Design of validation studies for estimating the odds ratio of exposure-disease relationships when exposure is misclassified

We compared several validation study designs for estimating the odds ratio of disease with misclassified exposure. We assumed that the outcome and misclassified binary covariate are available and that the error-free binary covariate is measured in a subsample, the validation sample. We considered designs in which the total size of the validation sample is fixed and the probability of selection into the validation sample may depend on outcome and misclassified covariate values. Design comparisons were conducted for rare and common disease scenarios, where the optimal design is the one that minimizes the variance of the maximum likelihood estimator of the true log odds ratio relating the outcome to the exposure of interest. Misclassification rates were assumed to be independent of the outcome. We used a sensitivity analysis to assess the effect of misspecifying the misclassification rates. Under the scenarios considered, our results suggested that a balanced design, which allocates equal numbers of validation subjects into each of the four outcome/mismeasured covariate categories, is preferable for its simplicity and good performance. A user-friendly Fortran program is available from the second author, which calculates the optimal sampling fractions for all designs considered and the efficiencies of these designs relative to the optimal hybrid design for any scenario of interest.     

Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios

A Bayesian adaptive design is proposed for dose-finding in phase I/II clinical trials to incorporate the bivariate outcomes, toxicity and efficacy, of a new treatment. Without specifying any parametric functional form for the drug dose-response curve, we jointly model the bivariate binary data to account for the correlation between toxicity and efficacy. After observing all the responses of each cohort of patients, the dosage for the next cohort is escalated, deescalated, or unchanged according to the proposed odds ratio criteria constructed from the posterior toxicity and efficacy probabilities. A novel class of prior distributions is proposed through logit transformations which implicitly imposes a monotonic constraint on dose toxicity probabilities and correlates the probabilities of the bivariate outcomes. We conduct simulation studies to evaluate the operating characteristics of the proposed method. Under various scenarios, the new Bayesian design based on the toxicity-efficacy odds ratio trade-offs exhibits good properties and treats most patients at the desirable dose levels. The method is illustrated with a real trial design for a breast medical oncology study.     

Design Aspects and Odds Ratio Estimation in Multicenter Case-Control Studies

In this paper we propose a method to be used in the planning stage of a case-control study. An allocation rule for controls in multicenter case-control studies is proposed which would assure a simple, efficient and unbiased estimation of the odds ratio in the pooled data. It is shown that the efficiency of the design increases with increasing correlation between study center and risk factor. Sources of bias and their implications for relative risk estimation are discussed. The method is demonstrated with data from a case-control study.     

Novel two-phase sampling designs for studying binary outcomes

In biomedical cohort studies for assessing the association between an outcome variable and a set of covariates, usually, some covariates can only be measured on a subgroup of study subjects. An important design question is—which subjects to select into the subgroup to increase statistical efficiency. When the outcome is binary, one may adopt a case-control sampling design or a balanced case-control design where cases and controls are further matched on a small number of complete discrete covariates. While the latter achieves success in estimating odds ratio (OR) parameters for the matching covariates, similar two-phase design options have not been explored for the remaining covariates, especially the incompletely collected ones. This is of great importance in studies where the covariates of interest cannot be completely collected. To this end, assuming that an external model is available to relate the outcome and complete covariates, we propose a novel sampling scheme that oversamples cases and controls with worse goodness-of-fit based on the external model and further matches them on complete covariates similarly to the balanced design. We develop a pseudolikelihood method for estimating OR parameters. Through simulation studies and explorations in a real-cohort study, we find that our design generally leads to reduced asymptotic variances of the OR estimates and the reduction for the matching covariates is comparable to that of the balanced design.     

On a supplemented case-control design

The supplemented case-control design consists of a case-control sample and of an additional sample of disease-free subjects who arise from a given stratum of one of the measured exposures in the case-control study. The supplemental data might, for example, arise from a population survey conducted independently of the case-control study. This design improves precision of estimates of main effects and especially of joint exposures, particularly when joint exposures are uncommon and the prevalence of one of the exposures is low. We first present a pseudo-likelihood estimator (PLE) that is easy to compute. We further adapt two-phase design methods to find maximum likelihood estimates (MLEs) for the log odds ratios for this design and derive asymptotic variance estimators that appropriately account for the differences in sampling schemes of this design from that of the traditional two-phase design. As an illustration of our design we present a study that was conducted to assess the influence to joint exposure of hepatitis-B virus (HBV) and hepatitis-C virus (HCV) infection on the risk of hepatocellular carcinoma in data from Qidong County, Jiangsu Province, China.     

