Combining matched and unmatched control groups in case-control studies

Multiple control groups in case-control studies are used to control for different sources of confounding. For example, cases can be contrasted with matched controls to adjust for multiple genetic or unknown lifestyle factors and simultaneously contrasted with an unmatched population-based control group. Inclusion of different control groups for a single exposure analysis yields several estimates of the odds ratio, all using only part of the data. Here the authors introduce an easy way to combine odds ratios from several case-control analyses with the same cases. The approach is based upon methods used for meta-analysis but takes into account the fact that the same cases are used and that the estimated odds ratios are therefore correlated. Two ways of estimating this correlation are discussed: sandwich methodology and the bootstrap. Confidence intervals for the pooled estimates and a test for checking whether the odds ratios in the separate case-control studies differ significantly are derived. The performance of the method is studied by simulation and by applying the methods to a large study on risk factors for thrombosis, the MEGA Study (1999-2004), wherein cases with first venous thrombosis were included with a matched control group of partners and an unmatched population-based control group.     

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.     

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.     

Comparative exposure ratios: A non-parametric,multifactor technique for case-control studies

The odds ratio in a two-by-two table is widely used in case-control studies to measure association between disease and a binary risk factor. In this article we propose a more general measure of association, the comparative exposure ratio (CER), which is the ratio of the number of case-control pairs where the case has greater exposure divided by the number where the control has greater exposure. In simple cases, the CER is an odds ratio or a weighted combination of odds ratios. In more general cases a CER continues to measure association even when an odds ratio computation is not feasible. Moreover, CERs improve on odds ratios in several ways: they do not require binary risk factors, or a choice of the scale of measurement of continuous risk factors; they make it possible to investigate multiple risk factors simultaneously, without multivariate parametric assumptions; they also can be used to detect patterns that might indicate possible causal pathways. We illustrate how various choices of the definition of ‘greater exposure’ make the CER a powerful and flexible tool. We give expressions for confidence intervals for CERs, and verify in a pilot simulation that they are valid. Finally, we illustrate with a case-control study of cervical dysplasia how exploratory inference using CERs can be carried out. (This research was partially supported by grants from the National Cancer Institute, CA 41108 and CA 25702).     

Case-control prostate cancer screening studies should not exclude subjects with lower urinary tract symptoms

OBJECTIVE: Prostate-specific antigen (PSA)/digital rectal exam (DRE) screening for prostate cancer has become standard medical practice; however, its effectiveness in terms of reducing prostate cancer mortality remains undetermined. Case-control screening studies may help determine screening efficacy, though the proper disposition of symptomatic subjects is unclear. This paper presents a prostate cancer-specific methodological modification for analyzing symptomatic case-control screening subjects. METHODS: Prostate cancer detection studies and case-control studies of PSA/DRE screening were reviewed, and the results for symptomatic and asymptomatic subjects were compared. RESULTS: Most PSA/DRE detection studies have found that the prostate cancer detection rate among symptomatic patients is the same as or lower than that among asymptomatic patients. Lower urinary tract symptoms (LUTS), often referred to as early prostate cancer symptoms, occur more often in benign prostatic hyperplasia (BPH), a more commonly diagnosed, nonmalignant disease. Screened symptomatic subjects are usually removed from the "screened" category in case-control studies even though BPH-related symptoms do not confer increased prostate cancer risk and odds ratios do not change with inclusion of symptomatic subjects in the analysis. CONCLUSION: Screened subjects with LUTS should remain in the "screened" category in case-control prostate cancer screening studies since these symptoms may not be associated with increased risk of prostate cancer or validity of the odds ratio.     

不同研究设计的相对危险度估计

根据不同的研究设计，在队列研究中可分别估计累积发病率比（ＣＩＲ）、发病密度比（ＩＤＲ）和发病比值（ＩＯＲ）。当疾病罕见时，这３个比之值很接近。在病例对照研究中，是否可用暴露比值比（ＥＯＲ）作为ＣＩＲ或ＩＤＲ的无偏估计，取决于抽样方法和疾病率高低。本文还讨论了在不同抽样设计下ＥＯＲ与ＣＩＲ或ＩＤＲ之间的关系。     

Response bias in a case-control study: analysis utilizing comparative data concerning legal abortions from two independent Swedish studies

Independent reports of legal abortions in two Swedish epidemiologic studies of breast cancer in young women, covering the same women and overlapping the same time period, have been compared in order to estimate a putative response bias. One study used case-control methods and obtained data by retrospective interviews from 317 cases and 512 controls. The other study was based on objectively documented information froma nationwide registry covering legally induced abortions. Analysis demonstrated a ratio between the odds ratios from the two studies of 1.5 (95 percent confidence interval 1.1-2.1) and an observed ratio of 22.4 (p less than 0.007) between underreporting of previous induced abortions among controls relative to overreporting among cases. This response bias may explain the tendency toward increased risk of breast cancer which, according to several case-control studies, appears to be associated with induced abortion.     

