Observational study and sampling balancing
In observational studies, however, it is not possible for individuals to be randomly assigned to an exposure. Often, individuals who share a particular risk factor have other characteristics in common that influence their risk of disease. Thus, because we cannot be sure that individuals with different exposure status are similar with respect to all other relevant factors, it is more difficult to determine if the association we observe between disease and our risk factor of interest is ‘real’, or whether it is influenced by other factors.
Confounding
Confounding occurs when an apparent association between an exposure and the disease is distorted by the presence of a third factor, which is associated with both the exposure and disease.
A potential confounder is any factor which is believed to have a real effect on the risk of the disease under investigation. This includes both factors that have a direct causal link with the disease (e.g. smoking and lung cancer), and factors that are good proxy measures of more direct unknown causes (e.g. age and social class).
Confounder / Mediator
For a variable to be a confounder, it must be associated with the exposure under study and it must also be independently associated with disease risk in its own right (i.e. in the absence of the exposure of interest). But it should not be on the causal pathway to the disease, which would mean it is a mediator rather than a confounder (discussed in section 1.4).
Confounder is independently associate with the effect (that is the exposure) and the outcome.
How to deal with confounding
Randomisation
Restriction
Matching
Randomisation
Randomisation – this is a procedure whereby study participants are randomly allocated to the exposure or control groups. This is the ideal method of controlling for confounders because it ensures that the distribution of known and, of unknown confounding variables will be similar in the groups to be compared, provided that the sample size is relatively large. But randomization can only be used in experimental studies and is not appropriate for all exposures of interest.
Restriction
Restriction - a procedure that limits participation in the study to people who are similar in relation to the confounder. For instance, if participation in a study is restricted to nonsmokers, any potential confounding effect of smoking will be removed.
Matching
Matching – this is a procedure whereby controls are selected in such a way that the distribution of potential confounders (e.g. age, sex or smoking habits) among the controls will be identical to those of the cases. This can be accomplished by selecting one or more controls for each case with similar characteristics (e.g. of the same age, sex or smoking habits) (pair matching) or by ensuring that as a group the controls will have similar characteristics as the cases (frequency matching). In practice, matching is used only in case-control studies (Lecture on Case-Control Studies) because it is too costly to match subjects in cohort studies.
How can confounding be accounted for in the analysis?
Stratification
Statistical modelling
It is only possible to control for confounders in the analysis if data on confounders were collected. The extent to which confounding can be controlled for will depend on the accuracy with which the confounding variables are measured. For instance, non-differential (random) misclassification a confounder will underestimate the effect of the confounder and consequently, will attenuate (reduce) the degree to which confounding can be controlled. The association between the exposure and disease will persist even after the adjustment because of residual confounding. But in contrast, to random misclassification of exposure or disease which reduces the effect size, random misclassification of a confounder can cause a bias in either direction, and will be in the same direction as the confounding.
Stratification
Stratification - a technique in which the strength of the association is measured separately within each well-defined and homogeneous category (stratum) of the confounding variable. For instance, if age is a confounder, the association will be measured separately in each age-group; the results can then be pooled together to obtain an overall summary measure of the association adjusted or controlled for the effects of the confounder, i.e., that takes into account differences between the groups in the distribution of confounders. It should be noted that standardisation is an example of stratification
Statistical Modelling
Statistical Modelling - more sophisticated statistical methods such as multivariable analysis, are available to control for confounding. They are particularly useful when it is necessary to adjust simultaneously for several confounders.
Analysis
Thus, to summarise, suppose we are interested in examining the relationship between an exposure A and a certain outcome B. We start by calculating the crude exposure effect estimate (e.g. rate ratio, risk ratio or odds ratio depending on the study design). This yields a value of 2.0. We then decide to examine the relationship between A and B separately for those exposed to a third variable C (stratum 1) and those who were not exposed (stratum 2).
(This would indicate the presence of an interaction between the occupational exposure and smoking. This is also called effect modification because the effect of the occupational exposure is modified by the presence of smoking. )
In situation I, there is no confounding, because the crude and the adjusted effect estimates are similar, and no effect modification, because the estimates are similar for both strata. In situation II, there is confounding, because the crude and the adjusted estimates differ, but no interaction, because the effect estimates are similar in the two strata. In situation III, there is strong effect modification between A and C because the stratum-specific estimates are markedly different for those exposed and those not exposed to C. In situation III, as the stratum-specific estimates differ (in fact, they are in opposite directions), both should be reported as it is not appropriate to calculate an overall adjusted estimate in such circumstances.
Statistical test for confounding
Finally, note that there is no formal statistical test for confounding (as there is for effect modification
Could the observed effect be causal?
If bias, confounding and chance do not seem to explain the observed association; can one conclude that the association is likely to be causal? In a paper published in 1965, Bradford Hill gave a list of aspects that need to be considered when assessing whether an association is likely to be causal. His guidelines will be briefly discussed here:
- Temporal relationship This is the only essential criterion. For a putative risk factor to be the cause of a disease it has to precede the disease. This is generally easier to establish from cohort studies but rather difficult to establish from cross-sectional or case-control studies when measurements of the possible cause and the effect are made at the same time. Under this heading it is useful to mention the term “reverse causality”. Some outcomes may result in changes in exposure (rather than the other way around) and this needs to be kept in mind when interpreting associations. For example, people with colon cancer are likely to change their diet, so any association between current diet and cancer risk may be explained by reserve causality (or reverse association).
- Plausibility The association is more likely to be causal if it is consistent with other knowledge (e.g. animal experiments, biological mechanisms, etc). However, lack of plausibility may simply reflect lack of scientific knowledge.
- Consistency If similar results have been found in different populations using different study designs then the association is more likely to be causal since it is unlikely that all studies were subject to the same type of errors. However, a lack of consistency does not exclude a causal association since different exposure levels and other conditions may reduce the impact of the causal factor in certain studies.
- Strength The strength of an association is measured by the magnitude of the relative risk. A strong association (big effect size) is more likely to be causal than is a weak association, which could more easily be the result of confounding or bias.
- Dose-response relationship Further evidence of a causal relationship is provided if increasing levels of exposure lead to increasing risks of disease.
- Specificity If a particular exposure increases the risk of a certain disease but not the risk of other diseases then this is strong evidence in favour of a cause-effect relationship. However, one-to-one relationships between exposure and disease are rare and lack of specificity should not be used to refute a causal relationship. 2.7. Reversibility When the removal of a possible cause results in a reduced disease risk, the likelihood of the association being causal is strengthened. Ideally, this should be assessed by conducting a randomised intervention trial. However, for many exposures/diseases such randomised trials are unethical, unacceptable, or impractical. 2.8. Coherence The putative cause-effect relationship should not seriously conflict with our knowledge of the natural history and biology of the disease. 2.9. Analogy The putative causal relationship will be further supported if there are analogies with other (well-established) cause-effect relationships.
Note
Good table on lecture notes
Randomisation
This usually involves comparing representative groups from two populations that are as similar as possible in all respects except the factor(s) that we are interested in studying. In experimental studies, the process of randomising individuals (or groups) to different exposures generally ensures that the different groups are equally balanced with respect to all relevant factors that might influence the risk of the outcome. Provided the study is conducted rigorously and is sufficiently large, if we see a difference in the incidence of the outcome between treatment groups at the end of the study, then we can conclude that this difference is caused by the treatment. For this reason, experimental studies provide the strongest evidence of a causal association between an exposure and disease.
Effect modification
Affects the effect (that is the exposure) and not the outcome. So it can only affect the outcome indirectly. If you tested for the association between the effect modifier and the outcome you wouldn’t find something.
