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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 The present study enables us to calculate the summarized odds ratio of hypothetical unpublished studies from odds ratios of published studies indirectly, employing a moment method by assuming the natural logarithm value of the odds ratio to be distributed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 We can then estimate summarized odds ratio in all studies, which include not only those published but also those unpublished.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

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

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

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

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

Regression analysis of the log odds ratio: a method for retrospective studies.

Quantification of the dependence of the odds ratio on concomitant variables associated with each of several 2 X 2 tables, using a regression model proposed by Zelen [1971], is an important tool for retrospective studies in epidemiology, An "exact" analysis may be based on the conditional likelihood obtained by fixing all the marginal totals. A symptotically this approach is equivalent to use of an unconditional log-linear model. The method is used to reanalyze data reported by Kneale [1971] on the relationship between obstetric radiation and childhood cancer.

Biometry

Small sample performance of tests of homogeneity of odds ratios in K 2 x 2 tables.

In this note we study, by simulation, small sample performance in terms of size of ten procedures for testing the homogeneity of odds ratios in K 2 x 2 contingency tables. These ten statistics are derived for 'large-stratum' settings. Our study concerns the behaviour of these statistics for 'small-stratum' settings.

Chi-Square Distribution

On estimating standardized risk differences from odds ratios.

An estimator proposed by Greenland and Holland (1991, Biometrics 47, 319-322) for a standardized risk difference parameter is shown to be a maximum likelihood estimator if the consistent estimator of the common odds ratio is appropriately chosen. The statistical problem under consideration is reparameterized. Likelihood equations are derived.

Epidemiologic Methods

Computation of exact confidence intervals for the odds ratio.

A time-sharing program written in BASIC language has been developed to compute exact confidence limits for the odds ratio parameter in a 2 x 2 table. The program offers the user a choice between the classical exact limits and limits based upon a recent redefinition of the exact p-value aimed at avoidance of conservatism in the classical procedure. The user selects the degree of confidence desired during a run of the program, which then computes the exact limits and p-value.?23Athor

Computers

The effect of dietary intake of fruits and vegetables on the odds ratio of lung cancer among Yunnan tin miners.

All newly diagnosed cases of lung cancer (N = 183) among male tin miners of Yunnan Province, China and age-sex matched occupational controls (N = 183 aged 45-79 years) were interviewed within 3 months following cancer diagnosis. The questionnaire included information about usual adult diet as well as employment and smoking histories. Over 95% of cases and controls were current smokers. The 27-item food frequency questionnaire included 11 fruits and vegetables rich in vitamin A and/or carotenoids. The effect of dietary intake of fruits and vegetables on risk of lung cancer was examined with adjustment for exposures to radon, arsenic, and smoking as previously documented risk factors for lung cancer. Tin miners with reduced intake of yellow and light green vegetables had statistically significant increased odds ratios (OR) of lung cancer (OR = 2.26 and OR = 2.39 for the lowest two quartiles of intake; P value for trend = 0.02) among cases compared with controls after multiple logistic regression adjustment for covariates; and this relationship was monotonic. Tin miners with reduced intake of tomatoes had statistically significant increased adjusted OR of lung cancer (OR = 2.64, OR = 3.09, OR = 2.36 for the three lowest quartiles of intake; P value for trend = 0.04). This is the first study to demonstrate a protective effect of vegetable intake versus the strong effects of smoking and occupational exposures on lung cancer risk.

Aged

An alternate method for calculating an odds ratio.

Methodological problems involved in the use of the standard Woolf-Haldane analysis of epidemiological retrospective studies are examined and an alternate method of analysis is proposed. This alternate method involves a population constructed to match the cases in numerical size and to match the controls in proportion of exposures. This method allows for finer subclassification of the data and provides a meaningful summary estimate of the relative risk. The proposed method is contrasted with the Woolf-Haldane method in the analysis of the relative risk of exposure to sick pet bird versus no pet bird for adult leukemia cases versus controls. Data is from the Tri-State Leukemia Survey. Mathematical considerations involved are contained in the appendices.

Epidemiologic Methods

Dichotomizing continuous outcome variables: dependence of the magnitude of association and statistical power on the cutpoint.

Dichotomizing a continuous outcome variable casts that variable in traditional epidemiologic terms (that is, disease, no disease). One consequence is overall reduced statistical power. A more fundamental concern is that the magnitude of various measures of association (for example, prevalence ratio, odds ratio) and statistical power depend on the cutpoint used to dichotomize the variable. The phenomenon is illustrated with a hypothetical situation assuming a two-level predictor variable and a normally distributed outcome variable. As the cutpoint is increased from lower to higher values, the prevalence ratio increases steadily, the odds ratio is described by a U-shaped curve, and statistical power is described by an inverted U-shaped curve. Furthermore, the extent of these effects depends on the difference between the means of the continuous outcome variable for the two levels of the predictor variable. An empirical example is given using data on education and blood pressure (dichotomized to create a high blood pressure vs low blood pressure variable). Except at each end of the distribution, the results follow the hypothetical example. The observation has implications for public health and medical treatment; different cutpoints should be examined to determine the optimal cutpoint in terms of policy and/or treatment decisions. The observation described here also has implications for statistical interpretation; statements about the magnitude of association or statistical significance have limited meaning unless both the cutpoint and the distribution of the outcome variable are specified.

Bias