Calculation of potential bias in the odds ratio illustrated by a study of saccharin use and bladder cancer

Criticisms of questionnaire studies often emphasize methodological weaknesses which, if unexamined, may lead to biased risk estimates. Observational studies of the relationship between saccharin use and the risk of bladder cancer illustrate this point. This paper describes the potential biases due to misclassification and to the use of prevalent rather than incident cases in a recent report by I. I. Kessler and J. P. Clark (1978, J. Amer. Med. Assoc.240, 349–355). Assuming the true risk ratio is greater than unity, nondifferential misclassification of exposure leads to an observed odds ratio or relative risk closer to the null value. Differential misclassification of exposure results in either an overestimate or an underestimate of the true risk. Varying the sensitivity and specificity of the exposure among cases and controls alters the risks ratios dramatically. The use of prevalent rather than incident cases in a hospital-based case-control study does not affect the risk measure unless it can be demonstrated that exposure differentially influences the force of morbidity or mortality. The exclusion of a large number of deceased cases in Kessler and Clark's report may underestimate the risk ratio by 18–28%. Unless other factors are discovered, the identified biases will not meaningfully alter the conclusion that there is no association between saccharin use and bladder cancer in Kessler and Clark's study.     

Recall bias in self-reported melanoma risk factors

The evidence implicating sun exposure in the etiology of melanoma derives largely from case-control studies in which the retrospective assessment of sun exposure suggests potential for significant recall bias. Previous attempts at characterizing and quantifying that bias have had significant methodological limitations. In the International Twin Study, a case-control study of melanoma risk factors in twins conducted from 1980 to 1991, the authors asked melanoma cases and their co-twins to quantify their own exposures and asked which twin had the greater exposure. Recall bias was investigated by assuming that, if bias had occurred, the odds ratio based on the case's response would differ significantly from the odds ratio based on the co-twin's response. Case-derived odds ratios were higher than the odds ratios for the controls for sunbathing in childhood and adulthood and for mole frequency and freckling in childhood, suggesting some recall bias. The odds ratios for ease of burning and tanning appeared unbiased. The belief that sunlight was a cause of melanoma appeared related to an increased odds ratio for sunbathing as a child. There is a continuing need to carefully assess recall bias in the study of melanoma risk factors.     

Sample size and power for case-control studies when exposures are continuous

In estimating the sample size for a case-control study, epidemiologic texts present formulae that require a binary exposure of interest. Frequently, however, important exposures are continuous and dichotomization may result in a 'not exposed' category that has little practical meaning. In addition, if risks vary monotonically with exposure, then dichotomization will obscure risk effects and require a greater number of subjects to detect differences in the exposure distributions among cases and controls. Starting from the usual score statistic to detect differences in exposure, this paper develops sample size formulae for case-control studies with arbitrary exposure distributions; this includes both continuous and dichotomous exposure measurements as special cases. The score statistic is appropriate for general differentiable models for the relative odds, and, in particular, for the two forms commonly used in prospective disease occurrence models: (1) the odds of disease increase linearly with exposure; or (2) the odds increase exponentially with exposure. Under these two models we illustrate calculation of sample sizes for a hypothetical case-control study of lung cancer among non-smokers who are exposed to radon decay products at home.     

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.     

Down with odds ratios: risk ratios in cohort studies and randomised clinical trials

Various effect measures are available for quantifying the relationship between an intervention or a risk factor and an outcome, such as the risk ratio and the odds ratio. Odds ratios are intended for use in case-control studies in which they are an appropriate measure for estimating the relative risk; however, this measure is also often presented in cohort studies and in randomized clinical trials. When used for cohort studies and randomized clinical trials, the odds ratio is often incorrectly interpreted as the risk ratio; the odds ratio then provides an overestimation of the risk ratio, especially when the outcome is frequent. The use of logistic regression to adjust for confounding is one of the reasons that odds ratios are presented. For cohort studies and randomized clinical trials, however, there are methods to estimate adjusted risk ratios; these include the Mantel-Haenszel method, log-binomial regression, Poisson regression with robust standard error, and 'doubling of cases' method with robust standard error. To avoid misinterpretation of odds ratios, risk ratios should be calculated in cohort studies and randomized clinical trials.     

