Revision class for incidence prevalence OR RR AR

Revision class Incidence PrevalenceRRORARDr. Raghupathy Anchala : 

Revision class Incidence PrevalenceRRORARDr. Raghupathy Anchala

Incidence Rate : 

Incidence Rate An incidence rate is a measure of the frequency with which an event, such as a new case of illness, occurs in a population over a period of time Incidence rate = new cases occurring during a given time period × 10n population at risk during the same time period In 1989, 733,151 new cases of gonorrhea were reported among the United States civilian population (2). The 1989 mid-year U.S. civilian population was estimated to be 246,552,000. Calculate the 1989 gonorrhea incidence rate

Answer : 

Answer 1. Define x and y: x = new cases of gonorrhea in U.S. civilians during 1989 y = U.S. civilian population in 1989 2. Identify x, y, and 10n: x = 733,151 y = 246,552,000 10n = 105 = 100,000 3. Calculate (x/y) × 10n: = .002974 × 100,000 = 297.4 per 100,000

Remember that : 

Remember that The numerator of an incidence rate should reflect new cases of disease which occurred or were diagnosed during the specified period. The numerator should not include cases which occurred or were diagnosed earlier. Notice that the denominator is the population at risk

Depending on the circumstances : 

Depending on the circumstances ….. the most appropriate denominator will be one of the following: • average size of the population over the time period • size of the population (either total or at risk) at the middle of the time period • size of the population at the start of the time period

Examples on calculations : 

Examples on calculations What is the one year incidence rate?

Practice questions : 

Practice questions Two surveys were done of the same community 12 months apart. Of 5,000 people surveyed, the first time, 25 had Diabetes Twelve months later, 35 had Diabetes, including the original 25 Calculate the prevalence of Diabetes at the end of second survey Compare the prevalence of Diabetes at second year with the 1-year incidence of DM Compare the prevalence of Diabetes at end of second year with incidence during the 12 month period.

Answers : 

Answers 1. Prevalence at the second survey: x = Diabetes positive at second survey = 35 y = population = 5,000 x/y × 10n = 35/5,000 × 1,000 = 7 per 1,000 2. 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 × 10n = 10/4,975 × 1,000 = 2 per 1,000

Attack Rate : 

Attack Rate An attack rate is a variant of an incidence rate, applied to a narrowly defined population observed for a limited time, such as during an epidemic. For a defined population (the population at risk), during a limited time period , Attack rate = Number of new cases among the population during the period Population at risk at the beginning of the period The attack rate is usually expressed as a percent

Example : 

Example Of 75 persons who attended a church picnic, 46 subsequently developed gastroenteritis. To calculate the attack rate of gastroenteritis we first define the numerator and denominator: x = Cases of gastroenteritis occurring within the incubation period for gastroenteritis among persons who attended the picnic = 46 y = Number of persons at the picnic = 75 Then, the attack rate for gastroenteritis is = 61% (?) Attack rate is a proportion—the persons in the numerator are also in the denominator. This proportion is a measure of the probability or risk of becoming a case. Among persons who attended the picnic, the probability of developing gastroenteritis was 61%, or the risk of developing gastroenteritis was 61%.

SAR : 

SAR A secondary attack rate is a measure of the frequency of new cases of a disease among the contacts of known cases Secondary attack rate = Number of cases among contacts of primary cases during the period × 10n total number of contacts To calculate the total number of household contacts, we usually subtract the number of primary cases from the total number of people residing in those households.

Solve this….. : 

Solve this….. Seven cases of hepatitis A occurred among 70 children attending a child care center Each infected child came from a different family The total number of persons in the 7 affected families was 32 One incubation period later, 5 family members of the 7 infected children also developed hepatitis A Calculate the attack rate in the child care center Calculate the secondary attack rate among family contacts of those cases.

