Chance, bias and confounding The observed statistical association between a certain outcome and and the hypothesized exposure could be a matter of chance Or it could be the result of systematic errors in collection of data (sampling, disease and exposure ascertainment) or its interpretation: the role of bias Or it could be due to the effect of additional variables that might be responsible for the observed association: the role of confounding Or it could be a real association

Confounder Is a factor that distorts the true relationship between an exposure and the disease outcome on account of its being associated with both the exposure as well as the disease This distortion (over/underestimation) of the true relation between exposure and disease can occur only if this factor is unequally distributed between the exposed and unexposed groups

Confounding A confounder is a third factor that is associated with the exposure and independently affects the risk of developing the disease It distorts the estimate of true relationship between the exposure and disease: it may result in association being observed when none in fact exists; or no association being observed when a true relationship does exist

Confounder A potential confounder must be predictive of disease independently of its association with the exposure under study This means that there must be an association between the confounder and disease even amongst the group unexposed to the exposure under investigation

Confounder This third factor should not be merely an intermediate step in the cause and effect relationship between the exposure and the disease outcome The association between the confounder and the disease need not be causal. It may a marker for for a risk factor other than the one under investigation in a study.

Confounding Confounding can lead to the observation of apparent differences between the study groups when they do not truly exist, or conversely, the observation of of no difference when they do exist.

An example of confounding A number of observational epidemiological studies have shown an inverse association between the consumption of vegetables rich in β carotene with the risk of cancer It is however possible that this association is confounded by other differences between the consumers and non-consumers of vegetables such as fiber, which is known to reduce the risk of cancer

Confounding: another example An observed association between the consumption of coffee and the risk of MI could be due, at least in part, to the effect of cigarette smoking, since coffee drinking is associated with smoking , and independent of coffee drinking, smoking is a risk factor for MI The potential or true confounders are not always as obvious as they are in the examples cited above

How to avoid confounding? If a confounding factor does not vary between the exposed and non-exposed, or those diseases and non-diseased, then by definition, there can be no confounding by that variable Thus if by design or analysis, the association between disease and exposure is evaluated only amongst those who are similar with respect to the confounding factor, there can be no confounding

Controlling confounders Restriction of the study population Matching Randomization of exposure Stratification Multivariable analysis

Common confounders Age and sex are almost universal confounders for all exposure – disease associations This is because they are markers for a whole lot of cumulative exposures. They may not be causally related to disease, but are markers for many other exposures which might be truly related to disease.

Confounding: the intermediate link Moderate consumption of alcohol is associated with reduced risk of CAD HDL cholesterol also is protective for CAD Moderate alcohol consumption increases HDL If one controls for HDL, the association between alcohol intake and the risk of CAD becomes weak or statistically insignificant. Being an intermediate link between alcohol and the risk of CAD, should HDL be considered a confounder at all? Should it be controlled?

Positive and negative confounding Tobacco smoking would be a positive confounder in association between coffee drinking and CAD The association between physical activity and CAD would be negatively confounded by gender, since women have lower risk of CAD and they also exercise less than men.

Randomization Applicable only to interventional studies Most powerful method to control for known, potential or unknown confounders if the sample size is sufficiently large

Restriction Reduces the number of eligible subjects for enrollment It limits generalizability of observations to only the restricted population use for drawing the random sample

Matching It includes elements of both design and analysis Mostly applicable to case-control study design It is expensive, difficult and time consuming By design, the effect of risk factor which has been matched can not be studied Confounding is avoided not just by matching but by special method of matched table analysis

Analysis Stratified analyses: Stratum specific estimates of association are calculated, and the differences amongst the strata are assessed by eyeballing, or performing appropriate tests of statistical significance Summary statistic for the pooled data is calculated as per the method of Mantel and Haenszel The magnitude of confounding is assessed by looking at the discrepancy between the crude and adjusted estimates (without applying any tests of statistical significance)

Confounding and effect modification Confounding distorts the true relationship between the exposure and disease and should be controlled Effect modification tells us that the association between exposure and disease is modified by a third factor. It should not be controlled for, the magnitude of effect modification should be reported and biological explanation for its presence sought.

Bias The study must be designed and conducted in such a manner that that every possibility of introducing a bias is anticipated and steps are taken to minimize its occurrence In spite of these precautions, the observed association should be carefully examined to see if it could be explained by bias. If indeed the study has elements of bias, it can not be rectified at the stage of analysis (unlike confounding)

Types of bias Selection bias: A particular problem in case control and retrospective cohort studies where both exposure and disease have occurred at the time of selection of individuals for the study Information bias

Selection bias Differential surveillance, diagnosis or referral of individuals in the study: e.g., women using estrogen have uterine bleeding more often, and seek medical attention for this symptom. Hence they are more likely to seek diagnostic evaluation than those who are not on estrogens resulting in more frequent diagnosis of uterine cancer in women on estrogens

Multivariate regression analysis Several potential confounders can be controlled; this is not easy in stratified analysis It is an efficient method of data analysis Several models for regression exist. Choice depends on the type of data to be analysed.