Multivariate analysis for matched case-control studies

A multivariate method based on the linear logistic model is presented for the analysis of case-control studies with pairwise matching. This technique enables one to investigate the effect of several variables simultaneously in the analysis while allowing for the matched design. The odds ratio is used as the basic measure of risk. One is able to control for variables which are not matching variables while investigating the odds ratio for a particular factor, and to estimate the change in the odds ratio as the level of one or more interval variables changes. The computing methods used for obtaining maximum conditional likelihood estimates of the parameters of interest are modifications of standard programs for logit regression.     

Secondary matching: a method for selecting controls in case-control studies on environmental risk factors

BACKGROUND: The problem of control selection was considered in a population-based case-control study on pleural mesothelioma in Spain. Random sampling from the population was discarded because of potential selection bias due to low participation. Selection of hospital controls by matching them to cases by hospital seemed unsuitable for investigating environmental exposures, as the choice of hospital may be related to the place of residence; controlling for residence may avoid bias but could produce overmatching. METHODS: A three-step procedure was proposed. First, a random sample of primary controls from the population census of the province of Barcelona was obtained. Second, the hospital closest to the residence of the primary control was identified as the control hospital. Third a secondary control was chosen among patients admitted to the hospital matched to the primary control by sex, age and municipality. RESULTS: An overall participation rate of 85% was achieved. The hospital control group showed a distribution of residences similar to that of the general population, and independent of the distribution of cases. CONCLUSIONS: This procedure may be considered as an alternative for control selection when studying environmental factors or, generally, when matching cases and controls by hospital is to be avoided. Its validity was assessed according to the principles of comparability with cases regarding the study base, accuracy of information, deconfounding and efficiency.     

Pooled exposure assessment for matched case-control studies

Exposure assessment using biologic specimens is important for epidemiology but may become impracticable if assays are expensive, specimen volumes are marginally adequate, or analyte levels fall below the limit of detection. Pooled exposure assessment can provide an effective remedy for these problems in unmatched case-control studies. We extend pooled exposure strategies to handle specimens collected in a matched case-control study. We show that if a logistic model applies to individuals, then a logistic model also applies to an analysis using pooled exposures. Consequently, the individual-level odds ratio can be estimated while conserving both cost and specimen. We discuss appropriate pooling strategies for a single exposure, with adjustment for multiple, possibly continuous, covariates (confounders) and assessment of effect modification by a categorical variable. We assess the performance of the approach via simulations and conclude that pooled strategies can markedly improve efficiency for matched as well as unmatched case-control studies.     

A matching method for improving covariate balance in cost-effectiveness analyses

In cost-effectiveness analyses (CEA) that use randomized controlled trials (RCTs), covariates of prognostic importance may be imbalanced and warrant adjustment. In CEA that use non-randomized studies (NRS), the selection on observables assumption must hold for regression and matching methods to be unbiased. Even in restricted circumstances when this assumption is plausible, a key concern is how to adjust for imbalances in observed confounders. If the propensity score is misspecified, the covariates in the matched sample will be imbalanced, which can lead to conditional bias. To address covariate imbalance in CEA based on RCTs and NRS, this paper considers Genetic Matching. This matching method uses a search algorithm to directly maximize covariate balance. We compare Genetic and propensity score matching in Monte Carlo simulations and two case studies, CEA of pulmonary artery catheterization, based on an RCT and an NRS. The simulations show that Genetic Matching reduces the conditional bias and root mean squared error compared with propensity score matching. Genetic Matching achieves better covariate balance than the unadjusted analyses of the RCT data. In the NRS, Genetic Matching improves on the balance obtained from propensity score matching and gives substantively different estimates of incremental cost-effectiveness. We conclude that Genetic Matching can improve balance on measured covariates in CEA that use RCTs and NRS, but with NRS, this will be insufficient to reduce bias; the selection on observables assumption must also hold.     

Statistical methods for haplotype-based matched case-control association studies

Kraft et al. [2005] proposed a method for matched haplotype-based association studies and compared the performances of six analytic strategies for estimating the odds ratio parameters using a conditional likelihood function. Zhang et al. [2006] modified the conditional likelihood and proposed a new method for matched haplotype-based association studies. The main assumptions of Zhang et al. were that the disease was rare, the population was in Hardy-Weinberg equilibrium (HWE), and the haplotypes were independent of the covariates and matching variable(s). In this article, we modify the estimation procedure proposed by Zhang et al. and introduce a fixation index so that the assumption of HWE is relaxed. Using the Wald test, we compare the current modified method with the procedure developed by Kraft et al. through simulations. The results show that the modified method is uniformly more powerful than that described in Kraft et al. Furthermore, the results indicate that the modified method is quite robust to the rare disease assumption.     

