Improving the efficiency of nested case-control studies of interaction by selecting controls using counter matching on exposure

BACKGROUND: Studies of the effect of exposure to a risk factor measured in an entire cohort may be augmented by nested case-control subsets to investigate confounding or effect modification by additional factors not practically assessed on all cohort members. We compared three control-selection strategies-matching on exposure, counter matching on exposure, and random sampling-to determine which was most efficient in a situation where exposure is a known, continuous variable and high doses are rare. METHODS: We estimated the power to detect interaction using four control-to-case ratios (1:1, 2:1, 4:1, and 8:1) in a planned case-control study of the joint effect of atomic bomb radiation exposure and serum oestradiol levels on breast cancer. Radiation dose is measured in the entire cohort, but because neither serum oestradiol level nor the true degree of interaction was known, we simulated values of oestradiol and hypothetical levels of oestradiol-radiation interaction. RESULTS: Compared with random sampling, power to detect interaction was similarly higher with either matching or counter matching with two or more controls. CONCLUSIONS: Because counter matching is generally at least as efficient as random sampling, whereas matching on exposure can result in loss of efficiency and precludes estimation of exposure risk, we recommend counter matching for selecting controls in nested case-control studies of the joint effects of multiple risk factors when one is previously measured in the full cohort.     

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.     

Selection of controls in injury case-control studies

PURPOSE: To assist in elucidating principles underlying the design of injury case-control studies.APPROACH: We begin by defining "event" as the sequence of circumstances that place a person at risk of injury (e.g. bicycle crash) and "injury given the event" as the resultant physical damage (e.g. head injury in bicycle crash). We then identify two broad classes of research question: 1) Studies of risk factors for the event, and, 2) Studies of risk factors for injury given the event. The study base for the first type of research question is all persons at risk of the event, while the study base for the second type is all persons who experience the event, and are therefore at risk of injury. It follows that in studies of risk factors for injury given the event, the controls should be a sample of all persons who experience the event. For example, in a study of bicycle helmets and head injuries, a suitable case group would be cyclists treated for head injury following a bicycle crash. The appropriate control group is drawn from the base population of all cyclists who crashed, including those who had no injuries. The control group may be restricted to cyclists who crashed and sought treatment for non-head injury under the assumption that the exposure distribution (prevalence of cycle helmet use) in the crash/no injury group is identical to the exposure distribution in the crash/non-head injury group.CONCLUSIONS: It is over ten years since innovative researchers in Seattle first applied the case-control design to the problem of bicycle crashes. Since then, successive bicycle injury studies at other centers have largely failed to extend and refine the Seattle methodology. A more critical approach to the design of case-control studies is required if we are to continue to advance the field of injury epidemiology.     

Using dead controls to adjust for confounders in case-control studies

The use of dead controls in a case-control study, the primary purpose of which is to control for confounding, leads to consistent relative risk estimates within stratum of the confounder, even if the causes of death of controls are associated with that confounder. Dead controls may be more comparable to dead cases in terms of data quality, and therefore, under these circumstances, the use of dead controls may be advantageous.     

Hospital visitors as controls in case-control studies.

OBJECTIVE: Selecting controls is one of the most difficult tasks in the design of case-control studies. Hospital controls may be inadequate and random controls drawn from the base population may be unavailable. The aim was to assess the use of hospital visitors as controls in a case-control study on the association of organochlorinated compounds and other risk factors for breast cancer conducted in the main hospital of the "Instituto Nacional de Cancer" - INCA (National Cancer Institute) in Rio de Janeiro (Brazil). METHODS: The study included 177 incident cases and 377 controls recruited among female visitors. Three different models of control group composition were compared: Model 1, with all selected visitors; Model 2, excluding women visiting relatives with breast cancer; and Model 3, excluding all women visiting relatives with any type of cancer. Odds ratios (OR) and 95% confidence intervals were calculated to test the associations. RESULTS: Age-adjusted OR for breast cancer associated with risk factors other than family history of cancer, except smoking and breast size, were similar in the three models. Regarding family history of all cancers, except for breast cancer, there was a decreased risk in Models 1 and 2, while in Model 3 there was an increased risk, but not statistically significant. Family history of breast cancer was a risk factor in Models 2 and 3, but no association was found in Model 1. In multivariate analysis a significant risk of breast cancer was found when there was a family history of breast cancer in Models 2 and 3 but not in Model 1. CONCLUSIONS: These results indicate that while investigating risk factors unrelated to family history of cancer, the use of hospital visitors as controls may be a valid and feasible alternative.     

