Frequency Measures used in Epidemiology

Alick MwambunguMwambungup@yahoo.com

Session 6

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Introduction to Frequency measures

• In epidemiology, many nominal variables have only two possible categories: alive or dead; case or control; exposed or unexposed etc.

• Such variables are called dichotomous variables.

• The frequency measures used with dichotomous variables are ratios,proportios,and rates.

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Rates, Ratios and Proportions

• Three general classes of mathematical parameters.

• Often used to relate the number of cases of a disease or health outcome to the size of the source population in which they occurred.

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Vocabulary

• Ratio (a/b) the generic term• Proportion (a/a+b ) Numerator is included in the

denominator

Range 0-1.0,Time may be specified ,but is not necessary.

• Rate (∆Y/∆X) – A measure of change in one quantity per unit change in another

• Risk- Probability that an event will occur

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Ratio

• Used to compare two quantities

1:1.1 ratio of female to male births

• Used to show quantity of disease in a population

cases

population

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Ratio

• Obtained by dividing one quantity by another. These quantities may be related or may be totally independent.

• Usually expressed as : X/Y x 10n

• Example: Number of still births per thousand live births

#stillbirths x 1000

#live births

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proportion

• A specific type of ratio in which the numerator is included in the denominator, usually presented as a percentage

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352 males undergoing bypass surgery

539 total patients undergoing bypass surgery

=

Calculation of proportion:

Males undergoing bypass surgery at Hospital A

Total patients undergoing bypass surgery at Hospital A

65.3%

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Rate

• A measure of how quickly something of interest happens.

• It measures the occurrence of an event in a population over time.

• The basic formula for a rate is as follows: Rate= number of cases or events occurring during a given time period x 10ᶰ

population at risk during the same time period

Time ,place and population must be specified for each type of rate.

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• As can be seen from the above discussions ,ratios, proportions and rates are not three distinctly different kinds of frequency measures.

• They are all ratios: proportions are a particular type ratio, and some rates are a particular type of proportion.

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• When we call a measure a ratio, we usually mean a non-proportional ratio

• when a measure is called a proportion, usually it means a proportional ratio that doesn’t measure an event over time

• When the term rate is used it usually means a proportional ratio that does measure an event in a population over time.

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Uses of Ratios, Proportions and Rates

• In public health, ratios and Proportions are used to characterize populations by age,sex,race,exposure and other variables.

• Ratios, proportions and most important rates are used to describe the three aspects of the human condition:

• Morbidity(Disease),mortality(Death) and Natality(Birth)

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Morbidity Frequency measures

• To describe the presence of disease in a population,or the probability(risk) of its occurrence-morbidity frequency measures are used.

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Measures of disease frequency

• Incidence (I): Measures new cases of a disease that develop over a period of time.

• Prevalence (P):Measures existing cases of a disease at a particular point in time or over a period of time.

• Prevalence can be viewed as describing a pool of disease in a population.

• Incidence describes the input flow of new cases into the pool.

• Fatality and recovery reflects the output flow from the pool.

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Prevalence versus Incidence

Prevalence Incidence• Existing cases New cases

• Measures how much Measures changes in

disease is in the pop disease occurrence

• Used for description, Used for investigating

planning health care the causes of disease

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Incidence

• Incidence quantifies the number of new events or cases of disease that develop in a population of individuals at risk during a specified time interval.

• There are two specific types of incidence measures, cumulative incidence and incidence rate or density.

• Cumulative incidence(CI) is the proportion of people who become diseased during a specified period of time and is calculated as:

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CI= number of new cases of a disease during a given period of time total population at risk• Cumulative incidence provides an estimate of the probability ,or risk,

that an individual will develop a disease during a specified period of time.

• For example, in a study of oral contraceptive(OC) and bacteriuria a total of 2390 women aged 16 to 49 years were identified who were free from bacteriuria.Of these ,482 were OC users at the initial survey in 1973.At the second survey in 1976 ,27 of the OC users had developed bacteriuria .