Sequential tests for gene-environment interactions in matched case-control studies

The sample size necessary to detect a significant gene x environment interaction in an observational study can be large. For reasons of cost-effectiveness and efficient use of available biological samples we investigated the properties of sequential designs in matched case-control studies to test for both non-hierarchical and hierarchical interactions. We derived the test statistics Z and V and their characteristics when applied in a two-sided triangular test. Results of simulations show good agreement with theoretical values for V and the type I error. Power values were larger than their theoretical values for very large sample sizes. Median gain in efficiency was about 27 per cent. For a 'rare' phenotype gain in efficiency was larger when the alternative hypothesis was true than under the null hypothesis. Sequential designs lead to substantial efficiency gains in tests for interaction in matched case-control studies.     

Estimating risks for matching factors in case-control studies

Matching for factors such as age and sex is a convenient method for minimizing confounding in case-control studies, but it does not allow inferences about the effects of the matching factors unless case ascertainment is virtually complete and the distribution of the matching factors in the source population is known. When this is so, the effect of a particular factor can be estimated by comparing the population distribution of that factor with what is observed in the case series. Such a comparison, however, may itself be confounded by other factors that are related to both the matching factors and the disease under investigation. This article proposes a method for evaluating matching factors as risk factors, which uses information on the distribution of potential confounders in the reference series and exposure relative risk estimates to adjust the person-time proportionality constant in a Poisson regression model. The method is particularly suited to data sets in which many of the elementary matching strata contain few or no cases and/or controls. It makes use of standard analytic procedures, but requires the estimation of an additional variance-covariance component for the estimated Poisson regression coefficients. Further factors that may confound the relationship between exposure and disease are easily accommodated. The method is demonstrated in two examples: a matched case-control study of drugs in relation to the rare blood dyscrasia, agranulocytosis, that was conducted in Europe and Israel, and a case-control study of ovarian cancer in Australia.     

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.     

A relative power table for nested matched case-control studies

OBJECTIVE: To calculate relative powers for nested case-control studies for different values of both relative risk and numbers of controls per case, given a fixed number of cases available for analysis. METHODS: Algebraic and numerical methods. RESULTS: In nested case-control studies, statistical power is a function of relative risk, rarity of exposure, number of case-control sets, and the number of controls per case. CONCLUSION: The dictum that sufficient power will be obtained in a nested case-control study by selecting only four controls per case cannot be sustained. Appropriate numbers need to be calculated for specific studies.     

Stratification-score matching improves correction for confounding by population stratification in case-control association studies

Proper control of confounding due to population stratification is crucial for valid analysis of case-control association studies. Fine matching of cases and controls based on genetic ancestry is an increasingly popular strategy to correct for such confounding, both in genome-wide association studies (GWASs) as well as studies that employ next-generation sequencing, where matching can be used when selecting a subset of participants from a GWAS for rare-variant analysis. Existing matching methods match on measures of genetic ancestry that combine multiple components of ancestry into a scalar quantity. However, we show that including nonconfounding ancestry components in a matching criterion can lead to inaccurate matches, and hence to an improper control of confounding. To resolve this issue, we propose a novel method that assigns cases and controls to matched strata based on the stratification score (Epstein et al. [2007] Am J Hum Genet 80:921-930), which is the probability of disease given genomic variables. Matching on the stratification score leads to more accurate matches because case participants are matched to control participants who have a similar risk of disease given ancestry information. We illustrate our matching method using the African-American arm of the GAIN GWAS of schizophrenia. In this study, we observe that confounding due to stratification can be resolved by our matching approach but not by other existing matching procedures. We also use simulated data to show our novel matching approach can provide a more appropriate correction for population stratification than existing matching approaches.     

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.     

Full-likelihood approaches to misclassification of a binary exposure in matched case-control studies

We consider analysis of matched case-control studies where a binary exposure is potentially misclassified, and there may be a variety of matching ratios. The parameter of interest is the ratio of odds of case exposure to control exposure. By extending the conditional model for perfectly classified data via a random effects or Bayesian formulation, we obtain estimates and confidence intervals for the misclassified case which reduce back to standard analytic forms as the error probabilities reduce to zero. Several examples are given, highlighting different analytic phenomena. In a simulation study, using mixed matching ratios, the coverage of the intervals are found to be good, although point estimates are slightly biased on the log scale. Extensions of the basic model are given allowing for uncertainty in the knowledge of misclassification rates, and the inclusion of prior information about the parameter of interest.     

Flexible matching in case-control studies of gene-environment interactions

Because of the lack of power of case-control study designs to detect gene-environment interactions, flexible matching has recently been proposed as a method of improving efficiency. In this paper, the authors consider a large-sample approximation method that allows estimation of the most efficient matching strategy when genotype and exposure are either independent or associated. The authors provide tables of the sample sizes required to detect gene-environment interactions if this flexible matching strategy is followed, and they make brief comparisons with other study designs.     