A meta-analysis of risk estimates for prostate cancer related to tire and rubber manufacturing operations

Studies investigating the association between prostate cancer and exposure to the tire and rubber manufacturing environment have reported weak and inconsistent results. A meta-analysis of nine cohort studies that used standard mortality ratios and three case-control studies that used odds ratios was conducted. The pooled results from the nine cohort studies showed a standard mortality ratio of 101 (95% confidence interval [CI] = 93,110), whereas the pooled results from the three case-control studies showed on odds ratio of 1.10 (95% CI = 0.94, 1.29). The standard mortality ratios were converted to odds ratios by dividing by 100. The overall pooled risk estimate from all 12 studies was 1.03 (95% CI = 0.96, 1.11). The conclusion of this meta-analysis is that work exposure in a rubber and tire manufacturing environment does not result in an increased risk of prostate cancer.     

The usefulness of average cost-effectiveness ratios

We demonstrate that average cost-effectiveness ratios (CERs) play an important role in the evaluation of the cost-effectiveness of treatments. Criticisms of the usefulness of CERs derive mostly from the context of resource allocation under a constrained budget in which some decisions are based on incremental CERs. However, we show that in many cases, these decision rules are equivalent to decision rules on CERs. This follows for mutually exclusive treatments first, because a treatment is eliminated by extended dominance if and only if there is a mixed treatment with a smaller CER, where the mixing parameter lies in a certain interval. Second, after elimination of treatments by domainance and by extended dominance, resources can be allocated in order of increasing CERs. Moreover, the CER is a parameter that characterizes clinical and economical properties of a treatment independent of its comparators. © 1997 John Wiley & Sons, Ltd.     

Estimating crude or common odds ratios in case-control studies with informatively missing exposure data

In case-control studies, the crude odds ratio derived from a 2 x 2 table and the common odds ratio adjusted for stratification variables are staple measures of exposure-disease association. While missing exposure data are encountered in the majority of such studies, formal attempts to deal with them are rare, and a complete-case analysis is the norm. Furthermore, the probability that exposure is missing may depend on true exposure status, so the missing-at-random assumption is often unreasonable. In this paper, the authors present an adjustment to the usual product binomial likelihood to properly account for missing data. Estimation of model parameters without restrictive assumptions requires an additional data collection effort akin to a validation study. Closed-form results are provided to facilitate point and confidence interval estimation of crude and common odds ratios after properly accounting for informatively missing data. Simulations assess performance of the likelihood-based estimates and inferences, and they display the potential for bias in complete-case analyses. An example is presented to illustrate the approach.     

Potenziell vermeidbare Risikofaktoren für primäre Kopfschmerzen

Background

Strategies to prevent primary headaches could be very beneficial, especially given that primary headaches can lead to the development of chronic headache. In order to establish headache prevention strategies, the modifiable risk factors for primary headaches need to be identified.

Material and methods

A systematic literature search on the risk factors for primary headaches was conducted independently by two persons using the databases MEDLINE and Embase. Further inclusion criteria were observational studies in adult general populations or case-control studies, where the effect sizes were reported as odds ratios or where the odds ratios could be calculated from the given data.

Results

In all, 24 studies were included in the analysis. There was a large amount of heterogeneity among the studies concerning headache acquisition, headache classification, and risk factors for headache development. Independent of headache trigger and definition of headache, the association between headache and the risk factor “stress” was very high: The meta-analysis shows an overall effect of 2.26 (odds ratio; 95?%-CI =?[1.79; 2.85]). Studies evaluating neck and shoulder pain also report a strong association with headache; however, these results could not be summarized in a meta-analysis. Equally, the overall effects of smoking and coffee consumption on headaches could not be verified because the effect sizes were rather small and predominantly noticeable only at higher doses.