• This results in a cumulative incidence of bacteriuria among OC users of 27 per 482 or 5.6% during this 3 –year period.

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Cumulative incidence

• A cumulative incidence of bacteriuria of 5.6% among OC users would be viewed very differently if it referred to a 6-month period, a 3-yr period or a 10-yr period.

• The cumulative incidence assumes that the entire population at risk at the beginning of the study period has been followed for the specified time interval for the development of the outcome under investigation.

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• Even if all subjects enter the study at the same time, some may become lost during the follow-up ,or the time during which the outcome could be observed ,will not be uniform for all participants.

• To account for these varying time periods of follow-up ,one approach would be to restrict the calculation of the incidence to a period of time during which the entire population provided the information.

• This would, however necessitate disregarding the additional follow-up information available for some of the population.

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Cumulative incidence

• Most common way to estimate risk• Always a proportion• Assumes a fixed cohort• For brief specified periods of time e.g. an

outbreak• Formula does not reflect continually changing

population size for dynamic cohorts- Does not allow subjects to be followed for

different time periods.

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Incidence Rate or Density

• A more precise estimate of the impact of exposure in a population that utilizes all available information is called the incidence rate(IR) or Incidence density.

• This is considered to be a measure of the instantaneous rate of development of disease in a population and is defined as:

ID= number of new cases of a disease during given time period

total person-time of observation

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Incidence Rate or Density

• As with any measure of incidence, the numerator of the incidence density is the number of new cases in the population.

• The denominator, however is now the sum of each individual’s time at risk or the sum of the time that each person remained under observation and free from disease.

• In presenting an incidence rate, it is essential to specify the relevant time units-that is-person-day,person-month,person-year,etc

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Incidence Rate or Density

• Figure 4-1 page 59(Epidemiology in Medicine) illustrates the calculation of person-time units, based on the experience of a hypothetical group of five subjects, two of whom developed the disease of interest during a 5-yr follow-up period.

• The cumulative incidence of disease could thus be calculated as 2 cases per 5 individuals over a 5-year period

• This measure of development of disease would be misleading ,since it does not reflect the fact that only one of the five subjects(Subject C) was infact observed for the entire follow-up period.

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• Subject A was observed for only 2 years before being lost to follow-up., while subjects B,D and E were followed for 3.0,4.0 and 2.5 yrs,respectively.

• The total time at risk for this population of five subjects, could be obtained by adding their individual times-16.5 person-years.

• The incidence density(ID) would be calculated as follows:

• ID=2 cases/16.5 person-years =12.2/100 person-years of observation

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Prevalence

• Measures existing cases of a health condition• Primary feature of a cross-sectional study• Two types of Prevalence: -Point Prevalence -Period Prevalence• Prevalence quantifies the proportion of individuals in a

population who have the disease at a specified instant and provides an estimate of the probability(risk),that an individual will be ill at a point in time.

• The formula for calculating the prevalence(P) is: P= Number of existing cases of a disease

total population

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Prevalence

• For example, in a visual examination survey conducted in Massachusetts among individuals 52 to 85years of age,310 of the 2477 persons examined had cataracts at the time of the survey.

• The prevalence of cataract in that age group was therefore 310 per 2477,or 12.5%.

• Thus prevalence can be thought of as the status of the disease in the population at a point in time and as such is also referred to as point prevalence.

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Point Vs. period prevalence

• The amount of disease present in a population is constantly changing.

• Sometimes, there is need to know how much of a particular disease is present in a population at a single point in time-to get a kind of ‘’stop action’’ or ‘snap shot’ look at the population with regard to that disease.

• Point prevalence is used for that purpose.

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• Point prevalence is not an incident rate, because the numerator includes pre-existing cases.

• It is a proportion because the persons in the numerator are also included in the denominator.

• At other times we want to know how much of a particular disease is present in a population over a longer period.

• Period prevalence is used in this case. The numerator in period prevalence is the number of persons who had a particular disease or attribute at any time during a particular interval.

• The interval can be a week,month,year etc.

