12b. Statistical methods – subgroups and interactions
What to write
Describe any methods used to examine subgroups and interactions.
Explanation
As discussed in detail under 17. Other analyses, many debate the use and value of analyses restricted to subgroups of the study population1,2. Subgroup analyses are nevertheless often done1. Readers need to know which subgroup analyses were planned in advance, and which arose while analysing the data. Also, it is important to explain what methods were used to examine whether effects or associations differed across groups (see 17. Other analyses).
Interaction relates to the situation when one factor modifies the effect of another (therefore also called ‘effect modification’). The joint action of two factors can be characterized in two ways: on an additive scale, in terms of risk differences; or on a multiplicative scale, in terms of relative risk (see 12b. Statistical methods – subgroups and interactions ). Many authors and readers may have their own preference about the way interactions should be analysed. Still, they may be interested to know to what extent the joint effect of exposures differs from the separate effects. There is consensus that the additive scale, which uses absolute risks, is more appropriate for public health and clinical decision making3. Whatever view is taken, this should be clearly presented to the reader, as is done in the example above4. A lay-out presenting separate effects of both exposures as well as their joint effect, each relative to no exposure, might be most informative. It is presented in the example for interaction under 17. Other analyses, and the calculations on the different scales are explained below.
Interaction (effect modification): the analysis of joint effects
Interaction exists when the association of an exposure with the risk of disease differs in the presence of another exposure. One problem in evaluating and reporting interactions is that the effect of an exposure can be measured in two ways: as a relative risk (or rate ratio) or as a risk difference (or rate difference). The use of the relative risk leads to a multiplicative model, while the use of the risk difference corresponds to an additive model5,6. A distinction is sometimes made between ‘statistical interaction’ which can be a departure from either a multiplicative or additive model, and ‘biologic interaction’ which is measured by departure from an additive model7. However, neither additive nor multiplicative models point to a particular biologic mechanism.
Regardless of the model choice, the main objective is to understand how the joint effect of two exposures differs from their separate effects (in the absence of the other exposure). The Human Genomic Epidemiology Network (HuGENet) proposed a lay-out for transparent presentation of separate and joint effects that permits evaluation of different types of interaction8. Data from the study on oral contraceptives and factor V Leiden mutation9 were used to explain the proposal, and this example is also used in item 17. Oral contraceptives and factor V Leiden mutation each increase the risk of venous thrombosis; their separate and joint effects can be calculated from the 2 by 4 table (see example 1 for 17. Other analyses) where the odds ratio of 1 denotes the baseline of women without Factor V Leiden who do not use oral contraceptives.
A difficulty is that some study designs, such as case-control studies, and several statistical models, such as logistic or Cox regression models, estimate relative risks (or rate ratios) and intrinsically lead to multiplicative modelling. In these instances, relative risks can be translated to an additive scale. In example 1 of 17. Other analyses, the separate odds ratios are 3.7 and 6.9; the joint odds ratio is 34.7. When these data are analysed under a multiplicative model, a joint odds ratio of 25.7 is expected (3.7 × 6.9). The observed joint effect of 34.7 is 1.4 times greater than expected on a multiplicative scale (34.7/25.7). This quantity (1.4) is the odds ratio of the multiplicative interaction. It would be equal to the antilog of the estimated interaction coefficient from a logistic regression model. Under an additive model the joint odds ratio is expected to be 9.6 (3.7 + 6.9 – 1). The observed joint effect departs strongly from additivity: the difference is 25.1 (34.7 – 9.6). When odds ratios are interpreted as relative risks (or rate ratios), the latter quantity (25.1) is the Relative Excess Risk from Interaction (RERI)10. This can be understood more easily when imagining that the reference value (equivalent to OR=1) represents a baseline incidence of venous thrombosis of, say, 1/10 000 women-years, which then increases in the presence of separate and joint exposures.
Examples
“Sex differences in susceptibility to the 3 lifestyle-related risk factors studied were explored by testing for biological interaction according to Rothman: a new composite variable with 4 categories (a − b − , a − b+, a+b − , and a+b+) was redefined for sex and a dichotomous exposure of interest where a− and b− denote absence of exposure. RR was calculated for each category after adjustment for age. An interaction effect is defined as departure from additivity of absolute effects, and excess RR caused by interaction (RERI) was calculated:
where RR(a+b+) denotes RR among those exposed to both factors where RR(a − b −) is used as reference category (RR = 1.0). Ninety-five percent CIs were calculated as proposed by Hosmer and Lemeshow. RERI of 0 means no interaction”4.
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