Slide 13: 

cases of hepatitis A among family contacts of children with hepatitis; A = 5 number of persons at risk in the families (total number of family members — children already infected) = 32 − 7 = 25 Secondary attack rate = (x/y) × 100 = (5/25) × 100 = 20%

Person Time rate : 

Person Time rate is a type of incidence rate that directly incorporates time into the denominator Typically, each person is observed from a set beginning point to an established end point (onset of disease, death, migration out of the study, or end of the study) The numerator is still the number of new cases The denominator is the sum of the time each person is observed, totaled for all persons Number of cases during observation period × 10n Time each person was observed, totaled for all persons

Example : 

Example Investigators enrolled 2,100 men in a study and followed them over 4 years to determine the rate of heart disease. The follow-up data are provided below calculate the person-time incidence rate of heart disease We assume that persons diagnosed with disease and those lost to follow-up were disease-free for half of the year, and thus contribute ½ year to the denominator Initial enrollment: 2,100 men free of disease After 1 year: 2,000 disease-free, 0 with disease, 100 lost to follow-up After 2 years: 1,900 disease-free, 1 with disease, 99 lost to follow-up After 3 years: 1,100 disease-free, 7 with disease, 793 lost to follow-up After 4 years: 700 disease-free, 8 with disease, 392 lost to follow-up

Slide 16: 

Initial enrollment: 2,100 men free of disease After 1 year: 2,000 disease-free, 0 with disease, 100 lost to follow-up After 2 years: 1,900 disease-free, 1 with disease, 99 lost to follow-up After 3 years: 1,100 disease-free, 7 with disease, 793 lost to follow-up After 4 years: 700 disease-free, 8 with disease, 392 lost to follow-up 1. Identify x: x = cases diagnosed = 1 + 7 + 8 = 16 2. Calculate y, the person-years of observation: (2,000 + 0 + 0.5 * 100) + (1,900 + 0.5 × 1 + 0.5 × 99) + (1,100 +0.5 × 7 + 0.5 × 793) + (700 +0.5 × 8+ 0.5 × 392) = 6,400 person-years of observation

Second way of calculating person years : 

Second way of calculating person years Initial enrollment: 2,100 men free of disease After 1 year: 2,000 disease-free, 0 with disease, 100 lost to follow-up After 2 years: 1,900 disease-free, 1 with disease, 99 lost to follow-up After 3 years: 1,100 disease-free, 7 with disease, 793 lost to follow-up After 4 years: 700 disease-free, 8 with disease, 392 lost to follow-up how many people were followed for how many years, as follows: 700 men × 4.0 years = 2,800 person-years 8 + 392 = 400 men × 3.5 years = 1,400 person-years 7 + 793 = 800 men × 2.5 years = 2,000 person-years 1 + 99 = 100 men × 1.5 years = 150 person-years 0 + 100 = 100 men × 0.5 years = 50 person-years Total = 6,400 person-years of observation

Difference between Attack and P-y : 

Difference between Attack and P-y 16 / 6 400 × 10n = .0025 × 10n or, if 10n is set at 1,000, there were 2.5 cases per 1,000 person-years of observation. This quantity is also commonly expressed as 2.5 cases per 1,000 persons per year In contrast, the attack rate comes out to 16/2,100 = 7.6 cases/1,000 population during the 4- year period This averages out to 1.9 cases per 1,000 persons per year. The attack rate is less accurate because it ignores persons lost to follow-up.

Risk Ratios : 

Risk Ratios Calculate the risk for females to develop Pellagra Calculate the risk for males to develop Pellagra Calculate the Risk Ratio for females to males to develop Pellagra Risk of illness among females = 46/ 1484 = = .031 Risk of illness among males = 18/1419 = = .013 Therefore, the risk of illness among females is .031 or 3.1% and the risk of illness among males is .013 or 1.3%. In calculating the risk ratio for females versus males, females are the group of primary interest and males are the comparison group. Risk ratio = (3.1 % / 1.3 % ) = 2.4 The risk of pellagra in females appears to be 2.4 times higher than the risk in males.

