Measures of Disease Occurrence Dr. Kamran Yazdani, MD MPH Department of Epidemiology & Biostatistics School of public health Tehran University of Medical Sciences

Learning Objectives: 1.Understand ratios, proportions, and rates. 2.Define, calculate, and interpret incidence. 3.Understand the use of person-time denominators. 4.Distinguish between cumulative incidence and incidence rate. 5.Define, calculate, and interpret prevalence. 6.Distinguish between point and period prevalence.

Learning Objectives (cont.): 7.Understand special types of incidence and prevalence measures. 8.Understand the interrelationship between incidence, prevalence, and duration of disease. 9.Differentiate the use of incidence and prevalence measures.

l The study of the distribution and determinants of health-related states and events in specified populations and l The application of this study to control of health problems Definition of Epidemiology

l Disease distribution Descriptive Studies l Disease determinants Analytic Studies Two essential components

These main tools in epidemiology are: Measuring Tools for Describing Categorical Outcomes Ratio Proportion Rate

= 5 / 2 = 2.5 / 1 The quotient of 2 numbers Numerator NOT necessarily INCLUDED in the denominator Allows to compare quantities of different nature Ratio

Ratio, Examples l# beds per doctor –850 beds/10 doctors –R = 85 beds for 1 doctor l# participants per facilitator l# inhabitants per latrine lSex ratio:Male / Female Female / Male lOdds ratio lRate ratio lPrevalence ratio

2 --- = 0.5 = 50% 4 Proportion The ratio of 2 numbers Numerator NECESSARELY INCLUDED in the denominator Quantities have to be of same nature Proportion always ranges between 0 and 1 Percentage = proportion x 100

Proportion, Examples lProportion of Myopia in a survey sample: –5600 samples, 168 myopic patients –Proportion of myopics = 168/5600 = 0.03 –Percentage of myopics = 3%

l Indicates the magnitude of a part, related to the total. l In epidemiology, tells us the fraction of the population that is affected. l Numerical value of a proportion:0 to 1.0 l Linked to probability theory (i.e. risk of developing disease) l For ease of usage, can multiply a proportion by 100 to get a percentage Example:p = 0.03 = 3% Proportions

l A proportion in which TIME forms part of the denominator l Speed of occurrence of an event over time Numerator - number EVENTS observed for a given time Denominator - population in which the events occur includes time Rates

l Epidemiologic rates contain the following elements: disease frequency (in the numerator) unit size of population time period during which an event occurs Rates

Calculate crude annual death rate in the US: Crude death rate = ( Annual death count / Reference population (during midpoint of year) ) x 1,000 Death count in U.S. during 1990:2,148,463 U.S. population on June 30, 1990:248,709,873 2,148,463 Crude death rate = x 1,000 = 8.64 / 1,000 / year 248,709,873 Rates – Example

Discussion Question What does a crude annual death rate of 8.64 per 1,000 per year mean?

Measures of Disease Ocurrence (frequency) Incidence How fast are new cases occurring? Prevalence How much disease is present now?

Incidence The development of new cases of a disease that occur during a specified period of time in previously disease-free or condition-free (“at risk”) individuals.

Incidence Incidence quantifies the “development” of disease --- Most fundamental measure of disease frequency and leads to the development of the concept of risk (i.e transition from non-diseased to diseased state) - Cumulative incidence (CI) (“Incidence proportion”) - Incidence rate (IR) (“Incidence density”)

Cumulative Incidence (CI) PROPORTION of individuals who become diseased during a specified period of time (e.g. all new cases during 1998) Range:0 to 1.0 Also referred to as “incidence proportion.”

Cumulative Incidence (CI) No. of new cases of disease during a given period CI = Total population at risk during the given period Example: During a 1-year period, 10 out of 100 “at risk” persons develop the disease of interest. 10 CI = -----=0.10 or10.0% 100

Cumulative Incidence (CI) l To accurately calculate cumulative incidence, we need to follow the entire population for the specified time interval. Often times, this does not fully occur. l Cumulative incidence provides an estimate of the probability (risk) that an individual will develop a disease during a specified period of time.