On the use of population attributable fraction to determine sample size for case-control studies of gene-environment interaction

Most methods for calculating the sample size needed to detect gene-environment interactions use odds ratios to measure the effect size. We show that for any combination of susceptible genotype prevalence and exposure prevalence and their associated risks, the odds ratio measuring strength of interaction corresponds to a population attributable fraction (PAF) because of interaction and vice versa. Simultaneous consideration of odds ratio for interaction and the associated PAF attributable to interaction provides additional insight to investigators evaluating the feasibility and public health relevance of a proposed study. We considered gene-environment interactions on a multiplicative scale, and assumed a dichotomous environmental exposure variable and a single two-allele disease-susceptibility locus. Our results show, for example, that for studies of exposures and genotypes that are common in a population (30%-50%), the PAF for interaction is large (>27%) even if the odds ratio for interaction is only moderate (approximately 2). If simultaneous estimates of interaction odds ratio and PAF indicate that the PAF is so large as to be implausible, the investigator may decide to reevaluate the study design based on detecting a more reasonable PAF. In this case, the associated odds ratio for interaction will be weaker and a considerably larger sample size may be needed.     

Adjusted odds ratios under nondifferential misclassification: application to prostate cancer

The high prevalence of unsuspected prostate cancer among middle-aged and elderly men is unique among cancers. With their uncertain natural history, unsuspected prostate cancer cases may be misclassified into control groups in which they can obscure the identification of prostate cancer risk factors in case-control studies. Assuming that the exposure experience of diagnosed and of unsuspected prostate cancers is the same (nondifferential misclassification), case-control odds ratios are biased toward the null, which may provide a rationale for reexamining findings in negative case-control studies of prostate cancer. This article reviews the evidence supporting a high prevalence of prostate cancer and describes formulae that can be used to adjust for misclassification bias in completed case-control studies and to estimate required sample sizes in proposed studies.     

Laryngeal cancer and occupational exposure to asbestos

Summary The risk of laryngeal cancer associated with occupational exposure to asbestos was evaluated by a review of published reports. In only two of 13 cohort studies was the standardized mortality ratio (SMR) significantly increased. Smoking (a risk factor for laryngeal cancer) may have been more prevalent among asbestos workers than among the comparison populations. This was not taken into account in any of the studies, and may have caused the SMRs to be overestimated. Two of eight case-control studies reported large odds ratios ( 13) for laryngeal cancer. Subsequent case-control studies did not confirm this higher risk; the odds ratios in these studies were 0.3 to 1.9. The conclusion of the review, based on data from 13 cohort and 8 case-control studies, is that neither case-control nor cohort studies have established an increased risk of laryngeal cancer for asbestos workers.     

A structural approach to the familial coaggregation of disorders

The demonstration that 2 disorders coaggregate in families is often the first step in the exploration of genetic factors common to the 2 disorders. Previous methods of analyzing familial coaggregation have used either (1) a typical measure of association (eg, the odds ratio) between a disorder in an individual and another disorder in family members, or (2) a linear structural equation model (SEM). The association method accommodates case-control sampling of families, but may not assess the causal effect of interest because it is not based on an underlying causal model. The SEM method is based on a causal model, but cannot easily accommodate case-control sampling or direct effects of 1 disorder on the other within individuals. We develop a new method of analyzing coaggregation based on directed acyclic graphs. Because this method is a generalization of structural equation models and uses measures of association that accommodate case-control sampling and direct effects, it combines the strengths of both previous methods. In the absence of direct effects between disorders, our approach provides a valid estimate of the causal coaggregation effect. In the presence of direct effects, our approach provides an upper-bound estimate and (assuming additive linear effects of latent familial and nonfamilial factors) a lower-bound estimate of the causal coaggregation effect. For illustration, we applied our method to a family study of binge eating disorder and bipolar disorder.     

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.     