Why RR is a measure of association? : 

Why RR is a measure of association? Risk of hand injury among mill workers was 0.9%. The risk among those who did not work in the mill was 4.4%. The relative risk of hand injury for mill workers versus non - mill workers is : Relative risk = risk ratio = 0.9%/4.4% = 0.2 The risk of hand injury in mill workers appears to be only 0.2 or one-fifth of the risk in non-mill workers In other words, working in the mill appears to protect against hand injury The relative risk is called a measure of association because it quantifies the relationship (association) between the so-called exposure (sex, mill employment) and disease (hand injury).

Rate Ratios : 

Rate Ratios A rate ratio compares two groups in terms of incidence rates, person-time rates, or mortality rates Like the risk ratio, the two groups are typically differentiated by demographic factors or by exposure to a suspected causative agent The rate for the group of primary interest is divided by the rate for the comparison group Rate ratio = (rate for group of primary interest / rate for comparison group) × 1 The interpretation of the value of a rate ratio is similar to that of the risk ratio

Calculate Rate Ratios…. : 

Calculate Rate Ratios…. Rate ratio = 0.57 / 0.07 = 8.1 The rate of lung cancer among smokers of 1-14 cigarettes is 8.1 times higher than the rate of lung cancer in nonsmokers.

ODDS Ratio : 

ODDS Ratio Odds ratio = (46*1401) / (18*1438) = 2.5 when the health outcome is uncommon, the odds ratio provides a good approximation of the relative risk we can calculate the odds ratio if we know the values in four cells in the two-by-two table; we do not need to know the size of the total exposed group and the total unexposed group. relevant when we analyze data from a case-control study, which has a group of cases and a group of non-cases or controls The size of the control group is arbitrary and the true size of the population from which the cases came is usually not known, so we usually cannot calculate rates or a relative risk. Nonetheless, we can still calculate an odds ratio, and interpret it as an approximation of the relative risk.

Attributable Proportion : 

Attributable Proportion attributable proportion is the proportion of disease in an exposed group attributable to the exposure. It represents the expected reduction in disease if the exposure could be removed (or never existed) Attributable Proportion = (risk for exposed group)−(risk for unexposed group) * 100 risk for exposed group Attributable proportion can be calculated for rates in the same way

Calculate for this : 

Calculate for this 1. Identify exposed group rate: lung cancer death rate for smokers of 1-14 cigarettes per day = 0.57 per 1,000 per year 2. Identify unexposed group rate: lung cancer death rate for nonsmokers = 0.07 per 1,000 per year 3. Calculate attributable proportion: = {(0.57 – 0.07) / 0.57} * 100 % = 0.877 × 100% = 87.7% Thus, assuming our data are valid (for example, the groups are comparable in age and other risk factors), then about 88% of the lung cancer in smokers of 1-14 cigarettes per day may be attributable to their smoking. Approximately 12% of the lung cancer cases in this group would have occurred anyway.

Measures of Association : 

Measures of Association Measures of association based on ratios Cohort Studies Relative risk and Odds ratio Case-Control Studies Odds of exposure and odds of disease Odds ratios: Standard case-control, When controls sampled from total population, For multiple exposure categories Estimates of relative risk, rate ratio Measures of association based on differences: attributable risk

Analysis of Prospective Cohort Data : 

Analysis of Prospective Cohort Data Calculate incidence rates Compare incidence rates across exposure groups Relative risk: How many times bigger is IExp compared to IUnexp Attributable (excess) risk: how much bigger is IExp compared to IUnexp

Relative Measure of Effect : 

Relative Measure of Effect Measures of association based on ratios are relative measures of association Relative risk (or risk ratio): ratio of two probabilities (incidences) based on population at the beginning of the follow-up interval. Often the ratio of risk for exposed individuals compared to non-exposed individuals: RRexp = q+ / q- Rate ratio: ratio of two rates (based on person-time) Odds ratio (or relative odds): ratio of two odds