Conclusion

A strong association between headache and the risk factors stress and neck and shoulder pain was confirmed. The effect sizes of smoking and coffee consumption on headaches were rather small.     

Paternal occupational exposure to electromagnetic fields and neuroblastoma in offspring

Investigators in Texas have reported an association between paternal employment in jobs linked with exposure to electromagnetic fields and risk of neuroblastoma in offspring. In an attempt to replicate this finding, the authors conducted a case-control study in Ohio. A total of 101 incident cases of neuroblastoma were identified through the Columbus (Ohio) Children's Hospital Tumor Registry. All cases were born sometime during the period 1942-1967. From a statewide roster of birth certificates, four controls were selected for each case, with individual matching on the case's year of birth, race, and sex, and the mother's county of residence at the time of the (index) child's birth. Multiple definitions were employed to infer the potential for paternal occupational exposure to electromagnetic fields from the industry/occupation statements on the birth certificates. Case-control comparisons revealed adjusted odds ratios ranging in magnitude from 0.5 to 1.9. For two of the exposure definitions employed--both of which are similar to one used by the Texas investigators--the corresponding odds ratios were modestly elevated (odds ratios = 1.6 and 1.9). Notably, the magnitude of these odds ratios is not inconsistent with the Texas findings, where the exposure definition referred to yielded an odds ratio of 2.1. Because the point estimates in this study are imprecise, and because the biologic plausibility of the association is uncertain, the results reported here must be interpreted cautiously. However, the apparent consistency between two independent studies suggests that future evaluation of the association is warranted.     

An insight on the use of multiple logistic regression analysis to estimate association between risk factor and disease occurrence

Multiple logistic regression is an accepted statistical method for assessing association between an anticedant characteristic (risk factor) and a quantal outcome (probability of disease occurrence), statistically adjusting for potential confounding effects of other covariates. Yet the method has potential drawbacks which are not generally recognized. This article considers one important drawback of logistic regression. Specifically the so-called main effect logistic model assumes that the probability of developing disease is linearly and additively related to the risk factors on the logistic scale. This assumption stipulates that for each risk factor, the odds ratio is constant over all reference exposure levels, and that the odds ratio exposed to two or more factors is equal to the product of individual risk factor odds ratios. If the observed odds ratios in the data follow this pattern, the model-predicted odds ratios will be accurate, and the meaning of the odds ratio for each risk factor will be straightforward. But if the observed odds ratios deviate from the model assumption, the model will not fit the data accurately, and the model-predicted odds ratios will not reflect those in the data. Although satisfactory fit can always be achieved by adding to the model polynomial and product terms derived from the original risk factors, the odds ratios estimated by such an interaction logistic model are difficult to interpret, viz., the odds ratio for each risk factor depends not only on the reference exposure levels of that factor, but also on the exposure level in other factors.(ABSTRACT TRUNCATED AT 250 WORDS)     

Defining exposure in case-control studies: a new approach

Many epidemiologists conducting case-control studies choose to dichotomize their exposure data to make the analysis of the data easier and its presentation more straightforward. The choice of a specific rule for dichotomization can have a large effect on the outcome measure, the odds ratio, although this effect is rarely studied. The authors present a graphic approach for exploring this effect, the quantile-quantile (Q-Q) plot. By examining a Q-Q plot, an investigator simultaneously gains information about the distribution of exposures among cases, the distribution of exposures among controls, and odds ratios at all possible cutpoints and their standard errors. In addition, by finding the slope at each point along the Q-Q curve, it is possible to estimate the rate ratios for each possible value of exposure. The authors view the use of the Q-Q plot as an exploratory tool. It enables the investigator to become more familiar with the data and check for irregularities such as outliers, nonlinearities, or nonmonotonic dose-response curves, and idiosyncratic variations of the odds ratio. The authors present an example evaluating the risk of low birth weight as a function of mother's age for Boston births in 1984.     