Application of the missing-indicator method in matched case-control studies with incomplete data

A common practice in matched case-control studies with incomplete data is to perform two analyses in parallel: a matched analysis of the complete pairs and an unmatched analysis of all subjects carried out after breaking the matching in the complete pairs. The missing-indicator method, which has the advantage of making use of the data in the incomplete pairs while still preserving the matching in the complete pairs, is recommended as an alternative method of analysis. It is shown here that its estimate of the odds ratio is a compromise between the odds ratios estimated by a matched analysis of the complete pairs and an unmatched analysis of the incomplete pairs. The method is illustrated using data from a matched case-control study of the risk of childhood leukemia from exposure to residential electric and magnetic fields.     

log-binomial模型估计的患病比及其应用

[导读]探讨有和无连续协变量时的log-binomial模型估计患病比的统计方法及其应用.文中使用禁烟立法态度与吸烟关联的研究实例,比较log-binomial模型估计的现患比(PR)与logistic回归模型估计的优势比(OR).当模型中无连续协变量时,采用最大似然估计拟合log-binomial模型;当因含有连续协变量导致模型不收敛时,则采用COPY方法估计PR.分别估计男、女禁烟立法态度与吸烟的关联.由于女性吸烟率低,用PR与OR所估计的关联结果相似.而男性吸烟率较高,OR值明显大于PR.当年龄作为连续协变量纳入模型时,导致log-binomial模型不收敛,采用COPY方法解决此问题.所有分析均在SAS软件中实现.结论:当患病率较高时,PR比OR更好地测量了暴露与疾病的关联.文中给出log-binomial回归模型和COPY方法估计PR的SAS程序.     

Case-control analysis with a continuous outcome variable

It is not uncommon for a continuous outcome variable Y to be dichotomized and analysed using logistic regression. Moser and Coombs (Statist. Med. 2004; 23:1843-1860) provide a method for converting the output from a standard linear regression analysis using the original continuous outcome Y to give much more efficient inferences about the same odds-ratio parameters being estimated by the logistic regression. However, these results apply only to prospective studies. This paper follows up Moser and Coombs by providing an efficient linear-model-based solution for data collected using case-control studies. Gains in statistical efficiency of up to 240 per cent are obtained even with small to moderate odds ratios. Differences in design efficiency between case-control and prospective sampling designs are found to be much smaller, however, when linear-model-based analyses are being used than they are when logistic regression analyses are being used.     

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.     

Future cases as present controls to adjust for exposure trend bias in case-only studies

Self-matched case-only studies (such as the case-crossover or self-controlled case-series method) control by design for time-invariant confounders (measured or unmeasured), but they do not control for confounders that vary with time. A bidirectional case-crossover design can be used to adjust for exposure-time trends. In pharmacoepidemiology, however, illness often influences future use of medications, making a bidirectional design problematic. Suissa's case-time-control design combines a case-crossover and case-control design, and adjusts for exposure-trend bias in the cases' self-controlled odds ratio by dividing that ratio by the corresponding self-controlled odds ratio in a concurrent matched control group. However, if not well matched, the control group may reintroduce selection bias. We propose a "case-case-time-control" that involves crossover analyses in cases and future-case controls. This person-time sampling strategy improves matching by restricting controls to future cases. We evaluate the proposed study design through simulations and analysis of a theoretically null relationship using Veterans Administration (VA) data. Simulation studies show that the case-case-time-control can adjust for exposure trends while controlling for time-invariant confounders. Use of an inappropriate control group left case-time-control analyses biased by exposure-time trends. When analyzing the relationship between vitamin exposure and stroke, using data on 3192 patients in the VA system, a case-crossover odds ratio of 1.5 (95% confidence interval = 1.3-1.7) was reduced to 1.1 (0.9-1.3) when divided by the concurrent exposure trend odds ratio (1.4) in matched future cases. This applied example demonstrates how our approach can adjust for exposure trends observed across time axes.     

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.     

Common referent versus shifting referent methods when using case-control data to examine patterns of incidence across multiple exposure variables

PURPOSE: In case-control studies, when odds ratios estimate rate ratios or risk ratios, trends in odds ratios can reflect trends in incidence in the underlying population. METHODS AND RESULTS: In this report, we use an empirical example and hypothetical data to compare two methods ("common referent" and "shifting referent") for calculating odds ratios from case-control data across multiple exposure variables. With common referent methods, a single independent variable is constructed from the joint distribution of all exposure variables. With shifting referent methods, each stratum-specific trend has its own referent. CONCLUSIONS: Using examples involving a single ordinal "trend" variable and a dichotomous "stratification" variable, we show that common referent odds ratios will reflect the pattern of incidence in the underlying population, whereas odds ratios calculated using shifting referent methods will not.