Cohort Studies Example : 

Cohort Studies Example Tasmania 1988-1990 cohort: sleeping position of 2607 one-month old infants versus sudden infant death syndrome (crib death) through 1 year of age. Koepsell and Weiss, 2003

Note about Confidence Intervals : 

Note about Confidence Intervals Var ( Ln (RR) ) ≈ b/a + d/c a+b c+d Var ( Ln (OR) ) ≈ 1/a + 1/b + 1/c + 1/d The 95% Confidence Interval of an estimate is: Est +/- 1.96 * [Var(Est)]1/2 95% CI for Ln RR: Ln RR +/- 1.96 * [Var(Ln RR)]1/2 95% CI for RR: exp(Ln RR - 1.96 * [Var(Ln RR)]1/2 ), exp(Ln RR + 1.96 * [Var(Ln RR)]1/2 ) This is NOT a symmetric confidence interval around RR. If CI does not include “1” (no effect), then this implies that there is a significant effect.

Case-Control Studies : 

Case-Control Studies Case-Control study for hip and forearm fractures outcome based on estrogen exposure. Consider as a cohort study and as a case-control study

Case-Control Studies : 

Case-Control Studies Cohort: Case-control: Retrospective Case-Control studies can estimate odds ratio of disease outcome because ORDisease = ORExposure = “cross-product” ratio

Case-Control Studies : 

Case-Control Studies In case-control studies, an unbiased sample of cases and controls yields an unbiased odds ratio. Not necessary that the sampling fraction be the same in cases and controls (e.g. can sample a majority of cases and a small proportion of controls). Since cases are usually less frequent, the sampling fraction for cases is generally greater than for controls.

Multiple Exposure Categories : 

Multiple Exposure Categories When there are more than two exposure categories, Calculate the odds ratios for each exposure compared to a reference exposure.

Absolute Measure of Effect : 

Absolute Measure of Effect Measures of association based on differences are absolute measures of effect Attributable risk in the exposed: the amount of risk among individuals exposed to a certain risk factor that can be attributed to the risk factor per se: ARexp = q+ - q- Can also be expressed as a percentage: % ARexp = [( q+ - q- ) / q+ ] x 100% ARexp

Attributable Risk : 

Attributable Risk ARexp = q+ - q- = 0.01064 - .00341 = .00723 That is, the “excess risk” for crib deaths attributed to a prone sleeping position is 7.2 per 1000 babies % ARexp = [( q+ - q- ) / q+ ] x 100% = (.00723 / .01064) x 100% = 68.0% That is, 68% of the crib deaths among prone sleepers can be attributed to the prone sleeping position

Population Attributable Risk : 

Population Attributable Risk Population attributable risk: The amount of risk in the population that can be attributed to a given risk factor. Usually expressed as a percentage: % Pop AR = ( qP – q− ) x 100% qP The Pop AR depends both on the RR (q+ / q- ) and the prevalence of the risk factor (pe) since the incidence in the population (qP) is the weighted sum of q+ and q- [i.e. qP = pexq+ + (1- pe)xq- ] Relationship explicitly expressed in Levin’s formula: % Pop AR = pe( RR - 1 ) x 100% pe( RR – 1) + 1

Population Attributable Risk : 

Population Attributable Risk ARexp ARexp PopAR PopAR Low Exposure Prevalence High Exposure Prevalence If 32% of babies sleep in the prone position, pe=0.32 % Pop AR = .32 * (3.12 - 1) x 100% = 40.4% .32 * (3.12-1) +1 That is, 40.4% of all crib deaths in the population can be attributed to prone sleeping. Note: if instead pe=0.032, then % Pop AR would be 6.4%

Acknowledgements : 

Acknowledgements The examples have been adapted based Dr. Maria Brooks lectures on basic epidemiology, GSPH, University of Pittsburgh The problems and exercises have been taken verbatim form CDC book on epidemiology These have been adapted solely for teaching purposes and for the practice of students.