976, Cancer Research 36, 209-215).

Adult↗

PubMed1989

Simultaneous interval estimates of the odds ratio in studies with two or more comparisons.

More than one odds ratio estimate will often arise from a single epidemiologic study. Examples of designs where this may occur include those where there is more than one case or control group, and investigations of several risk factors as part of the same study. Various methods for presenting multiple interval estimates are discussed, including: the naive method, the Bonferroni method, the Dunn method, the Scheffé method, and the Dunnett method. For rectangular regions the Dunnett method gives a region with the most appropriate confidence level, but this region contains a different set of odds ratio estimates than are implied by the usual significance tests. A confidence ellipse circumscribed by the Scheffé limits gives the best agreement with the significance tests. Each of these methods is illustrated with a numerical example.

Epidemiologic Methods↗

PubMed1997

Use of the odds ratio to translate neuropsychological test scores into real-world outcomes: from statistical significance to clinical significance.

Standard parametric tests generate p values and effect sizes, but often these are difficult to translate into real-world outcomes. In this study, the odds ratio was applied to neuropsychological testing and was compared to parametric approaches. Participants were 26 community-dwelling adults with possible or probable Alzheimer's disease and 25 matched healthy community-dwelling volunteers. Odds ratios were computed to estimate the probability of concurrent diagnosis given neuropsychological performance level. Odds ratios discriminated the groups at magnitudes that could not be discerned from t-test significance tables. These values were compared to sensitivity, specificity, and overall accuracy. Clinical and research applications and implications were addressed.

Aged↗

PubMed2003

The diagnostic odds ratio: a single indicator of test performance.

Diagnostic testing can be used to discriminate subjects with a target disorder from subjects without it. Several indicators of diagnostic performance have been proposed, such as sensitivity and specificity. Using paired indicators can be a disadvantage in comparing the performance of competing tests, especially if one test does not outperform the other on both indicators. Here we propose the use of the odds ratio as a single indicator of diagnostic performance. The diagnostic odds ratio is closely linked to existing indicators, it facilitates formal meta-analysis of studies on diagnostic test performance, and it is derived from logistic models, which allow for the inclusion of additional variables to correct for heterogeneity. A disadvantage is the impossibility of weighing the true positive and false positive rate separately. In this article the application of the diagnostic odds ratio in test evaluation is illustrated.

Diagnosis↗