Aspects of the design and analysis of high-dimensional SNP studies for disease risk estimation

The state of readiness for high-dimensional single nucleotide polymorphism (SNP) epidemiologic association studies is described, as background for a discussion of statistical aspects of case-control study design and analysis. Specifically, the important role that multistage designs can play in the elimination of false-positive associations and in the control of study costs will be noted. Also, the trade-offs associated with using pooled DNA at early design stages for additional important cost reductions will be discussed in some detail. An odds ratio approach to relating SNP alleles to disease risk using pooled DNA will be proposed, in conjunction with a simple empirical variance estimator, based on comparisons among log-odds ratio estimators from distinct pairs of case and control pools. Simulation studies will be presented to evaluate the moderate sample size properties of such multistage designs and estimation procedures. The design of an ongoing three-stage study in the Women's Health Initiative to relate 250,000 SNPs to the risk of coronary heart disease, stroke, and breast cancer will provide illustration, and will be used to motivate the choice of simulation configurations.     

Relative Efficiency of the Case-Control to the Cohort Design in Epidemiology

In deriving the efficiency of the stratified to the simple random sample design in survey research, the critical link between the designs is the population analysis of variance. Analogously, the efficiency of the case-control to the cohort design in epidemiologic research can be derived using Bayes' theorem as the essential connection between the designs. Prior information on the odds of the disease is also required. A numerical example using data from Fleiss' text is used to illustrate the result.     

Notes on Confidence Limits for the Odds Ratio in Case-Control Studies under Inverse Sampling

When the disease of interest is rare or chronic, we often apply the case control study design and the odds ratio to determine the possibly risk factors. In this paper, three simple closed-form interval calculation procedures for the odds ratio under inverse sampling are proposed. Results on the basis of a Monte Carlo simulation to evaluate and compare the performance of these three procedures are presented. A discussion on the limitation of the proposed procedures when the probability of exposure is extremely common in both the case and the control groups and a suggestion to overcome this limitation are included as well.     

Covariate measurement error adjustment for matched case-control studies

We propose a conditional scores procedure for obtaining bias-corrected estimates of log odds ratios from matched case-control data in which one or more covariates are subject to measurement error. The approach involves conditioning on sufficient statistics for the unobservable true covariates that are treated as fixed unknown parameters. For the case of Gaussian nondifferential measurement error, we derive a set of unbiased score equations that can then be solved to estimate the log odds ratio parameters of interest. The procedure successfully removes the bias in naive estimates, and standard error estimates are obtained by resampling methods. We present an example of the procedure applied to data from a matched case-control study of prostate cancer and serum hormone levels, and we compare its performance to that of regression calibration procedures.     

Use of Polytomous Logistic Model in Matched Case-Control Studies

Binary logistic model has been found useful for estimating odds ratio in case of dichotomous exposure variable under matched case-control retrospective design. We describe the use of polytomous logistic model for estimating odds ratios when the exposure of prime interests, relative to disease incidence, has more than two levels. An illustrative example is presented and discussed.     

The analysis of stratified 2 x 2 contingency tables

We consider the problem of testing for independence against the consistent superiority of one treatment over another when the response variable is binary and is compared across two treatments in each of several strata. Specifically, we consider the randomized clinical trial setting. A number of issues arise in this context. First, should tables be combined if there are small or zero margins? Second, should one assume a common odds ratio across strata? Third, if the odds ratios differ across strata, then how does the standard test (based on a common odds ratio) perform? Fourth, are there other analyzes that are more appropriate for handling a situation in which the odds ratios may differ across strata? In addressing these issues we find that the frequently used Cochran–Mantel–Haenszel test may have a poor power profile, despite being optimal when the odds ratios are common. We develop novel tests that are analogous to the Smirnov, modified Smirnov, convex hull, and adaptive tests that have been proposed for ordered categorical data. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Saline-filled breast implant safety and efficacy: a multicenter retrospective review