Adjusting for differential misclassification in matched case-control studies utilizing health administrative data

In epidemiological studies of secondary data sources, lack of accurate disease classifications often requires investigators to rely on diagnostic codes generated by physicians or hospital systems to identify case and control groups, resulting in a less-than-perfect assessment of the disease under investigation. Moreover, because of differences in coding practices by physicians, it is hard to determine the factors that affect the chance of an incorrectly assigned disease status. What results is a dilemma where assumptions of non-differential misclassification are questionable but, at the same time, necessary to proceed with statistical analyses. This paper develops an approach to adjust exposure-disease association estimates for disease misclassification, without the need of simplifying non-differentiality assumptions, or prior information about a complicated classification mechanism. We propose to leverage rich temporal information on disease-specific healthcare utilization to estimate each participant's probability of being a true case and to use these estimates as weights in a Bayesian analysis of matched case-control data. The approach is applied to data from a recent observational study into the early symptoms of multiple sclerosis (MS), where MS cases were identified from Canadian health administrative databases and matched to population controls that are assumed to be correctly classified. A comparison of our results with those from non-differentially adjusted analyses reveals conflicting inferences and highlights that ill-suited assumptions of non-differential misclassification can exacerbate biases in association estimates.     

病例-对照研究中1:M配比资料OR及χ2的简易计算方法

OR和χ²是病例-对照研究中十分重要的分析指标。本文介绍了1:M(3~4)配比资料OR和χ²的简便计算方法,该方法便于实际运用。     

Sample size requirements for matched case-control studies of gene-environment interaction.

Consideration of gene-environment (GxE) interaction is becoming increasingly important in the design of new epidemiologic studies. We present a method for computing required sample size or power to detect GxE interaction in the context of three specific designs: the standard matched case-control; the case-sibling, and the case-parent designs. The method is based on computation of the expected value of the likelihood ratio test statistic, assuming that the data will be analysed using conditional logistic regression. Comparisons of required sample sizes indicate that the family-based designs (case-sibling and case-parent) generally require fewer matched sets than the case-control design to achieve the same power for detecting a GxE interaction. The case-sibling design is most efficient when studying a dominant gene, while the case-parent design is preferred for a recessive gene. Methods are also presented for computing sample size when matched sets are obtained from a stratified population, for example, when the population consists of multiple ethnic groups. A software program that implements the method is freely available, and may be downloaded from the website http://hydra.usc.edu/gxe.     

Estimation of attributable risk for case-control studies with multiple matching

Kuritz and Landis considered case-control studies with multiple matching and proposed an asymptotic interval estimator of the attributable risk based on Wald's statistic. Using Monte Carlo simulation, Kuritz and Landis demonstrated that their interval estimator could perform well when the number of matched sets was large (>or=100). However, the number of matched sets may often be moderate or small in practice. In this paper, we evaluate the performance of Kuritz and Landis' interval estimator in small or moderate number of matched sets and compare it with four other interval estimators. We note that the coverage probability of Kuritz and Landis' interval estimator tends to be less than the desired confidence level when the probability of exposure among cases is large. In these cases, the interval estimator using the logarithmic transformation and the two interval estimators derived from the quadratic equations developed here can generally improve the coverage probability of Kuritz and Landis' interval estimator, especially for the case of a small number of matched sets. Furthermore, we find that an interval estimator derived from a quadratic equation is consistently more efficient than Kuritz and Landis' interval estimator. The interval estimator using the logit transformation, although which performs poorly when the underlying odds ratio (OR) is close to 1, can be useful when both the probability of exposure among cases and the underlying OR are moderate or large.     

Risk factors for premature myocardial infarction: a matched case-control study

Background: Myocardial infarction in young age is increasing. Identifying risk factors could be important for health promotion. We studied classic atherosclerotic risk factors in premature myocardial infarction. Methods: In this matched case-control study, which was conducted from 2005 to 2007 in Birjand County, the east of Iran, atherosclerotic risk factors (hyperten-sion, family history of coronary artery diseases, obesity, diabetes mellitus, dyslipidemia) of 98 patients affected by acute myocardial infarction aged under 50 years were compared with that of 98 healthy neighborhood controls. Results: Mean levels of cholesterol, triglyceride, low-density lipoprotein, as well as systolic blood pressure and body mass index were significantly higher in cases than in controls. There was a positive association between coronary artery disease at younger age and dyslipidemia OR=2.8 [95% CI: 1.5, 5.2], smoking OR=6.4 [95% CI: 3.0, 13.5], systolic hypertension OR=3.1 [95% CI: 1.5, 6.3], family history of coronary artery diseases OR=10.9 [95% CI: 3.2, 37.9] and diabetes OR=2.5 [95% CI: 1.04, 6.2]. Conclusion: Smoking, systolic hypertension and dyslipidemia were the most common risk factors among patients with premature myocardial infarction.     

Assessing the adequacy of the logistic regression model for matched case-control studies

We apply results for the detection of outliers in logistic regression to the analysis of matched pairs data and illustrate the techniques with data from a matched pairs study of the relationship between iron-binding proteins and mortality in the Solomon Islands. Although the study includes 90 matched pairs, the conclusions change substantially with deletion of one or two pairs. Thus, even with reasonably large data sets, single observations may have a great impact on the results of an analysis. The identification of influential observations should constitute part of the analysis of matched case-control data.