DI thus has no relation to individuals as such, and does not measure the frequency of diseased individuals. The interest rate is a case in point here; the interest rate represents the force with which a given capital grows in the course of a time period. The interest rate does not specify the amount of money earned, only the force that operates on the capital. The interest rate also shows that the fundamental dimension of the rate is the time without which the rate is meaningless.
In the context of enzymatic transformations, DI is also viewed as the speed of transformation of a substrate into a given metabolite under enzyme activity during a given time period. To sum up, DI is a measure of speed, force, density, intensity, and is a property of the inducing factor of the observed event. DI is therefore a rate that cannot be confounded with a proportion or probability.
As a force, DI is related to causal research. In Newtonian physics a force induces a movement; analogically DI engenders diseased individuals the frequency of which is measured by CI. CI is simply defined as the ratio of incident cases to the at-risk population at the beginning of the observation period when losses to follow-up are non existent.
The denominator of CI is not time anymore nor any sum of contributed time periods; it is rather the number of individuals at risk. CI thus determines a frequency that measures the proportion of individuals getting diseased, or the proportion of smokers in a party if one is willing to take up the model suggested at the outset of this paper. One will note the fundamental difference between DI and CI; DI measures the intensity of cigarette smoking in the disco while CI measures the frequency of smokers in a party.
Even though the DI of non-recurring events may also be a measure of the frequency of individuals, it remains that DI is fundamentally the force of a phenomenon that takes its meaning from the general case of recurring events. DI is therefore a property of the risk factors or the force that acts upon individuals at risk while CI concerns the individuals themselves. Similarly, the speed of a car is a property of its engine, while the frequency of road accidents may be viewed as a consequence of the speed of the car.
In epidemiologic terms, one would say that the force of risk factor elicit diseased individuals as cigarette smoking determines smokers. Things go as though both concepts would measure different dimensions of the same reality. Thus, a force of. Thus, things go as though the two measures belonged to different compartments as in the accompanying Image.
Figure 1. DI and CI are two irreducible concepts that find applications in specific cohort designs although both measures can be computed in a given design. The consequence is that a rate and a probability are not interchangeable.
As a measure of the force of the inducing risk factor, DI has no individual meaning. Link to a text description of the results. The "X"s indicate when subjects reported pain relief. The "O"s at the end indicate subjects who did not report relief of pain. Whenever cumulative incidence is determined, one determines the proportion of subjects who experienced the outcome of interest during a block of time, without taking into account when subjects developed the outcome. Visually, however, it is clear that if we consider when subjects experienced relief, the rate was greater in the subjects receiving the new drug.
In this hypothetical study all subjects were observed for a maximum of 10 hours, and some did not achieve pain relief, while others got relief after varying periods of time. We can calculate the average rate of pain relief in each group by adding up the duration of pain for subjects in each group and dividing by the number of subjects in each group.
Note that once a subject experiences the outcome of pain relief, they are no longer considered to be under observation. So, the rate of pain relief was greater in the group receiving the new drug. What we have calculated is the incidence rate. This is a true rate, because time is an integral part of the calculation, analogous to miles per hour a rate of speed or gallons per minute a rate of flow. Question: A participant in a prospective cohort study or a randomized clinical trial stops contributing additional "disease-free observation time" when they develop the outcome of interest or become lost to follow-up for any reason death, failure to respond to phone calls, letters and emails, etc.
Does this mean that they are no longer in the study? The study was conducted in a group of female prostitutes. The the remaining ten women were followed for six years beginning in January Each woman was contacted and retested at the beginning of January each year.
The table below summarizes the findings these ten subjects. The dashed lines indicate continued follow-up. The incidence rate , however, can take these problems into account, because the denominator is the total "at risk" observation time contributed by all ten subjects.
The column at the far right indicates each subject's "at risk" observation time, and the sum for the ten subjects was 26 years.
Note that person-time stopped being counted as soon as the subject was found to be HIV positive, because the subject was no longer "at risk" of developing the outcome—they already had experienced it. For example, Subject 1 contributed one person-year even though she was followed for all six years. Incidence rates are often computed in prospective cohort studies e. It is more accurate than cumulative incidence, but it requires repeated follow-up observations on each subject, and studies like this can be very expensive and time consuming.
Also consider that subjects are sometimes recruited into studies at different times. Each subject's disease-free observation time or "at risk" time can be calculated as the time from their entry into the study until a they get the disease, b they become lost to follow-up, or c the study ends. For example, consider a hypothetical clinical trial that was conducted to determine whether taking low-dose aspirin reduced the frequency of heart attacks in middle-aged and elderly men.
The time line below summarizes events 12 subjects labeled , all of whom were allocated to the placebo-treated group. The first 5 subjects were enrolled in , and the next 7 subjects were enrolled one year later. All subjects began taking aspirin upon enrollment. Therefore their "exposure" to aspirin began upon enrollment as indicated by the solid black dots. The red "X"s indicate when subjects had a heart attack; their exposure time at risk ends there, since having a first heart attack means that they were no longer at risk of having a first heart attack; they had the outcome of interest at that point.
Subject 2 had a heart attack in ; subject 5 had one in ; subject 11 had one in The open circles indicated six subjects who were lost to follow-up. They stopped responding to all requests for follow up after that point.
We know that they had not had a heart attack up to that point, but we don't know what happened to them after that, so they stop contributed observed exposure time at risk. Subject 1 was lost to follow up in ; 6 was lost in ; 7 was lost in ; 8 was lost in ; 9 was lost in ;.
All of this information can be taken into account in order to compute the average rate at which heart attacks occur in this group of 12 men being treated with low-dose aspirin.
We can do this in a way that is analogous to example 2 above. Sign In. Advanced Search. Search Menu. Article Navigation. Close mobile search navigation Article Navigation. Volume Oxford Academic. Google Scholar. Select Format Select format. Permissions Icon Permissions. Section Navigation. Facebook Twitter LinkedIn Syndicate. Lesson 3: Measures of Risk. Minus Related Pages. Incidence proportion or attack rate or risk. Number of new cases of disease during specified time interval.
Summed person-years of observation or average population during time interval. Number of current cases new and preexisting at a specified point in time. Number of current cases new and preexisting over a specified period of time. Synonyms for incidence proportion Attack rate Risk Probability of developing disease Cumulative incidence. Number of new cases of disease or injury during specified period Size of population at start of period.
More About Denominators The denominator of an incidence proportion is the number of persons at the start of the observation period. Overall attack rate is the total number of new cases divided by the total population. A food-specific attack rate is the number of persons who ate a specified food and became ill divided by the total number of persons who ate that food, as illustrated in the previous potato salad example.
A secondary attack rate is sometimes calculated to document the difference between community transmission of illness versus transmission of illness in a household, barracks, or other closed population. It is calculated as:. Number of cases among contacts of primary cases Total number of contacts. Number of new cases of disease or injury during specified period Time each person was observed, totaled for all persons.
All new and pre-existing cases during a given time period Population during the same time period. Persons having a particular attribute during a given time period Population during the same time period.
EXAMPLE: Calculating Prevalence In a survey of 1, women who gave birth in Maine in , a total of reported taking a multivitamin at least 4 times a week during the month before becoming pregnant. Exercise 3. Incidence proportion Incidence rate Prevalence None of the above. Next Page: Mortality Frequency Measures.
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