Cumulative Incidence (CI) l Keep in mind that over any appreciable period of time, it is usually technically impossible to measure risk. l This is because if a population is followed over a period of time, some people in the population will die from causes other than the outcome under study l The phenomenon of being removed from a study through death from other causes is referred to as ”competing risks”.

Cumulative Incidence (CI) l When the follow-up of patients is incomplete, we have to use the survival analysis methods: –Life Table –Kaplan-Meier

Cumulative Incidence Incidence proportion Risk CI assumes that entire population at risk followed up for specified time period x x x x x x x x disease onset Month 1 Month12 CI = 7/12 per year = 0.58 per year

Incidence Rate (IR) No. new cases of disease during a given period IR = Total “person-time” of observation Range = 0 to Infinity Since the number of cases is divided by a measure of time of observation, rather than people, this helps address the problem of competing risks.

Incidence Rate (IR) When we observe a group of individuals for a period of time in order to ascertain the DEVELOPMENT of an event…. - The actual time each individual is observed will most likely vary. What is person time?

Discussion Question In a 2-year study of the development of disease X, why might the actual time each individual is observed vary?

Discussion Question Because: Subjects may be recruited at different times Subjects may emigrate Subjects may choose to leave study Subjects may die Subjects may get the disease we are studying

Person-Time PersonFollow-up Time on Study Person Yrs < D 2 3< WD Jan. Jan. Jan. Jan. Study Period:3 Years Study Participants:5 Person Years of Observation:10 Average Duration of Follow-Up:2.0 Years

No. new cases of disease during a given period IR = Total “person-time” of observation So, 1 case IR = = 1 case per 10 P-Y follow-up 10 P-Y Whereas, 1 case CI = =0.20=20.0% 5 persons Incidence Rate (IR)

When we use individual data (cohort study): We use person-time as the denominator Incidence Density When we use aggregate data: We use the average population as the denominator Incidence Rate Assumptio: homogenous distribution of events and losses (or additions) e.g. Crude Death Rate Incidence Rate (IR)

The IR of 1 case per 10 P-Y is equivalent to 0.2 cases per 2 years: which suggests a 20% risk of disease development within 2 years of follow-up. Whereas, the CI risk estimate of 20% (1 case per 5 persons) was based on a period of 3 years of follow- up. Comparison of IR and CI

Risk and rate are often used interchangeably by epidemiologists but there are differences Comparison of IR and CI

Risk is a probability statement assuming an individual is not removed for any other reason during a given period of time As such, risk ranges from 0 to 1 (no chance to 100% probability of occurrence) Risk requires a reference period and reflects the cumulative incidence of a disease over that period Example: 1 in a million chance of developing cancer in a 70 year lifetime Comparison of IR and CI

Rates can be used to estimate risk if the time period is short (annual) and the incidence of disease over the interval is relatively constant If however, individuals are in a population for different periods of time for any reason, then you should estimate risk by incidence density Comparison of IR and CI

Discussion Question Previously, we said that the incidence rate can range from 0 to infinity! How can this be?

Discussion Question Example 100 subjects have been followed up for 2 month. 20 events have occurred during this time. What is the IR in P-Y?

Discussion Question Example 100 subjects have been followed up for 2 month. 20 events have occurred during this time. What is the IR in P-Y? IR = (20/100) / 2 = 1 per 10 person-month = 12 per 10 P-Y = 120%/year Therefore, as time increases, IR approaches infinity.

Incidence Rate (IR) NOTE:The selection of the time unit for the denominator is arbitrary, and is not directly interpretable: Example:100 cases / person year can also be expressed as: 10,000 cases / person century 8.33 cases / person month 1.92 cases / person week 0.27 cases / person day

In general: Risk estimates derived from IR and CI calculations will be similar when: Follow-up loss is minimal The disease of interest occurs infrequently. CI is most useful if interest centers on the probability than an individual will become ill over a specified period of time. IR is preferred if interest centers on how fast the new cases are occurring in the population. Comparison of IR and CI

Measures of Prevalence lPrevalence –Point prevalence lDo you have health condition now? –Period prevalence lHave you had health condition during past six months? –Lifetime prevalence lHave you ever had health condition?