Patterns of bias due to differential misclassification by case–control status in a case–control study

BACKGROUND: Case-control study is still one of the most commonly used study designs in epidemiological research. Misclassification of case-control status remains a significant issue because it will bias the results of a case-control study. There exist two types of misclassification, differential versus nondifferential. It is commonly accepted that nondifferential misclassification will bias the results of the study towards the null hypothesis. Conversely, no reports have assessed the impact and direction of differential misclassification on odds ratio (OR) estimate. The goal of the present study is to demonstrate by statistical derivation that patterns exist on the bias induced by differential misclassification. METHODS: Based on a 2 x 2 case-control study design, we derive the odds ratio without misclassification, and those with misclassification according to: (1) controls are misclassified as cases by exposure status; (2) cases are misclassified as controls by exposure status; and (3) both controls and cases are misclassified by exposure status simultaneously. Furthermore, mathematical derivations are shown for each of the ratios of the two odds ratios with and without misclassification. These methods are carried out by simulation analyses. RESULTS: Simulation analyses show that quite a number of biased odds ratios tend to move away from the null hypothesis and result in approaching zero or infinity with increasing proportion of misclassification among cases, controls, or both. These patterns are associated with the exposure status and the values of unbiased odds ratio (<1, 1, or >1). CONCLUSIONS: Our findings suggest that, unlike nondifferential misclassification, differential misclassification of case-control status in a case-control study may not weaken the exposure-outcome association towarding the null hypothesis. Care needs to be taken for interpreting the results of a case-control study when there exists differential misclassification bias, a practical issue in epidemiological research.     

Accounting for error due to misclassification of exposures in case-control studies of gene-environment interaction

We consider analysis of data from an unmatched case-control study design with a binary genetic factor and a binary environmental exposure when both genetic and environmental exposures could be potentially misclassified. We devise an estimation strategy that corrects for misclassification errors and also exploits the gene-environment independence assumption. The proposed corrected point estimates and confidence intervals for misclassified data reduce back to standard analytical forms as the misclassification error rates go to zero. We illustrate the methods by simulating unmatched case-control data sets under varying levels of disease-exposure association and with different degrees of misclassification. A real data set on a case-control study of colorectal cancer where a validation subsample is available for assessing genotyping error is used to illustrate our methods.     

Risk factors for acute myeloid leukemia and multiple myeloma: a combination of GIS and case-control studies

Risk factors for acute myeloid leukemia (AML) and multiple myeloma (MM) include exposure to toxic chemicals present in tobacco smoke, as well as to emissions from industrial operations and petroleum refinery waste dumps. The study reported here identified these risk factors among case patients and control patients in Orange County, California, from 1984 to 1993 and determined the significance of the risk factors in the study population. A case-control study was performed for 604 cases of AML and 643 cases of MM; there were 7,112 control subjects who had colon cancer. The model included the variables smoking history, occupational history, and residence in a census tract with a petroleum refinery waste dump. A geographic information system (GIS) analysis also was performed to correlate the incidence of AML and MM with proximity to the six dump sites that received large amounts of petroleum refinery waste. Current smokers were found to be at an increased risk of AML with an odds ratio of 2.0. Laborer/equipment cleaners and transportation workers/movers were at risk of AML with odds ratios of 3.5 and 2.4, respectively. Construction/resource extraction workers were at risk of MM with an odds ratio of 2.8. GIS analysis determined that the risk for MM was 1.6 cases per mile for 10 or more years of residence near a large chemical dump. The authors were able to identify census tracts with a high incidence of AML and MM, and to perform distance analysis using a statistical measure of spatial randomness. The case-control study identified occupational and lifestyle risk factors for AML and MM that were not apparent from census-tract-level data.     

Employer policies toward guns and the risk of homicide in the workplace

This population-based case-control study of North Carolina workplaces evaluated the hypothesis that employers' policies allowing firearms in the workplace may increase workers' risk of homicide. Workplaces where guns were permitted were about 5 times as likely to experience a homicide as those where all weapons were prohibited (adjusted odds ratio=4.81; 95% confidence interval=1.70, 13.65). The association remained after adjustment for other risk factors. The findings suggest that policies allowing guns in the workplace might increase workers' risk of homicide.     

