You can examine the risk of an outcome, such as disease, given the incidence of the outcome in relation to an exposure, such as a suspected risk or protection factor for a disease.

The type of data used by this function is counts or frequencies (number of individuals with a study characteristic). If you want to analyze person-time data (e.g. months of follow up) instead of counts you can see incidence rates.

In studies of the incidence of a particular outcome in two groups of individuals, defined by the presence or absence of    a particular characteristic, the odds ratio for the resultant fourfold table becomes the relative risk. Relative risk is used for prospective studies where you follow groups with different characteristics to observe whether or not                    a particular outcome occurs:


Outcome rate exposed (Pe) = a/(a+c)

Outcome rate not exposed (Pu) = b/(b+d)

Relative risk (RR) = Pe/Pu

Risk difference (RD) = Pe-Pu

Estimate of population exposure (Px) = (a+c)/(a+b+c+d)

Population attributable risk % = 100*(Px*(RR-1))/(1+(Px*(RR-1)

In retrospective studies where you select subjects by outcome not by group characteristic then you would use the odds ratio ((a/c)/(b/d)) and not the relative risk.

In addition to the relative measure of effect (relative risk) you may wish to express the absolute effect size in your study as the risk difference. Risk difference is sometimes referred to as attributable risk and when expressed in percent terms it is also referred to as attributable proportion, attributable rate percent and preventive fraction. Attributable risk or risk difference is used to quantify risk in the exposed group that is attributable to the exposure.

Population attributable risk estimates the proportion of disease in the study population that is attributable to the exposure. In order to calculate population attributable risk, the incidence of exposure in the study population must be known or estimated

Population  attributable risk and population attributable risk factor are also measures of effect but more specifically are measures of population impact.

Risks (defined as the probability of a new occurrence disease among individuals in an initially disease free population, over a defined period of time) can be compared by two ways, either ratios (relative comparison) or difference (absolute comparison).

Relative Risk (RR)

For a given disease, we can know the risk among exposed (r1), and the risk among unexposed (r0). Hence we can calculate the risk ratio as follows:

RR = r1 / r0

Similarly we can also calculate rate ratios if we know the rate of disease (rate of occurrence of new disease) in an exposed group (r1), and the rate of disease in an unexposed group (r0).

RR = r1 / r0

We can then also stratify the extent of exposure, and calculate rate ratio for each strata. This allows us to compare measure of disease frequency in each level against the baseline frequency (unexposed) level. See the example below:

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