Our center undertook an industry-funded, outcomes-based, multicenter, retrospective review to evaluate the safety and efficacy of saline-filled breast implants. Our review was part of a pre-market approval review process mandated by the U.S. Food and Drug Administration. The design of our review was modeled on a Plastic Surgery Educational Foundation outcomes study previously conducted by our center. For this study, several significant changes were made to our previous protocol, including improved patient tracking, stronger biostatistical support, and a mandatory 10-year minimum patient follow-up period. Physician-reported and patient-reported data on 450 patients with 882 saline-filled breast implants placed between January 1, 1980, and June 30, 1986, were obtained. Mean patient follow-up period was 13.0 years. Most implants (93.9 percent) were placed for breast augmentation. Seventy-four percent were placed in a submammary position; 25.6 percent, subpectorally; and 0.2 percent, subcutaneously. The overall complication rate was 20.2 percent. Reoperation for capsular contracture or implant deflation was necessary in 104 of 450 patients (23.1 percent). Deflation occurred in 73 implants (8.3 percent) and was underreported according to the physicians' record review alone. This deflation rate is higher than the 5.5 percent previously reported by our center. However, 26 of these 73 deflations (35.6 percent) occurred in a single cohort of patients at one center using Surgitek saline implants. If this cohort is excluded, the deflation rate drops to 5.8 percent, a figure more consistent with data published in the literature and found in our previous study. Of the 73 deflations, spontaneous deflation was reported for 50 (74.6 percent), and the remainder were iatrogenic. Actuarial survival of the non-Surgitek implants was 98.4 percent to 99.8 percent at 5 years and 96.9 percent to 98.9 percent at 10 years (95 percent confidence interval). Risk factors for implant deflation included the use of Surgitek saline-filled implants (odds ratio = 17.5, p < 0.01), use of Heyer-Schulte and Mentor model 1800 implants (odds ratio = 3.0, p < 0.01), and implant size greater than 450 cc (odds ratio = 1.01, p < 0.02). Risk factors for capsular contracture included submammary implant position (odds ratio = 2.05, p = 0.03) and implant size greater than 450 cc (odds ratio = 1.01, p < 0.01). Overall, satisfaction was high: 93 percent of patients were "satisfied" or "very satisfied" with their implants. As in our earlier study, risk factors for patient dissatisfaction were reconstruction after mastectomy (odds ratio = 7.6, p = 0.011), significant breast firmness (odds ratio = 6.2, p < 0.001), and patient desire for smaller implants (odds ratio = 3.0, p = 0.020). In conclusion, our review provides additional outcomes-based evidence that saline-filled breast implants remain a safe, effective alternative to silicone gel-filled models.     

Blowfly strike in England and Wales: the relationship between prevalence and farm and management factors

Abstract. In order to develop and evaluate control strategies for blowfly strike, a greater understanding of the epidemiology is essential. A postal survey of sheep farmers yielded information about ten farm and management factors and their relationship to blowfly strike prevalence. The risk of a farm reporting at least one case of blowfly strike increased as flock size and stocking density increased (adjusted odds ratio of 1.13 for an increase in flock size of 100 sheep and 1.38 for an increase in stocking density of ten sheep per hectare). As farm altitude increased, the risk of blowfly strike decreased (adjusted odds ratio 0.67 for an increase in farm altitude of 100 m). The risk of high strike prevalence (more than 2% of sheep struck) decreased as both farm altitude and flock size increased. High strike prevalence was also associated with on-farm sheep carcase disposal (odds ratio 1.35). Farmers in the south-west of England were more likely to report at least one case of blowfly strike and high strike prevalence compared to all other regions.     

The use of random controls in genetic association studies

BACKGROUND: The optimal control sample would be ethnically-matched and at minimal risk of developing the disease. Alternatively, one could collect random individuals from the population or select individuals to reduce the number of at-risk individuals in the sample. The effect of randomly selected individuals in a control sample on the statistical power and the odds ratio estimate was investigated. METHODS: Case and control genotype distributions were simulated using standard genetic models with an additional term representing the proportion of unidentified cases in the control sample. Power and odds ratio were calculated from the genotype distributions generated under different sampling scenarios using established methods. RESULTS: Random sampling of controls resulted in a loss in power and a reduction in the odds ratio estimate to a degree that is determined by the proportion of random sampling and the prevalence of the disease. Random sampling resulted in a 19% loss in power for a disease having prevalence of 0.20, compared to a control sample that contained no at-risk individuals. Having random controls results in a decrease in the odds ratio estimate. CONCLUSIONS: Investigators planning case-control genetic association studies should be aware of the statistical costs of different ascertainment approaches.     