Importance of Prevalence Data lBurden of illness in population –Treatment needs –Burden on social services –Burden on individual well-being

“Point” Prevalence The usual prevalence Number of existing cases P = Total population At a set point in time (i.e. September 30, 1999)

“Point” Prevalence Example: On June 30, 1999, neighborhood A has: population of 1, current cases of hepatitis B So,P = 29 / 1600 = or 1.8%

“Period” Prevalence Number of existing cases Pp = Total population During a time period (i.e. May 1 - July 31, 1999) Includes existing cases on May 1, and those newly diagnosed until July 31.

“Period” Prevalence Example: Between June 30 and August 30, 1999, neighborhood A has: average population of 1, existing cases of hepatitis B on June 30 6 incident (new) cases of hepatitis B between July 1 and August 30 So,Pp = (29 + 6) / 1600 = or 2.2%

“lifetime” Prevalence Number of existing cases LP = Total population During any time in the past

Prevalence In general, a person’s probability of being captured as a prevalent case is proportional to the duration of his or her disease. Thus, a set of prevalent cases tends to be skewed toward cases with more chronic forms of the disease.

Discussion Question How are incidence and prevalence of disease related?

Discussion Question Prevalence depends on: - Incidence rate - Disease duration House Guests Example

Relationship between prevalence and incidence WHEN (the steady state is in effect): a) Incidence rate (I) has been constant over time b) The duration of disease (D) has been constant over time: ID = P / (1 – P) P = ID / (1 + ID) c) If the prevalence of disease is low (i.e. < 0.10 or 0.05): P = ID

Relationship between prevalence and incidence

High prevalence may reflect: High risk Prolonged survival without cure Low prevalence may reflect: Low risk Rapid fatal disease progression Rapid cure Examples: Ebola, Common cold

Relationship between prevalence and incidence l Cancer of the pancreas –Incidence low –Duration short –Prevalence low l Adult onset diabetes –Incidence low –Duration long –Prevalence high l Roseola infantum –Incidence high –Duration short –Prevalence low l Essential hypertension –Incidence high –Duration long –Prevalence high

Study design for Incidence & Prevalence Incidence (follow-up studies): - Cohort study - Clinical trial Prevalence: - Cross-sectional - Case-Control (prevalent cases)

Uses of Incidence & Prevalence Measures Prevalence: Snap shot of disease or health event l Help health care providers plan to deliver services l Indicate groups of people who should be targeted for control measures l May signal etiologic relationships, but also reflects determinants of survival

Uses of Incidence & Prevalence Measures Incidence: Measure of choice to: ---Estimate risk of disease development ---Study etiological factors ---Evaluate primary prevention programs

Discussion Question Why is incidence preferred over prevalence when studying the etiology of disease?

Because, in the formula: P = I x D D is related to : - The subject’s constitution - Access to care - Availability of treatment - Social support - The severity of disease Discussion Question

l So prevalent cases reflect factors related to the incidence of disease (Etiological factors), AND factors related to the duration of disease (Prognostic factors) l Thus, they are not adequate for studies trying to elucidate Disease Etiology Discussion Question

PROBLEMS WITH INCIDENCE AND PREVALENCE MEASURES Problems with Numerators: Frequently, the diagnosis of cases is not straightforward Where to find the cases is not always straightforward

PROBLEMS WITH INCIDENCE AND PREVALENCE MEASURES Problems with Denominators: Classification of population subgroups may be ambiguous (i.e race/ethnicity) It is often difficult to identify and remove from the denominator persons not “at risk” of developing the disease.

Exercise JanFebMarAprMayJunJul Ratio males / female=?Prevalence March1=? Proportion of women=?Prevalence March-July=? Incidence Proportion March-July=?

Exercise ABCDEABCDE Time at risk x x Total years at risk time followed x disease onset ID = ? What is the interpretation?