Lesson 3: Measures of Risk
Section 5: Measures of Association
The key to epidemiologic analysis is comparison. occasionally you might observe an incidence rate among a population that seems high gear and wonder whether it is actually higher than what should be expected based on, say, the incidence rates in other communities. Or, you might observe that, among a group of casepatients in an outbreak, respective report having eaten at a especial restaurant. Is the restaurant precisely a popular one, or have more casepatients eaten there than would be expected ? The direction to address that concern is by comparing the observed group with another group that represents the expect level .
A measure of association quantifies the relationship between exposure and disease among the two groups. vulnerability is used broadly to mean not merely exposure to foods, mosquitoes, a partner with a sexually catching disease, or a toxic lay waste to dump, but besides implicit in characteristics of persons ( for exemplar, historic period, slipstream, sex ), biological characteristics ( immune condition ), acquired characteristics ( marital condition ), activities ( occupation, leisure activities ), or conditions under which they live ( socioeconomic status or access to checkup manage ) .
The measures of association described in the following part compare disease occurrence among one group with disease happening in another group. Examples of measures of association include gamble ratio ( relative risk ), rate proportion, odds ratio, and proportionate mortality ratio.
Risk ratio
Definition of risk ratio
A gamble proportion ( RR ), besides called proportional gamble, compares the risk of a health consequence ( disease, injury, risk component, or death ) among one group with the risk among another group. It does thus by dividing the risk ( incidence symmetry, attack pace ) in group 1 by the risk ( incidence proportion, attack rate ) in group 2. The two groups are typically differentiated by such demographic factors as sexual activity ( for example, males versus females ) or by exposure to a suspected risk divisor ( for example, did or did not eat potato salad ). Often, the group of primary interest is labeled the exposed group, and the comparison group is labeled the unexposed group .
Method for Calculating risk ratio
The formula for risk ratio ( RR ) is :
Risk of disease (incidence proportion, attack rate) in comparison group risk of disease ( incidence proportion, fire rate ) in group of primary interestRisk of disease ( incidence proportion, attack rate ) in comparison group
A risk proportion of 1.0 indicates identical risk among the two groups. A gamble proportion greater than 1.0 indicates an increased risk for the group in the numerator, normally the disclose group. A gamble proportion less than 1.0 indicates a decreased gamble for the exposed group, indicating that possibly exposure actually protects against disease happening .
EXAMPLES: Calculating Risk Ratios
Example A: In an outbreak of tuberculosis among prison inmates in South Carolina in 1999, 28 of 157 inmates residing on the East fender of the dormitory developed tuberculosis, compared with 4 of 137 inmates residing on the West wing. ( 11 ) These data are summarized in the twobytwo postpone sol called because it has two rows for the exposure and two column for the result. here is the general format and notation .
table 3.12A General Format and Notation for a TwobyTwo board
Ill  Well  Total  

Total  a + c = V1  b + d = V0  T 
Exposed  a  b  a + b = H1 
Unexposed  c  d  c + d = H0 
In this example, the exposure is the dormitory wing and the result is tuberculosis ) illustrated in board 3.12B. Calculate the gamble ratio .
table 3.12B incidence of Mycobacterium Tuberculosis Infection Among Congregated, HIVInfected Prison Inmates by Dormitory Wing — South Carolina, 1999
Developed tuberculosis?  