Estimating standardized risk differences from odds ratios

Holland (1989, Biometrics 45, 1009-1016) gave simple formulas for an "adjusted" risk difference based on the Mantel-Haenszel odds ratio estimator and its variance. This "adjusted" risk difference is, in general, inconsistent, but Holland's variance formula is an immediate corollary of a more general formula by Greenland (1987, Journal of Chronic Diseases 40, 1087-1094). We show how, under a large-stratum limiting model, one can derive consistent estimators of standardized risk differences from any consistent odds ratio estimator. We also show how one can derive nonparametric standardized estimators under a sparse-data limiting model.     

On cross-odds ratio for multivariate competing risks data

The cross-odds ratio is defined as the ratio of the conditional odds of the occurrence of one cause-specific event for one subject given the occurrence of the same or a different cause-specific event for another subject in the same cluster over the unconditional odds of occurrence of the cause-specific event. It is a measure of the association between the correlated cause-specific failure times within a cluster. The joint cumulative incidence function can be expressed as a function of the marginal cumulative incidence functions and the cross-odds ratio. Assuming that the marginal cumulative incidence functions follow a generalized semiparametric model, this paper studies the parametric regression modeling of the cross-odds ratio. A set of estimating equations are proposed for the unknown parameters and the asymptotic properties of the estimators are explored. Non-parametric estimation of the cross-odds ratio is also discussed. The proposed procedures are applied to the Danish twin data to model the associations between twins in their times to natural menopause and to investigate whether the association differs among monozygotic and dizygotic twins and how these associations have changed over time.     

Effectiveness of helmets in skiers and snowboarders: case-control and case crossover study

Objective To determine the effect of helmets on the risk of head and neck injuries in skiers and snowboarders.Design Matched case-control and case crossover study.Setting 19 ski areas in Quebec, Canada, November 2001 to April 2002.Participants 1082 skiers and snowboarders (cases) with head and neck injuries reported by the ski patrol and 3295 skiers and snowboarders (controls) with non-head or non-neck injuries matched to cases at each hill.Main outcome measures Estimates of matched odds ratios for the effect of helmet use on the risk of any head or neck injury and for people requiring evacuation by ambulance.Results The adjusted odds ratio for helmet use in participants with any head injury was 0.71 (95% confidence interval 0.55 to 0.92), indicating a 29% reduction in the risk of head injury. For participants who required evacuation by ambulance for head injuries, the adjusted odds ratio for helmet use was 0.44 (0.24 to 0.81). Similar results occurred with the case crossover design (odds ratio 0.43, 0.09 to 1.83). The adjusted odds ratio for helmet use for participants with any neck injury was 0.62 (0.33 to 1.19) and for participants who required evacuation by ambulance for neck injuries it was 1.29 (0.41 to 4.04).Conclusions Helmets protect skiers and snowboarders against head injuries. We cannot rule out the possibility of an increased risk of neck injury with helmet use, but the estimates on which this assumption is based are imprecise.     

Assessment of Noninferiority (and Equivalence) for Simple Crossover Trials Using Bayesian Approach

To assess the noninferiority or equivalence of a general drug to a standard one, researchers generally use the odds ratio of patient response rates to evaluate the relative treatment efficacy. In this paper, we use a logistic random effects model to test noninferiority and equivalence based on the odds ratio of patient response rates for crossover trials with binary data. We use Bayesian sampling algorithm, data augmentation, and scaled mixture of normal representation to implement the approach and improve efficiency. The performance of the proposed approach is assessed via simulation and real data examples.     

The case-only odds ratio as a causal parameter

In the simplest case-only design, cases of a disease are cross-classified into a 2 x 2 table describing a genotype attribute and exposure to some environmental agent. In some instances, the genetic attribute has described inherited genes; in other instances, it has described mutations, for instance, damage to proto-oncogenes or tumor suppressor genes leading to cancer. Here, the population case-only odds ratio is written as a causal parameter in terms of potential outcomes with and without exposure to the agent. It is shown that the case-only odds ratio makes sense as a causal parameter with inherited genes, but its magnitude does not have a causal interpretation with mutations, although deviations from 1 do provide information. The difference is that the environmental agent certainly did not cause an individual to inherit particular genes, but it may have caused the mutation.     

On logit confidence intervals for the odds ratio with small samples

Unless the true association is very strong, simple large-sample confidence intervals for the odds ratio based on the delta method perform well even for small samples. Such intervals include the Woolf logit interval and the related Gart interval based on adding .5 before computing the log odds ratio estimate and its standard error. The Gart interval smooths the observed counts toward the model of equiprobability, but one obtains better coverage probabilities by smoothing toward the independence model and by extending the interval in the appropriate direction when a cell count is zero.