6b. Matching criteria
What to write
Cohort study: For matched studies, give matching criteria and number of exposed and unexposed.
Case-control study: For matched studies, give matching criteria and the number of controls per case.
Explanation
Matching is much more common in case-control studies, but occasionally, investigators use matching in cohort studies to make groups comparable at the start of follow-up. Matching in cohort studies makes groups directly comparable for potential confounders and presents fewer intricacies than with case-control studies. For example, it is not necessary to take the matching into account for the estimation of the relative risk1. Because matching in cohort studies may increase statistical precision investigators might allow for the matching in their analyses and thus obtain narrower confidence intervals.
In case-control studies matching is done to increase a study’s efficiency by ensuring similarity in the distribution of variables between cases and controls, in particular the distribution of potential confounding variables1,2. Because matching can be done in various ways, with one or more controls per case, the rationale for the choice of matching variables and the details of the method used should be described. Commonly used forms of matching are frequency matching (also called group matching) and individual matching. In frequency matching, investigators choose controls so that the distribution of matching variables becomes identical or similar to that of cases. Individual matching involves matching one or several controls to each case. Although intuitively appealing and sometimes useful, matching in case-control studies has a number of disadvantages, is not always appropriate, and needs to be taken into account in the analysis (see below).
Even apparently simple matching procedures may be poorly reported. For example, authors may state that controls were matched to cases ‘within five years’, or using ‘five year age bands’. Does this mean that, if a case was 54 years old, the respective control needed to be in the five-year age band 50 to 54, or aged 49 to 59, which is within five years of age 54? If a wide (e.g., 10-year) age band is chosen, there is a danger of residual confounding by age (see below), for example because controls may then be younger than cases on average.
Matching in case-control studies
In any case-control study, sensible choices need to be made on whether to use matching of controls to cases, and if so, what variables to match on, the precise method of matching to use, and the appropriate method of statistical analysis. Not to match at all may mean that the distribution of some key potential confounders (e.g., age, sex) is radically different between cases and controls. Although this could be adjusted for in the analysis there could be a major loss in statistical efficiency.
The use of matching in case-control studies and its interpretation are fraught with difficulties, especially if matching is attempted on several risk factors, some of which may be linked to the exposure of prime interest3,4. For example, in a case-control study of myocardial infarction and oral contraceptives nested in a large pharmaco-epidemiologic data base, with information about thousands of women who are available as potential controls, investigators may be tempted to choose matched controls who had similar levels of risk factors to each case of myocardial infarction. One objective is to adjust for factors that might influence the prescription of oral contraceptives and thus to control for confounding by indication. However, the result will be a control group that is no longer representative of the oral contraceptive use in the source population: controls will be older than the source population because patients with myocardial infarction tend to be older. This has several implications. A crude analysis of the data will produce odds ratios that are usually biased towards unity if the matching factor is associated with the exposure. The solution is to perform a matched or stratified analysis (see 12dii. Statistical methods – matching cases and controls). In addition, because the matched control group ceases to be representative for the population at large, the exposure distribution among the controls can no longer be used to estimate the population attributable fraction (see 16c. Main results – risk#measures-of-association)5. Also, the effect of the matching factor can no longer be studied, and the search for well-matched controls can be cumbersome – making a design with a non-matched control group preferable because the non-matched controls will be easier to obtain and the control group can be larger. Overmatching is another problem, which may reduce the efficiency of matched case-control studies, and, in some situations, introduce bias. Information is lost and the power of the study is reduced if the matching variable is closely associated with the exposure. Then many individuals in the same matched sets will tend to have identical or similar levels of exposures and therefore not contribute relevant information. Matching will introduce irremediable bias if the matching variable is not a confounder but in the causal pathway between exposure and disease. For example, in vitro fertilization is associated with an increased risk of perinatal death, due to an increase in multiple births and low birth weight infants6. Matching on plurality or birth weight will bias results towards the null, and this cannot be remedied in the analysis.
Matching is intuitively appealing, but the complexities involved have led methodologists to advise against routine matching in case-control studies. They recommend instead a careful and judicious consideration of each potential matching factor, recognizing that it could instead be measured and used as an adjustment variable without matching on it. In response, there has been a reduction in the number of matching factors employed, an increasing use of frequency matching, which avoids some of the problems discussed above, and more case-control studies with no matching at all7. Matching remains most desirable, or even necessary, when the distributions of the confounder (e.g., age) might differ radically between the unmatched comparison groups1,2.
Grouping
There are several reasons why continuous data may be grouped8. When collecting data it may be better to use an ordinal variable than to seek an artificially precise continuous measure for an exposure based on recall over several years. Categories may also be helpful for presentation, for example to present all variables in a similar style, or to show a dose-response relationship.
Grouping may also be done to simplify the analysis, for example to avoid an assumption of linearity. However, grouping loses information and may reduce statistical power9 especially when dichotomization is used10–12. If a continuous confounder is grouped, residual confounding may occur, whereby some of the variable’s confounding effect remains unadjusted for (see 12a. Statistical methods)13,14. Increasing the number of categories can diminish power loss and residual confounding, and is especially appropriate in large studies. Small studies may use few groups because of limited numbers.
Investigators may choose cut-points for groupings based on commonly used values that are relevant for diagnosis or prognosis, for practicality, or on statistical grounds. They may choose equal numbers of individuals in each group using quantiles15. On the other hand, one may gain more insight into the association with the outcome by choosing more extreme outer groups and having the middle group(s) larger than the outer groups16. In case-control studies, deriving a distribution from the control group is preferred since it is intended to reflect the source population. Readers should be informed if cut-points are selected post hoc from several alternatives. In particular, if the cut-points were chosen to minimise a P value the true strength of an association will be exaggerated17.
When analysing grouped variables, it is important to recognise their underlying continuous nature. For instance, a possible trend in risk across ordered groups can be investigated. A common approach is to model the rank of the groups as a continuous variable. Such linearity across group scores will approximate an actual linear relation if groups are equally spaced (e.g., 10 year age groups) but not otherwise. Il’yasova et al18. recommend publication of both the categorical and the continuous estimates of effect, with their standard errors, in order to facilitate meta-analysis, as well as providing intrinsically valuable information on dose-response. One analysis may inform the other and neither is assumption-free. Authors often ignore the ordering and consider the estimates (and P values) separately for each category compared to the reference category. This may be useful for description, but may fail to detect a real trend in risk across groups. If a trend is observed, a confidence interval for a slope might indicate the strength of the observation.
Examples
Cohort study
“For each patient who initially received a statin, we used propensity-based matching to identify one control who did not receive a statin according to the following protocol. First, propensity scores were calculated for each patient in the entire cohort on the basis of an extensive list of factors potentially related to the use of statins or the risk of sepsis. Second, each statin user was matched to a smaller pool of non-statin-users by sex, age (plus or minus 1 year), and index date (plus or minus 3 months). Third, we selected the control with the closest propensity score (within 0.2 SD) to each statin user in a 1:1 fashion and discarded the remaining controls.”19.
Case-control study
“We aimed to select five controls for every case from among individuals in the study population who had no diagnosis of autism or other pervasive developmental disorders (PDD) recorded in their general practice record and who were alive and registered with a participating practice on the date of the PDD diagnosis in the case. Controls were individually matched to cases by year of birth (up to 1 year older or younger), sex, and general practice. For each of 300 cases, five controls could be identified who met all the matching criteria. For the remaining 994, one or more controls was excluded...”20.
Training
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