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• Example:

• In a survey of patients at an STD clinic,180 of 300 patients interviewed reported use of a condom at least once during the 2 months before the interview.

• The period prevalence of condom use over the last 2 months is:

• 180/300x 100 = 60%

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Comparison of prevalence and incidence

Example:

Two surveys were done in the same community 12 months apart. Of 5,000 people surveyed the first time,25 had antibodies to histoplasmosis.Twelve months later,35 had antibodies,including the original 25.Calculate the prevalence at the second survey and incidence.

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1.Prevalence at the second survey

X=antibody positive=35

Y=population=5,000

x/y x 10ᶰ=35/5000x1000

=7 per 1,000

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• Incidence during the 12-month period:

• X=number of new positives during the 12-month period=35-25=10

• Y=population at risk=5,000-25=4,975

• x/y x10ⁿ=10/4,975 x1,000=2 per 1,000

• High prevalence of a disease within a population may reflect high risk, or it may reflect prolonged survival without cure.

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• Conversely, low prevalence may indicate low incidence, a rapidly fatal process, or rapid recovery.

• Prevalence is often used rather than incidence to measure the occurrence of chronic diseases such as osteoarthritis which have long duration and dates of onset which difficult to pinpoint.

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Interrelationship between incidence and prevalence

• The proportion of the population that has a disease at a point in time (prevalence) and the rate of occurrence of new disease during a period of time(Incidence) are closely related.

• Prevalence depends on both the incidence rate and the duration of the disease from onset to termination.

• If the incidence of a disease is low but those affected have the condition for a long period of time, the prevalence will be high relative to the incidence rate.

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• If the incidence rate is high but the duration is short ,either through prompt recovery or death, the prevalence will be low relative to the incidence.

• This interrelationship between incidence and prevalence can be expressed mathematically by saying that the prevalence(P) is proportional to the product of the Incidence rate(I) and the average duration of the disease(D).

P=I x D When two of the measures are known, the third

can be calculated by substitution.

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• Example: Average annual incidence rate of lung

cancer in Connecticut between 1973 to 1977 was 45.9 per 100,000.and the average annual prevalence was 23.0 per 100,000.Calculate the average duration of lung cancer?

D=P/I =23.0/105 =0.5 year.

45.9/105/year

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House Guest Example

P=IXD

Incidence (I) Prevalence (P)How quickly new Existing count at steady state

Guests arrive Duration(D)-5 days, length of stay

☺☺ ☺☺

☺☺☺☺

☺☺☺☺

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Mortality Frequency Measures

• A mortality rate is a measure of the frequency of occurrence of death in a defined population.

Mortality rate =deaths occurring during a given time period x 10ⁿ # of the population among which deaths occurred

• Crude mortality rate is the mortality rate from all causes of death for a population.

• Cause specific mortality rate is the mortality rate from a specified cause for a population.

• The numerator is the number of deaths attributed to a specific cause.

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Age-specific mortality rate

• This is the mortality rate limited to a particular age group. The numerator is the number of deaths in that age groups; the denominator is the number of persons in that age group in the population.

• Some specific types of age-specific mortality rates are neonatal,postneonatal,and infant mortality rates.

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Mortality Rates• Infant mortality rate: Death under one year of age during a given

time interval divided by number of live births reported during the same time interval.

• These are most commonly used rates for measuring the risk of dying during the first year of life. These rates are some of the most frequently used measures for comparing health services among nations.

• Neonatal mortality rates: Are an index of the risk of dying in the first 28 days of life. The numerator is the number of deaths in one year for children younger than 28 days of age. The denominator is the number of live births in the same year.

• Post neonatal mortality rate: This is an index of the risk of death in infants aged 28 days to 11months during a given time interval divided by live births during the same time interval.

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Death-to-case ratio

• Is the number of deaths attributed to a particular disease during a specified time period divided by the number of new cases of that disease identified during the same time period

• Death-to-case ratio=no.of deaths of particular disease during specified period. No of new cases of the disease identified during same period.