Simple methods for assessing haplotype-environment interactions in case-only and case-control studies

For investigating haplotype-environment interactions in case-control studies, one can implement statistical methods based either on a retrospective likelihood (modeling the probability of haplotype and environment conditional on disease status) or a prospective likelihood (modeling the probability of disease status conditional on haplotype and environment). Retrospective approaches are generally more powerful than prospective approaches, but require an explicit model of the joint distribution of haplotype and environmental factors in the sample with the latter being particularly unattractive to specify. To resolve this issue, we propose a number of simple retrospective procedures for haplotype-environment interaction analysis that do not require explicit modeling of environmental covariates in the sample. We first consider a cases-only procedure, followed by a simple likelihood for case-control data that is proportional to the full-retrospective likelihood. Finally, we consider a retrospective procedure for inference on haplotype-environment interaction effects in matched or finely-stratified case-control studies. Our methods are based on the assumptions that haplotypes and environmental covariates are independent in the target population and that disease is rare. We illustrate our approaches using case-control data from the Finland-United States Investigation of Non-Insulin Dependent Diabetes Mellitus (FUSION) genetic study and simulated data.     

Follow-up of controls participating in case-control studies for cancer risk factors

Case-control studies have been carried out in Alberta in the last seven years to investigate possible risk factors for cancer of the prostate, skin and ovary. For each study, controls were randomly selected from an age- and sex-matched population. The information obtained from each control that agreed to participate in each study (n = 1236) included name, sex, date of birth, address and date of participation as well as the specific questions for each study. A review of these controls was carried out in 1988 by checking the number of deaths through death certificate listings from Vital Statistics (n = 142) and cancer incidence through the population-based Alberta Cancer Registry (n = 134). Of the 619 controls interviewed for the prostate cancer case control study in 1982 and 1983, 25 have been diagnosed with cancer of the prostate. From the non-melanoma skin cancer study, 15 cases from the 409 controls interviewed in 1983-1984 have been diagnosed with non-melanoma skin cancer. As for the 208 controls for ovarian cancer interviewed in 1985-1986 no new cases have been diagnosed. This possible ascertainment bias should be taken under consideration when case-control study analyses are carried out.     

The exposure odds ratio in nested case-control studies with competing risks

A nested case-control study, also known as an ambidirectional study, is a case-control study within a cohort study. Although distortion by competing risks is well-recognized in follow-up studies, the problem has not been as widely appreciated in nested case-control studies. This paper extends previous work concerning the bias associated with competing risks for nested case-control studies. Specifically, the distorting effect of competing risks is illustrated for three methods of control selection. Assuming the proportional hazards model, the authors derived formulas for the bias of the odds ratio when competing risks cannot be ignored. Examples illustrate the magnitude of bias that occurs when the exposure of interest is associated with competing causes of death or withdrawal.     

Cancer case-control studies with other cancers as controls

Theoretical considerations concerning the use of other cancer patients as controls in cancer case-control studies are reviewed. Selection bias may be a problem in that some other cancers may be caused by the exposure under study biasing the odds ratio towards unity. Such bias is noted to be greatest with low prevalence exposures associated with high attributable risks for other cancers. However, it may be possible to identify selection bias with other cancer controls using census or other general population data. In addition, using other cancers as controls has important advantages with regard to recall and interviewer bias, which may be of unknown magnitude and direction when using general population controls. A further disadvantage of general population controls is that separate selection of decreased controls should usually be made for deceased cases, whereas a mixture of live and deceased controls can be expected when selecting other cancer patients as controls. Since there are also logistical and cost advantages in using other cancer patients as controls, this study design is likely to be used increasingly in the future, particularly in cancer registry settings.     

Selection of controls in case-control studies. II. Types of controls.

Types of control groups are evaluated using the principles described in paper 1 of the series, "Selection of Controls in Case-Control Studies" (S. Wacholder et al. Am J Epidemiol 1992;135:1019-28). Advantages and disadvantages of population controls, neighborhood controls, hospital or registry controls, medical practice controls, friend controls, and relative controls are considered. Problems with the use of decreased controls and proxy respondents are discussed.     

Selection bias in case-control studies using relatives as the controls

Investigators have suggested using relatives of cases as the control group when studying complex diseases thought to have a major genetic component. However, there is a concern about possible bias and we developed a model to examine the possibility of bias in the selection of relatives as the control group. Assuming the exposure-specific risks of disease remain constant over time, the results indicate that even when there is a correlation in the exposure status among relatives, selection of controls from relatives of cases does not, of itself, introduce bias in the estimate of effect.     

Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies

This article describes how genetic components of disease susceptibility can be evaluated in case-control studies, where cases and controls are sampled independently from the population at large. Subjects are assumed unrelated, in contrast to studies of familial aggregation and linkage. The logistic model can be used to test collapsibility over phenotypes or genotypes, and to estimate interactions between environmental and genetic factors. Such interactions provide an example of a context where non-hierarchical models make sense biologically. Also, if the exposure and genetic categories occur independently and the disease is rare, then analyses based only on cases are valid, and offer better precision for estimating gene-environment interactions than those based on the full data.     

An analytical method for assessing patterns of familial aggregation in case-control studies.

This paper describes an analytical method that is used to assess patterns of disease aggregation within family based on family history information collected in case-control studies. In such a study, cases and controls are thought of as probands whose relatives are identified, and relatives' phenotypes and other covariates such as age, sex, and genealogical relationship with the probands are recorded. By modeling the dependence of relatives' phenotypes on case-control status and other covariates, this method yields adjusted odds ratios that quantify familial aggregation. The estimated standard errors are obtained for statistical inference since the method acknowledges the potential correlations between relatives' phenotypes by using the estimating equations technique. In population-based case-control studies, the estimates and statistical inferences are generalizable to the general population. To illustrate this method, we analyzed a case-control study of colorectal cancer involving 5,190 relatives of 792 cases and 4,478 relatives of 680 population-based controls conducted in Hawaii. Although detailed results will be presented elsewhere, the colorectal cancer was found to aggregate within family with an odds ratio of 2.74 (95% confidence interval (CI): 1.78-4.21). Among parents, the odds ratio for familial aggregation was 2.38 (95% CI: 1.25-4.54). The corresponding value for siblings was 3.09 (95% CI: 1.87-5.11). It was also found that the odds ratio increases from about 2.00 for relatives of the probands who were 50 years or older to 7.66 and 12.84 for relatives of the probands who were between 40 and 50 years and under 40 years, respectively, suggesting that the familial aggregation of colorectal cancer decreases as probands' age increases.     

Selection of controls in case-control studies. I. Principles.

A synthesis of classical and recent thinking on the issues involved in selecting controls for case-control studies is presented in this and two companion papers (S. Wacholder et al. Am J Epidemiol 1992;135:1029-50). In this paper, a theoretical framework for selecting controls in case-control studies is developed. Three principles of comparability are described: 1) study base, that all comparisons be made within the study base; 2) deconfounding, that comparisons of the effects of the levels of exposure on disease risk not be distorted by the effects of other factors; and 3) comparable accuracy, that any errors in measurement of exposure be nondifferential between cases and controls. These principles, if adhered to in a study, can reduce selection, confounding, and information bias, respectively. The principles, however, are constrained by an additional efficiency principle regarding resources and time. Most problems and controversies in control selection reflect trade-offs among these four principles.     

Selecting cases and controls for DNA sequencing studies using family histories of disease

Recent improvements in sequencing technology have enabled the investigation of so‐called missing heritability, and a large number of affected subjects have been sequenced in order to detect significant associations between human diseases and rare variants. However, the cost of genome sequencing is still high, and a statistically powerful strategy for selecting informative subjects would be useful. Therefore, in this report, we propose a new statistical method for selecting cases and controls for sequencing studies based on family history. We assume that disease status is determined by unobserved liability scores. Our method consists of two steps: first, the conditional means of liability are estimated with the liability threshold model given the individual's disease status and those of their relatives. Second, the informative subjects are selected with the estimated conditional means. Our simulation studies showed that statistical power is substantially affected by the subject selection strategy chosen, and power is maximized when affected (unaffected) subjects with high (low) risks are selected as cases (controls). The proposed method was successfully applied to genome‐wide association studies for type 2 diabetes, and our analysis results reveal the practical value of the proposed methods. Copyright © 2017 John Wiley & Sons, Ltd.     

The validity of case-control studies with nonrandom selection of controls

An unbiased estimate of the rate ratio can be obtained using a case-control design in which each case is matched to one or more controls randomly selected from population members at risk and in the same stratum as the case at the time of disease onset. However, the nonrandom assignment of controls to cases is quite frequent in case-control research. It occurs, for example, in matched case-control studies using either friend controls or neighborhood controls. Many valid random designs, in contrast to most nonrandom designs, require enumeration of a substantial fraction of the study base. Therefore, there may be important cost and logistic advantages to using valid nonrandom designs. In this paper we determine those nonrandom case-control designs that can produce unbiased estimates of the rate ratio and discuss the implications of our findings for the design of case-control studies. We conclude, as did Flanders and Austin, that friend-case-control studies should generally be avoided. On the other hand, in a typical neighborhood-matched, case-control study, any bias attributable to nonrandom control selection is usually too small to affect substantive conclusions.