A Causal Association Between Factor and Outcome Can Refer to
Section 5: Measures of Association
The key to epidemiologic analysis is comparison. Occasionally you might detect an incidence rate among a population that seems high and wonder whether it is actually higher than what should be expected based on, say, the incidence rates in other communities. Or, you might discover that, among a group of case-patients in an outbreak, several report having eaten at a particular eating place. Is the eating place simply a pop one, or have more case-patients eaten there than would be expected? The way to address that concern is by comparison the observed group with another group that represents the expected level.
A measure out of clan quantifies the relationship between exposure and disease amidst the two groups. Exposure is used loosely to hateful not only exposure to foods, mosquitoes, a partner with a sexually transmissible illness, or a toxic waste material dump, simply besides inherent characteristics of persons (for example, age, race, sex activity), biologic characteristics (allowed condition), acquired characteristics (marital status), activities (occupation, leisure activities), or conditions under which they live (socioeconomic status or access to medical care).
The measures of clan described in the post-obit section compare disease occurrence among one group with disease occurrence in another group. Examples of measures of association include risk ratio (relative risk), rate ratio, odds ratio, and proportionate mortality ratio.
Risk ratio
Definition of risk ratio
A risk ratio (RR), as well called relative risk, compares the risk of a health event (disease, injury, risk cistron, or decease) among i group with the take chances among some other group. It does so by dividing the risk (incidence proportion, assault rate) in grouping one past the run a risk (incidence proportion, attack rate) in grouping 2. The two groups are typically differentiated past such demographic factors as sexual activity (e.g., males versus females) or by exposure to a suspected risk factor (due east.g., did or did not eat spud salad). Frequently, the grouping of master interest is labeled the exposed grouping, and the comparison group is labeled the unexposed group.
Method for Calculating gamble ratio
The formula for risk ratio (RR) is:
Take chances of disease (incidence proportion, assail rate) in group of primary interest 
Risk of disease (incidence proportion, set on charge per unit) in comparison group
A risk ratio of 1.0 indicates identical hazard among the 2 groups. A risk ratio greater than 1.0 indicates an increased take chances for the grouping in the numerator, usually the exposed grouping. A risk ratio less than 1.0 indicates a decreased gamble for the exposed group, indicating that perhaps exposure actually protects against illness occurrence.
EXAMPLES: Calculating Risk Ratios
Example A: In an outbreak of tuberculosis among prison inmates in Due south Carolina in 1999, 28 of 157 inmates residing on the East wing of the dormitory adult tuberculosis, compared with iv of 137 inmates residing on the West wing.(11) These data are summarized in the two-by-ii table and then called because it has two rows for the exposure and two columns for the outcome. Here is the general format and notation.
Table 3.12A General Format and Notation for a Two-by-Two Table
| Ill | Well | Total | |
|---|---|---|---|
| Total | a + c = V1 | b + d = Five0 | T |
| Exposed | a | b | a + b = H1 |
| Unexposed | c | d | c + d = H0 |
In this example, the exposure is the dormitory wing and the outcome is tuberculosis) illustrated in Table 3.12B. Summate the hazard ratio.
Tabular array 3.12B Incidence of Mycobacterium Tuberculosis Infection Amid Congregated, HIV-Infected Prison Inmates past Dormitory Wing — S Carolina, 1999
| Developed tuberculosis? | |||
|---|---|---|---|
| Yep | No | Total | |
| Total | 32 | 262 | T = 294 |
| East wing | a = 28 | b = 129 | H1 = 157 |
| West fly | c = 4 | d = 133 | H0 = 137 |
Information Source: McLaughlin SI, Spradling P, Drociuk D, Ridzon R, Pozsik CJ, Onorato I. All-encompassing transmission of Mycobacterium tuberculosis among congregated, HIV-infected prison inmates in South Carolina, United States. Int J Tuberc Lung Dis 2003;7:665–672.