• The figures used for the numerator and denominator must apply to the same population.

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Death-to-case ratio• The death figures in the numerator are not necessarily included in

the denominator, however, some of the deaths may have occurred in persons who developed the disease before the specified period.

• E.g. In 1987,there were 22,157 new cases of tuberculosis reported in the United States. During the same year ,1,755 deaths occurred that were attributed to tuberculosis

• Presumably ,many of the deaths occurred in persons who had initially contracted tuberculosis years earlier. Thus many of the 1,755 deaths in the numerator are not among the 22,517new cases in the denominator.

• Therefore, the death-to-case ratio for 1987 is:• 1,755/22,517 x 10n number of deaths per 100 can be calculated by

multiplying the abs by 100.

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Case-fatality rate

• The Case-Fatality rate is the proportion of persons who die from a particular condition (Cases). The formula is:

Deaths from a specific disease x 10ⁿ Cases of that disease• Unlike the death-to-case ratio, which is simply the ratio of

cause- specific deaths to cases during a specified time, the case-fatality rate is a proportion and requires that the deaths in the numerator be limited to the cases in the denominator.

• Thus, if 11 newborns were to develop listeriosis and two of these newborns died as a result, the case-fatality rate would be

2deaths/11 cases =18.2%AM

Proportional Mortality Rates

• Defined as the number of deaths assigned to a specific cause in a calendar year, divided by the total number of deaths in that year, the quotient multiplied by 100

• Example:Country X - total deaths from all causes in 1970: 1,500,000; deaths from cancer: 675,000Proportional mortality ratio= 675,000/1,500,000 x 100

= 45% of total deaths per year from cancer

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Standardized Mortality Ratios

• One problem that arises in comparing crude rates of disease between populations is that the groups may differ with respect to certain underlying characteristics ,such as age,sex,or race that may affect the overall rate of disease.

• For example, the crude mortality rate from cancer in the US in 1940 was 120 per 100,000,as compared with 183 per 100,000 in 1980.

• These crude rates ,indicating an overall 53-percent increase in cancer mortality during this 40 –year period, have erroneously suggested a trend so alarming as to be considered indicative of an epidemic of cancer

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Standardisation and the SMR• Age and sex specific rates can be compared between times,

places and sub-populations• Age and sex specific rates may be imprecise in small studies• Age and sex specific tables are usually large and difficult to

assimilate• If so, you may calculate the summary, overall (crude) rate• Overall actual rates (crude) rates may mislead• Age and sex structure of the compared population probably

differs• If so, age and sex are confounding variables• Therefore, we need to adjust (or standardise) the rates for

age, sex or both

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Standardized Mortality ratios • The standardized mortality ratio or SMR is the ratio of

observed deaths to expected deaths according to a specific in a population and serves as an indirect means of adjusting a rate.

• The figure for observed deaths is usually obtained for a particular sample of a population.

• The figure for expected deaths reflects the number of deaths for the larger population from which the study sample has been taken.

• e.g. national level of mortality attributed to a particular health outcome.

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Standardized Mortality Ratios

• An SMR is essentially a comparison of the number of the observed deaths in a population with the number of expected deaths if the age-specific death rates were the same as a standard population. It is expressed as a ratio of observed to expected deaths, multiplied by 100.

• SMRs equal to 100 imply that the mortality rate is the same as the standard mortality rate. A number higher than 100 implies an excess mortality rate whereas a number below 100 implies below average mortality.

• An SMR is calculated as the number of deaths observed within an area divided by the expected number of deaths within that area. This ratio is then multiplied by 100.

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• The calculation used to determine the SMR is simply: number of observed deaths/number of expected deaths.

• SMR=Observed deaths) x 10n expected death

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Standardized Mortality Ratio

• To arrive at the expected number of deaths, for each age group, the standard age-specific death rate is multiplied by the local population in that age group.

• The number of expected deaths in each age group are then summed across all ages to arrive at the expected number of deaths for the local population.

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• See attached sheet form calculations.

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