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Epidemiology Prof (Dr) RN Basu CONTENT TOPIC SLIDE NO> 12.Measures of association 154 Risk ratio 156 Rate ratio 159 Odds ratio 160 13.Measures of public health impact 164 Attributable proportion 165 Vaccine efficacy or vaccine effectiveness 167 14.Mathematical model in infectious disease 169 155 Measures of Association • Measures of Association • The key to epidemiologic analysis is comparison • A measure of association quantifies the relationship between exposure and disease among two groups • Here, exposure is used in generic sense • It may mean not only exposure to foods, mosquitos, a partner with sexually transmissible disease, or a toxic waste dump • But it also may mean: • inherent characteristics of persons, (such as age, race, sex), • biologic characteristics (marital status), • activities (such as occupation, leisure activities), or • conditions under which they live (socioeconomic status or access to medical care) 156 Measures of Association • The measures of association for occurrence of disease in one group with disease occurrence in another group are: • Risk ratio (relative risk) • Rate ratio, and • Mortality ratio • Risk ratio • It is called relative risk of a health event • It compares the risk of a health event (disease, injury, risk factor, or death) • Comparison is done between risk of one group with risk of another group 157 Measures of Association • Method of calculation of risk ratio: • Dividing the risk (incidence proportion, attack rate) in group 1 by the risk (incidence proportion, attack rate) in group 2 • The two groups are differentiated by demographic factors or by exposure to a suspected risk factor • Demographic characteristics may be like: • Sex (male versus female) • Exposure to suspected risk factor (such as did or did not eat in a particular restaurant) • Often the group of primary interest is labelled the exposed group and the comparison group is labelled the unexposed group 158 Measures of Association • Formula of calculating risk ratio (RR) is: • A risk ratio of 1.0 indicates identical risk among both groups • A risk ratio greater than 1.0 indicates an increased risk for the group in the numerator • A risk ratio of less than 1.0 indicates a decreased risk for the exposed group • It indicates that perhaps exposure actually protects against disease occurrence 159 Measures of Association • Rate ratio • This ratio compares the incidence rates, or mortality rates of two groups • Like risk ratio, the two groups may be differentiated demographic factors or by exposure to a suspected causative agent • The formula is: • The interpretation is similar to that of the risk ratio 160 Measures of Association • Odds ratio (OR) Also called cross-product ratio • It is another measure of association • It quantifies the relationship between an exposure with two categories and health outcome • Example: • Exposure and Disease in a hypothetical population of 10,000 persons 161 Measures of Association • Odds ratio formula (refer to the table in the previous slide) 162 Measures of Association • From the data in the previous table both Risk Ratio as well as the Odds ratio can be calculated 1. Risk ratio = 5.0 / 1.0 = 5.0 2. Odds ratio = (100 x 7920) / (1900 x 80) = 5.2 • In these cases, both the ratios are closer to each other • The attractive features of odds ratio are that • When the health outcome is uncommon, the odds ratio provides a reasonable approximation of risk ratio, and • Odds ratio can be calculated with data from case control study, whereas neither a risk ratio nor a rate ratio can be calculated 163 Measures of Association • The odds ratio is the measure of choice in a case control study • A case-control study is based on enrolling a group of persons with disease (“case-patients”) and a comparable group without disease (“controls”) • The number of persons in the control group is decided by the investigator • Often, the size of the population from which the case-patients came is not known • As a result, risks, rates, risk ratios or rate ratios cannot be calculated from the typical case-control study • An odds ratio can be calculated and interpreted as an approximation of the risk ratio, particularly when the disease is uncommon in the population 164 Measures of Public Health Impact • For public health purposes it is necessary to ascertain what impact an exposure will have on public health outcome • Measures of association is a quantifiable measure to establish a relationship between exposure and disease • Therefore, causal relationship between these factors can be known • It does not provide what impact this relationship will have on public health • To ascertain, two measures of public health impact are usually used: 1. Attributable proportion 2. Efficacy or effectiveness 165 Measures of Public Health Impact • Attributable proportion • This is also known as attributable risk percent • This is a measure of the public health impact of a causative factor • To calculate this measure, certain assumptions are made • That is, the occurrence of disease in an unexposed group represents a baseline or expected risk for the disease • A further assumption is made • That if the risk of disease in the exposed group is higher than the risk in the unexposed group, the difference can be attributed to the exposure 166 Measures of Public Health Impact • Thus the attributable proportion is the amount of disease in the exposed group attributable to the exposure • It represents the expected reduction in disease if the exposure could be removed • This measure is used when there is only one risk factor • Its use is not appropriate when there are multiple risk factors 167 Measures of Public Health Impact • Vaccine efficacy or vaccine effectiveness • This measures the proportionate reduction in cases among vaccinated persons • Vaccine efficacy is used when the study is carried out under ideal condition, e.g., during a clinical trial • Vaccine effectiveness is used when study is carried out in field trials where conditions may be less ideal • Both are measured among vaccinated and unvaccinated persons and determining the percentage reduction in risk of disease among vaccinated persons in comparison to the unvaccinated persons 168 Measures of Public Health Impact • Greater reduction of disease in vaccinated persons would mean effectiveness and efficiency is higher • The formula for calculation is as below: • The measure is interpreted as the proportionate reduction in disease among the vaccinated group 169 Mathematical Model in Infectious Disease Epidemiology • Mathematical modelling • The concept of modelling for infectious disease transmission was first described by Daniel Bermoulli in 1766 • But the concept was really understood in 20th century • The concept demonstrated that infectious disease transmission dynamics is non- linear • It was not fully understood then why an epidemic ended before all the susceptible individuals were infected • The hypothesis put forward then assumed that the virulence of the pathogen changed during an epidemic 170 Mathematical Model in Infectious Disease Epidemiology • Later (1906) it was recognised that the real cause was diminishing density of susceptible persons of halting the spread of the epidemic • In the last decade of the 20th century, the concept of a threshold quantity that separates different dynamic regimes was initiated • An infectious disease can spread in susceptible population only if the basic reproduction number is above a threshold value • The concept is applied for an immunisation programme • It says that it is not necessary to vaccinate the entire population to terminate spread of an infectious disease 171 Mathematical Model in Infectious Disease Epidemiology • Historical data analysis of the pandemic outbreak of influenza A has shown that the basic reproduction number has been low but the serial interval is short • These findings leads to the strategy that spread of influenza A can be stopped with moderate levels of intervention • But the interventions must be done quickly for it to be effective • Contrary to this, measles have a high reproduction number and would need wide vaccination levels for elimination • Thus mathematical modelling can help in arriving at an intervention strategy and evaluation of existing intervention 172 Mathematical Model in Infectious Disease Epidemiology • Transmission Model • There are many dynamic processes that contribute to disease transmission • In a mathematical model these dependent processes need to be analysed and then formulated in a mathematical way • Developing a mathematical model forces one to focus on the essential processes involved in defining the epidemiology of the infectious diseases • The modelling can show the parameters that are most important and are amenable to control • Mathematical modelling integrates knowledge from different disciplines like microbiology, social sciences and clinical sciences 173 Mathematical Model in Infectious Disease Epidemiology • For many infectious diseases such as influenza and smallpox, the people can be classified in three categories: • Susceptible • Infected, or • Recovered and immune • Those who are susceptible in the population move through these three stages of infection 174 Mathematical Model in Infectious Disease Epidemiology • This is the concept of herd immunity • When a sufficient number of people have been vaccinated, the pathogen will not find a susceptible host for propagation of the disease • The concept was validated during the eradication of smallpox in 1970’s • Coverage of 80% of
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