To calculate the take a chance ratio, showtime calculate the risk or attack rate for each group. Here are the formulas:
Set on Charge per unit (Risk)
Set on rate for exposed = a ⁄ a+b
Set on rate for unexposed = c ⁄ c+d
For this example:
Run a risk of tuberculosis among East wing residents = 28 ⁄ 157 = 0.178 = 17.8%
Risk of tuberculosis among West wing residents = iv ⁄ 137 = 0.029 = 2.9%
The risk ratio is merely the ratio of these two risks:
Risk ratio = 17.8 ⁄ 2.9 = half-dozen.i
Thus, inmates who resided in the East wing of the dormitory were 6.ane times every bit likely to develop tuberculosis as those who resided in the West fly.
EXAMPLES: Computing Risk Ratios (Continued)
Case B: In an outbreak of varicella (chickenpox) in Oregon in 2002, varicella was diagnosed in 18 of 152 vaccinated children compared with 3 of 7 unvaccinated children. Summate the gamble ratio.
Table three.13 Incidence of Varicella Among Schoolchildren in nine Affected Classrooms — Oregon, 2002
| Varicella | Non-case | Total | |
|---|---|---|---|
| Total | 21 | 138 | 159 |
| Vaccinated | a = 18 | b = 134 | 152 |
| Unvaccinated | c = 3 | d = 4 | 7 |
Data Source: Tugwell BD, Lee LE, Gillette H, Lorber EM, Hedberg K, Cieslak PR. Chickenpox outbreak in a highly vaccinated school population. Pediatrics 2004 Mar;113(3 Pt i):455–459.
Risk of varicella among vaccinated children = xviii ⁄ 152 = 0.118 = 11.8%
Risk of varicella amid unvaccinated children = 3 ⁄ 7 = 0.429 = 42.nine%
Risk ratio = 0.118 ⁄ 0.429 = 0.28
The adventure ratio is less than 1.0, indicating a decreased risk or protective effect for the exposed (vaccinated) children. The chance ratio of 0.28 indicates that vaccinated children were merely approximately i-fourth as probable (28%, actually) to develop varicella equally were unvaccinated children.
Charge per unit ratio
A rate ratio compares the incidence rates, person-time rates, or mortality rates of two groups. As with the take chances ratio, the two groups are typically differentiated by demographic factors or by exposure to a suspected causative agent. The charge per unit for the group of main involvement is divided by the rate for the comparing group.
Rate ratio =
Charge per unit for group of primary involvement Rate for comparison group
The interpretation of the value of a rate ratio is like to that of the risk ratio. That is, a rate ratio of 1.0 indicates equal rates in the two groups, a rate ratio greater than i.0 indicates an increased adventure for the group in the numerator, and a rate ratio less than 1.0 indicates a decreased risk for the grouping in the numerator.
EXAMPLE: Calculating Rate Ratios (Continued)
Public health officials were called to investigate a perceived increment in visits to ships' infirmaries for acute respiratory illness (ARI) by passengers of prowl ships in Alaska in 1998.(13) The officials compared passenger visits to ship infirmaries for ARI during May–August 1998 with the same menses in 1997. They recorded 11.vi visits for ARI per ane,000 tourists per week in 1998, compared with v.three visits per i,000 tourists per week in 1997. Calculate the rate ratio.
Rate ratio = xi.half dozen ⁄ 5.iii = 2.2
Passengers on cruise ships in Alaska during May–August 1998 were more than than twice as likely to visit their ships' infirmaries for ARI than were passengers in 1997. (Note: Of 58 viral isolates identified from nasal cultures from passengers, near were flu A, making this the largest summertime influenza outbreak in North America.)
Practice 3.7
Table 3.xiv illustrates lung cancer bloodshed rates for persons who continued to smoke and for smokers who had quit at the time of follow-up in 1 of the archetype studies of smoking and lung cancer conducted in Swell Britain.
Using the data in Table 3.14, calculate the post-obit:
- Rate ratio comparing current smokers with nonsmokers
- Rate ratio comparing ex-smokers who quit at least 20 years ago with nonsmokers
- What are the public health implications of these findings?
