Page 46 - Clinical Small Animal Internal Medicine

14 Section 1 Evaluation and Management of the Patient

of a population at risk of experiencing the outcome. The and heart disease is greater among smokers than non-
VetBooks.ir population is then followed forward in time, and within smokers. However, no one would seriously entertain
making such a correspondence between the association
a specific time period cumulative incidence is defined as
the proportion of the individuals initially at risk that
and any causal effect. Therefore, statements about “risk”
newly develop the outcome (assuming no individuals of carrying matches with lung cancer and heart disease
have been lost to follow‐up), and can only strictly fall differences and ratios are best reserved for situations
between 0 and 1. If 300 Yorkshire terriers were followed where the justification for alleging a causal relation is
from birth for five years without any dental interven- supported by knowledge other than purely statistical.
tions, and at the end of this time the presence of tooth
resorption was found in 100 dogs, then the five‐year Incidence Rates
cumulative incidence of tooth resorption would be 0.33
(assuming that there were no dogs that spontaneously When patients are not all followed for the same amount
recovered from it). of time, the cumulative incidence should not be utilized
Cumulative incidence alone is not a measure of asso- because the reasons for loss to follow‐up (known as right
ciation. However, comparing two or more cumulative censoring) could be related to the risk of the outcome
incidences under different conditions allows such asso- developing. Instead, another, less intuitive measure of
ciations to be quantified. Suppose that in addition to the incidence that allows for different follow‐up in each indi-
finding in Yorkshire terriers above, the five‐year cumula- vidual is the incidence rate (also sometimes called the
tive incidence of tooth resorption in border collies was hazard rate). In contrast to cumulative incidence, a pro-
also measured as 0.10. Two important statements can portion that has an interpretation always linked to a
now be made about these two figures. First, that over the defined period of time, the incidence rate in a population
five‐year follow‐up period the difference in cumulative is a joint function of the number of new (incident) out-
incidences between Yorkshire terriers and border collies come occurrences divided by the sum of the individual
is 0.20 (0.30 – 0.10). Second, that over the five‐year fol- times at risk of an outcome among the members of the
low‐up period there is a three‐fold increase (0.30/0.10) in population, and is expressed as the number of outcomes
the cumulative incidence in Yorkshire terriers compared per unit of time (for example, days, months, years, etc.).
to border collies. These two measures of association are Incidence rates are analogous to speeds; across popula-
known as the cumulative incidence difference and the tions, they estimate the average number of outcomes
cumulative incidence ratio, respectively. Other terms expected to occur per quantity of time.
that remain in use include risk difference and attributa- Incidence rates have particular utility in studies meas-
ble risk for the former, and risk ratio and relative risk for uring the time from onset of follow‐up to when an event
the latter (these terms should be used with caution, how- occurs. Such events can be recovery, death, remission, or
ever, because risk implies causation, and statistical meas- other outcomes. One of the most common applications
ures are distinct from causal measures without for incidence rates is in survival studies of comparative
corresponding strong causal assumptions that must be treatment efficacy, where particular interest is in the rate
invoked). of death (or, conversely, survival).
Nevertheless, the cumulative incidence ratio is par- Suppose that in Yorkshire terriers the incidence rate of
ticularly well suited to effectively communicating rela- tooth resorption = 0.3 case/dog‐year (or, equivalently, 30
tive impacts of factors on health in clinical practice cases/100 dog‐years). This can be interpreted to mean
because of its intuitive understandability. Statistical nov- that if 100 dogs were each followed for one year, that 30
ices can appreciate, for example, a statement such as: cases would be expected; it can also be interpreted to
“The incidence of parvovirus in unvaccinated puppies mean that if 50 dogs were each followed for two years, 30
under 6 months of age is 10‐fold greater than in vacci- cases would be expected, and so on. The independence
nated puppies.” of the incidence rate from the number of individuals is
Our understanding of how vaccines, the immune sys- perhaps best understood through the analogy of measur-
tem, and viral infections work could also reasonably ing the average speed of automobiles: whether 60 cars
allow us to modify this statement by substituting the each travel one mile in one minute or one car travels 60
word “risk” for “incidence.” Such strong biologic knowl- miles in 60 minutes, under both scenarios the total dis-
edge is not always apparent, however, which should tance traveled is 60 miles, the total amount of time trave-
motivate caution when using words with causal interpre- led is 60 minutes, and the speed is 60 miles per hour.
tations like “risk” or “likelihood.” Physicians would have As with cumulative incidence, it is frequent to see inci-
no hesitancy in making the correspondence between the dence rates compared on a ratio scale to measure relative
association of tobacco smoke with lung cancer and heart associations; these are called incidence rate ratios or haz-
disease with the statement that the risk of lung cancer ard ratios. An incidence rate ratio greater than 1 implies