柳州市人群甲型肝炎疫苗接种的流行病学及费用效果分析

分7个不同的年龄组队列，比较接种甲型肝炎（甲肝）减毒活疫苗（H2株）后15年每一队列人群接种与否甲肝感染及发病的差异，并根据甲肝患病及甲肝疫苗接种的医疗费用和对质量修正生命年（QALY）的影响，推算接种的费用效果比（CER）。不接种情况下推算的不同年龄别人群发病率与本次研究人群的实际资料接近。说明计算模型可靠。基础假设的结果显示，每获得一个QALY，全人口组的平均费用是152277．60元，超过同期人均生产总值的11倍。各年龄组单位效果的费用变化范围从113369．30元（10－19岁组）到292138．30元（≥50岁组）。但对高危人群接种的分析显示，其CER显著改善。所以，甲肝疫苗在中等疫情的城市人群中普遍使用是不合算的；预防接种应只面向高危人群。另外，灵敏度分析显示主要参数的改变均不会改变本文的结论。     

Invited commentary: Decomposing with a lot of supposing

In this issue of the Journal, VanderWeele and Vansteelandt (Am J Epidemiol. 2010;172(12):1339-1348) provide simple formulae for estimation of direct and indirect effects using standard logistic regression when the exposure and outcome are binary, the mediator is continuous, and the odds ratio is the chosen effect measure. They also provide concisely stated lists of assumptions necessary for estimation of these effects, including various conditional independencies and homogeneity of exposure and mediator effects over covariate strata. They further suggest that this will allow effect decomposition in case-control studies if the sampling fractions and population outcome prevalence are known with certainty. In this invited commentary, the author argues that, in a well-designed case-control study in which the sampling fraction is known, it should not be necessary to rely on the odds ratio. The odds ratio has well-known deficiencies as a causal parameter, and its use severely complicates evaluation of confounding and effect homogeneity. Although VanderWeele and Vansteelandt propose that a rare disease assumption is not necessary for estimation of controlled direct effects using their approach, collapsibility concerns suggest otherwise when the goal is causal inference rather than merely measuring association. Moreover, their clear statement of assumptions necessary for the estimation of natural/pure effects suggests that these quantities will rarely be viable estimands in observational epidemiology.     

A method for spatial analysis of risk in a population-based case-control study

Spatial distributions of disease occurrence and risk have traditionally served as a tool for identifying exposures of public health concern. Current software for manipulating geographic data (GIS) now allows many kinds of analyses not feasible before. This paper presents a method for producing a "picture" of disease risks based on residential history data from a population based case-control study. We illustrate the method using geographically coded data on individual-level risk factors, such as age and smoking, from a cancer study of the Upper Cape Cod region of Massachusetts for 1983-1986. Our results show the association between lung cancer and residential location as an indicator of exposure. Crude and adjusted odds ratios were estimated by adaptive rate stabilization and mapped using kriging as an interpolation method to examine the risk of lung cancer in the region. The crude and adjusted surfaces for various smoothing parameters were compared to identify areas of increased lung cancer not explained by standard risk factors. Such spatial patterns of disease risk may provide clues to exposures of importance or confirm associations with previously suspected exposures.     

Severe pain at interval IUD insertion: a case-control analysis of patient risk factors

This investigation, using a case-control analysis approach on an IUD data set from a less-developed country center, delineated four risk factors in patient characteristics that are associated with severe pain at interval IUD insertion. They are: higher education (greater than or equal to seven years), low-parity (1-2 live births), longer open interval (greater than or equal to 13 months) between the end of the last pregnancy and insertion, and non-breastfeeding at the time of insertion. Adjusted relative risks estimated by odds ratios are 2.1, 2.7, 2.7 and 5.0, respectively. For women with a combination of the above risk factors, they have a further increased (additive in nature) risk of suffering severe insertion pain. Similar analysis was also performed on a developed country center data set for which only the effect of education and parity could be studied; an odds ratio of 5.0 for nulliparity was obtained. The plausibility of these findings as well as their clinical and programmatic implications are discussed.