The Little Things
“The little things are infinitely the most important.” – Sherlock Holmes.
Clinical, epidemiological and genetic studies often seek to understand the “risk factors” for diseases. In this pursuit, we often encounter terms which have important distinctions, but are sometimes used interchangeably by scientists and clinicians, for example, risks, rates and odds. It is important to understand these distinctions and use the terms in their distinctive context. Here, I seek to define some of these terms.
Risk
Risk is defined as the number of new cases that occur during a specified time period in a population. It involves only new cases, and individuals must be free from the condition at the start of the time period. It is either expressed as a proportion (divided by the total population) ranging from 0 to 1, or as a percent ranging from 0 to 100. This is also referred to as absolute risk or incidence.
Prevalence
Prevalence is defined as the number of cases existing in a population. A prevalence rate is the total number of cases of a disease existing in a population divided by the total population.
Exposure (or risk factor)
An exposure is an event (treatment, presence or absence of some factors, environmental or genetic makeup, etc), also called a risk factor, that changes the risk of disease.
Risk ratio (or relative risk)
Risk ratio, also called relative risk, often abbreviated as RR, is defined as the ratio of the disease risk \(r_e\) among individuals exposed to a certain exposure (or risk factor) to the disease risk \(r_0\) among nonexposed individuals.
\[ \textrm{RR} = \frac{r_e}{r_0} \]
Susceptibility
Susceptibility (\(s\)) is coupled with exposure. In the general context, exposures that lead to excess disease risk are considered to increase disease susceptibility. Susceptibility depends on the underlying model of disease causation and has been defined (or measured) in many different ways depending on the context. Due to lack of an exact definition, I will follow Khoury et. al. (Khoury et al. 1989), who used the simple sufficient cause model to derive the general relation of \(s\) to risk. Under this model, we assume some exposure E is part of a sufficient cause for the disease and we denote by \(s\) the proportion of individuals who have all other components except E. Thus, \(s\) is the proportion of “susceptible” persons who, if exposed, would contract the disease.
To derive the general relation of \(s\) to risk, we consider two events: 1) the event A that the individual is susceptible (via exposure to E), and 2) the event B that a person has a sufficient cause that does not involve exposure E. The probability of events A and B are related as follows:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
We note that, by definition \(s = P(A)\), the risk of exposed is \(r_e = P(A \cup B)\), and the risk of unexposed is \(r_0 = P(A \cap B)\). Combining these, we have,
\[ s = r_e - r_0 + P(A \cap B) \]
Since \(P(A \cap B) \ge 0\) and \(P(A \cap B) \le r_0\), we have
\[ r_e - r_0 \le s \le r_e \]
If A and B were independent, then \(P(A \cap B) = P(A)P(B)\) and we would have, \[ s_{\textrm{ind}} = \frac{r_e - r_0}{1 - r_0} \]
It is important to note that the definition (and measure) of susceptibility will change under other disease causation models. The concept of susceptibility helps communicate the risk of developing a disease but does not provide a rigorous definition.