Yes  No  Total  
Total  32  262  T = 294 
East wing  a = 28  b = 129  H1 = 157 
West wing  c = 4  d = 133  H0 = 137 
Data beginning : McLaughlin SI, Spradling P, Drociuk D, Ridzon R, Pozsik CJ, Onorato I. acrosstheboard transmission of Mycobacterium tuberculosis among congregate, HIVinfected prison inmates in South Carolina, United States. Int J Tuberc Lung Dis 2003 ; 7:665–672 .
To calculate the risk proportion, first calculate the risk or attack rate for each group. here are the formulas :
Attack Rate (Risk)
Attack rate for exposed = a ⁄ a+b
Attack rate for unexposed = coulomb ⁄ c+d
For this case :
risk of tuberculosis among East wing residents = 28 ⁄ 157 = 0.178 = 17.8 %
hazard of tuberculosis among West wing residents = 4 ⁄ 137 = 0.029 = 2.9 %
The risk ratio is merely the proportion of these two risks :
Risk ratio = 17.8 ⁄ 2.9 = 6.1
frankincense, inmates who resided in the East wing of the dormitory were 6.1 times deoxyadenosine monophosphate probable to develop tuberculosis as those who resided in the West wing .
EXAMPLES: Calculating Risk Ratios (Continued)
Example B: In an outbreak of chickenpox ( chickenpox ) in oregon in 2002, chickenpox was diagnosed in 18 of 152 immunize children compared with 3 of 7 unvaccinated children. Calculate the risk ratio .
board 3.13 incidence of Varicella Among Schoolchildren in 9 Affected Classrooms — Oregon, 2002
Varicella  Noncase  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 immunize school population. Pediatrics 2004 Mar ; 113 ( 3 Pt 1 ) :455–459 .
gamble of chickenpox among immunize children = 18 ⁄ 152 = 0.118 = 11.8 %
risk of chickenpox among unvaccinated children = 3 ⁄ 7 = 0.429 = 42.9 %
Risk ratio = 0.118 ⁄ 0.429 = 0.28
The hazard ratio is less than 1.0, indicating a decreased gamble or protective effect for the exposed ( vaccinated ) children. The risk proportion of 0.28 indicates that immunize children were merely approximately onefourth as probably ( 28 %, actually ) to develop chickenpox as were unvaccinated children .
Rate ratio
A rate ratio compares the incidence rates, persontime rates, or mortality rates of two groups. As with the gamble proportion, the two groups are typically differentiated by demographic factors or by vulnerability to a suspected causative agentive role. The rate for the group of primary interest is divided by the rate for the comparison group .
Rate proportion =
Rate for comparison group Rate for group of basal interestRate for comparison group
The rendition of the respect of a rate ratio is similar to that of the risk ratio. That is, a pace proportion of 1.0 indicates peer rates in the two groups, a rate ratio greater than 1.0 indicates an increased risk for the group in the numerator, and a rate ratio less than 1.0 indicates a decreased hazard for the group in the numerator .
EXAMPLE: Calculating Rate Ratios (Continued)
Public health officials were called to investigate a sensed increase in visits to ships ’ infirmaries for acute respiratory illness ( ARI ) by passengers of cruise ships in Alaska in 1998. ( 13 ) The officials compared passenger visits to ship infirmaries for ARI during May–August 1998 with the same period in 1997. They recorded 11.6 visits for ARI per 1,000 tourists per workweek in 1998, compared with 5.3 visits per 1,000 tourists per week in 1997. Calculate the rate proportion.
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Rate ratio = 11.6 ⁄ 5.3 = 2.2
Passengers on cruise ships in Alaska during May–August 1998 were more than doubly as likely to visit their ships ’ infirmaries for ARI than were passengers in 1997. ( note : Of 58 viral isolates identified from adenoidal cultures from passengers, most were influenza A, making this the largest summer influenza outbreak in North America. )
Exercise 3.7
postpone 3.14 illustrates lung cancer deathrate rates for persons who continued to smoke and for smokers who had depart at the clock of followup in one of the authoritative studies of smoke and lung cancer conducted in Great Britain .
Using the data in table 3.14, calculate the take after :
 Rate ratio comparing current smokers with nonsmokers
 Rate ratio comparing exsmokers who quit at least 20 years ago with nonsmokers
 What are the public health implications of these findings?
mesa 3.14 Number and Rate ( Per 1,000 Personyears ) of Lung Cancer Deaths for Current Smokers and Exsmokers by Years Since Quitting, Physician Cohort Study — Great Britain, 1951–1961
Cigarette smoking status  Lung cancer deaths  Rate per 1000 personyears  Rate Ratio 

Current smokers  133  1.30  
For exsmokers, years since quitting:  
< 5 years  5  0.67  9.6 
5–9 years  7  0.49  7.0 
10–19 years  3  0.18  2.6 
20+ years  2  0.19  
Nonsmokers  3  0.07  1.0 (reference group) 
Data source : Doll R, Hill AB. Mortality in relative to fume : 10 years ’ observation of british doctors. Brit Med J 1964 ; 1:1399–1410, 1460–1467 .
Check your answer .
Odds ratio
An odds ratio ( OR ) is another bill of association that quantifies the relationship between an photograph with two categories and health consequence. Referring to the four cells in postpone 3.15, the odds proportion is calculated as
Odds ratio = (
b ) (
d ) = ad ⁄ 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 = sum numeral of persons with disease ( casepatients )
b+d = entire number of persons without disease ( controls )
The odds ratio is sometimes called the crossproduct ratio because the numerator is based on multiplying the value in cell “ a ” times the measure in cell “ five hundred, ” whereas the denominator is the product of cell “ bel ” and cell “ c. ” A line from cell “ a ” to cell “ vitamin d ” ( for the numerator ) and another from cell “ bel ” to cell “ hundred ” ( for the denominator ) creates an adam or crabbed on the twobytwo board .
postpone 3.15 exposure and Disease in a conjectural population of 10,000 Persons
Disease  No Disease  Total  Risk  

Total  180  9,820  10,000  
Exposed  a = 100  b = 1,900  2,000  5.0% 
Not Exposed  c = 80  d = 7,920  8,000  1.0% 
EXAMPLE: Calculating Odds Ratios
Use the data in board 3.15 to calculate the risk and odds ratios .

Risk ratio
5.0 ⁄ 1.0 = 5.0 
Odds ratio
( 100 × 7,920 ) ⁄ ( 1,900 × 80 ) = 5.2
Notice that the odds ratio of 5.2 is close up to the risk ratio of 5.0. That is one of the attractive features of the odds ratio — when the health consequence is rare, the odds ratio provides a reasonable estimate of the risk ratio. Another attractive feature is that the odds ratio can be calculated with data from a casecontrol sketch, whereas neither a hazard ratio nor a rate proportion can be calculated .
In a casecontrol study, investigators enroll a group of casepatients ( distributed in cells a and carbon of the twobytwo postpone ), and a group of noncases or controls ( distributed in cells boron and five hundred ) .
The odds ratio is the measuring stick of choice in a casecontrol learn ( see Lesson 1 ). A casecontrol survey is based on enrolling a group of persons with disease ( “ casepatients ” ) and a comparable group without disease ( “ controls ” ). The number of persons in the control group is normally decided by the research worker. Often, the size of the population from which the casepatients came is not known. As a consequence, risks, rates, hazard ratios or rate ratios can not be calculated from the distinctive casecontrol survey. however, you can calculate an odds proportion and interpret it as an approximation of the hazard ratio, peculiarly when the disease is uncommon in the population .
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Exercise 3.8
Calculate the odds proportion for the tuberculosis data in board 3.12. Would you say that your odds ratio is an accurate approximation of the gamble ratio ? ( tip : The more common the disease, the further the odds proportion is from the gamble ratio. )
Check your answer .