Table three.fourteen Number and Rate (Per 1,000 Person-years) of Lung Cancer Deaths for Current Smokers and Ex-smokers by Years Since Quitting, Medico Accomplice Written report — Groovy Great britain, 1951–1961
| Cigarette smoking status | Lung cancer deaths | Rate per thou person-years | Charge per unit Ratio |
|---|---|---|---|
| Current smokers | 133 | 1.xxx |  |
| For ex-smokers, years since quitting: | |||
| <v years | v | 0.67 | 9.half-dozen |
| 5–9 years | seven | 0.49 | 7.0 |
| 10–19 years | 3 | 0.18 | 2.half-dozen |
| 20+ years | 2 | 0.19 |  |
| Nonsmokers | 3 | 0.07 | 1.0 (reference grouping) |
Data Source: Doll R, Hill AB. Mortality in relation to smoking: 10 years' observation of British doctors. Brit Med J 1964; i:1399–1410, 1460–1467.
Check your reply.
Odds ratio
An odds ratio (OR) is another measure of association that quantifies the relationship betwixt an exposure with two categories and health outcome. Referring to the four cells in Table 3.15, the odds ratio is calculated as
Odds ratio = (
a b
)(
c d
) = advertising ⁄ bc
where
a = number of persons exposed and with disease
b = number of persons exposed but without disease
c = number of persons unexposed but with disease
d = number of persons unexposed: and without disease
a+c = total number of persons with disease (case-patients)
b+d = total number of persons without disease (controls)
The odds ratio is sometimes called the cantankerous-product ratio because the numerator is based on multiplying the value in prison cell "a" times the value in cell "d," whereas the denominator is the product of cell "b" and cell "c." A line from jail cell "a" to prison cell "d" (for the numerator) and another from cell "b" to cell "c" (for the denominator) creates an x or cantankerous on the two-by-2 table.
Table 3.xv Exposure and Disease in a Hypothetical Population of 10,000 Persons
| Illness | No Disease | Full | Risk | |
|---|---|---|---|---|
| Total | 180 | ix,820 | 10,000 | |
| Exposed | a = 100 | b = 1,900 | 2,000 | 5.0% |
| Not Exposed | c = lxxx | d = 7,920 | 8,000 | one.0% |
Instance: Calculating Odds Ratios
Use the information in Tabular array 3.15 to calculate the risk and odds ratios.
- Chance ratio
5.0 ⁄ 1.0 = 5.0
- Odds ratio
(100 × seven,920) ⁄ (1,900 × eighty) = five.2
Notice that the odds ratio of 5.two is close to the risk ratio of 5.0. That is i of the attractive features of the odds ratio — when the health result is uncommon, the odds ratio provides a reasonable approximation of the adventure ratio. Another bonny feature is that the odds ratio can be calculated with data from a instance-control study, whereas neither a take chances ratio nor a rate ratio can be calculated.
In a example-control study, investigators enroll a group of case-patients (distributed in cells a and c of the ii-by-two table), and a group of non-cases or controls (distributed in cells b and d).
The odds ratio is the measure of choice in a case-command report (see Lesson 1). A case-control study is based on enrolling a group of persons with disease ("instance-patients") and a comparable grouping without disease ("controls"). The number of persons in the control group is usually decided by the investigator. Oftentimes, the size of the population from which the case-patients came is not known. Equally a result, risks, rates, run a risk ratios or rate ratios cannot be calculated from the typical instance-control study. Nevertheless, you can calculate an odds ratio and translate it as an approximation of the risk ratio, particularly when the disease is uncommon in the population.
Practise 3.eight
Summate the odds ratio for the tuberculosis data in Table 3.12. Would you say that your odds ratio is an accurate approximation of the take a chance ratio? (Hint: The more than common the affliction, the further the odds ratio is from the chance ratio.)
Cheque your respond.
Source: https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section5.html