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Descriptive Epidemiology: Rates, Ratios, etc.   To Epidemiology Theme page

1. Core Knowledge:

Measures of Disease Occurrence or Frequency

These involve rates, ratios or proportions:

RATES.  A rate is a measure of the frequency with which an event occurs in a defined population in a defined time (e.g., number of deaths per hundred thousand Canadians in one year).  It has a time dimension, whereas a PROPORTION (e.g., number of Canadians with cancer divided by the total population) does not. 

RATIOS. The value obtained by dividing one quantity by another: the male to female ratio in your class.  A ratio often compares two rates, for example comparing death rates for women and men at a given age. 

The important difference between a rate and a ratio is that for a rate, the numerator is included in the population defined by the denominator (e.g., number of new cases of a disease divided by the total population). This is not necessarily so for a ratio. In a ratio, the numerator and denominator are usually separate and distinct quantities, neither being included in the other (e.g., number of males in the class compared to the number of females).

INCIDENCE.  Incidence = Number of new cases in a fixed time period / Number of people at risk.  Usually the period of study is chosen to be one year, in which case we speak of the annual incidence.  This gives a proportion, ranging from 0 to 1, that is useful in communicating the idea of risk: what is the probability that my patient will get this disease within the time-frame?  Note that you may also see the term CUMULATIVE INCIDENCE to represent the incidence proportion.

There are a couple of practical difficulties in calculating the incidence proportion that lead to another way to present incidence.  First, everyone being studied has to be followed for the complete year, but unfortunately, some may die from some other cause or be lost to follow-up which makes the resulting calculation uncertain (can you be sure they would not have got the disease if they had lived?)  Second, many diseases can occur more than once and we have to decide how to handle recurrences.  If you include them, the incidence proportion could exceed 1.0, which feels uncomfortable. If you accept only first diagnoses, you may underestimate the true burden of disease. Therefore, an alternative is to express incidence as a rate: number of cases per time of observation, typically the number of cases per person-year of observation.  Incidence rates are equivalent to recording speed in kms per hour and, like speed, the incidence rate gives an instantaneous reading of the frequency with which the disease will occur, or the expected time-delay until the next case. You may also see the term HAZARD RATE.  

SURVIVAL ANALYSIS AND LIFE TABLES. The calculation of an incidence rate assumes that incidence remains constant during the period of study.  But if a long period of study is used, the risk of dying may change over time.  Here, it becomes necessary to calculate incidence rates over shorter periods of time (during which they are relatively constant) and then aggregating them. This is the purpose of survival analysis and the calculations are presented in the form of a life table.  A life table typically shows the probability of dying across different age groups.  From the incidence proportions the table shows the survival probability for each age-group, and in a final column, the cumulative survival probability across age groups; this can be graphed.  Where a study compares survival following an experimental therapy, survival analysis can illustrate the pattern of prognosis over time in the experimental and control groups and statistical methods such as the Cox Proportional Hazards model can be used to calculate the significance of the effect of the intervention (or of any other influence).

 PREVALENCE. "How many people actually have the disease at any point in time?"  Prevalence = Number of people with the disease at a given time / Number of people at risk.  It is thus a proportion, rather than a rate, although you may sometimes see it called a "rate." Prevalence provides a good way to indicate the burden of disease in a population. It is influenced by the incidence and by the duration of the condition: under most circumstances, prevalence = incidence × disease duration.

MORTALITY RATE. The number of deaths per thousand population per year: in effect, the incidence of death in a population. It can refer to all causes of death, or can be a cause-specific mortality rate. In comparing mortality rates in different populations, Standardization is often used to correct for demographic differences between the populations.

CASE FATALITY RATE. The proportion of people with a specified condition who die within a specified time.  The time frame is typically the period during which the patient is sick from the disease.  This works for an infectious disease but can be problematic for a chronic disease like a cancer that may remit for a period and then prove fatal after a recurrence.  In such instances we tend to speak of mortality or survival rates rather than case fatality.

ATTACK RATE The attack rate, or case rate, refers to the cumulative incidence of infection over a period of time. This is typically used during an epidemic.  The time period may not be indicated, but would typically refer to the period of the outbreak: "During the influenza outbreak the attack rate was 12%".

COMPARING RATES.  A common reason for recording these various types of rates is to identify factors that are associated with a disease.  To measure the association between a factor and a disease, it is common to compare rates of the disease among people exposed to the factor and other people not exposed.  This can be done either as a relative statistic (e.g., relative risk), or in an absolute manner (e.g., rate difference)

RELATIVE RISK   The  ratio of the risk of disease (or death) among people who are exposed to the risk factor, to the risk among people who are unexposed.  This is synonymous with risk ratio.  Alternatively, relative risk is defined as the ratio of the cumulative incidence rate among those exposed, to the rate among those not exposed.  To estimate a relative risk, you need a cohort study, from which incidence can be calculated.
An RR of 1.0 means that the two incidence rates are equal so the factor has no effect. An RR of 2 would indicate that the exposed people were twice as likely to get the disease; an RR of 0.5 means they were half as likely, so the factor protected them from the disease.

ODDS RATIO. The term "odds" is defined differently according to the situation under discussion, but it is the ratio of the probability of occurrence of an event to that of non-occurrence.  If 60 smokers develop a cough and 40 do not, the odds of developing the cough are 60:40 (or 1.5).   [Note that the probability of developing a cough is 60/100, or 0.6].

The odds ratio expresses the association between a risk factor and a disease by comparing the likelihood of disease under two circumstances, such as the risk of a cough among smokers compared to non-smokers.  The ratio of the two odds is closely related to the concept of relative risk, but the very useful feature is that the odds ratio can be calculated from a case-control study, and does not require knowing incidence rates. The odds ratio is calculated as:

Not exposed
Got the disease
Did not get the disease
Odds Ratio = ad / bc

RATE DIFFERENCE.  (Incidence rate of disease among those exposed) - (incidence among those not exposed).  This is useful in showing the excess morbidity due to the exposure (the "Attributable risk"), which, in turn, can be used to indicate the health benefit of removing the exposure.


Links to:   Standardization of rates

Updated November 11, 2014