"An odds ratio will approximate the risk ratio if the rare disease assumption is met. Using the 2x2 table format discussed above, the risk ratio (RR=risk in exposed/risk in unexposed) can be expressed as the following ratio:"
"RR=a/(a+c)/b/(b+d)"
"If “a” and “b” are both small numbers, then the equation for RR can be approximated by RR= a/c/b/d which rearranges to RR=(ad)/(bc) which is the "cross product" formula for the odds ratio. The rare disease assumption is often made when disease prevalence is less than 10%"
"If “a” and “b” are both small numbers, then the equation for RR can be approximated by RR= a/c/b/d which rearranges to RR=(ad)/(bc) which is the "cross product" formula for the odds ratio. The rare disease assumption is often made when disease prevalence is less than 10%"
"If “a” and “b” are both small numbers, then the equation for RR can be approximated by RR= a/c/b/d which rearranges to RR=(ad)/(bc) which is the "cross product" formula for the odds ratio. The rare disease assumption is often made when disease prevalence is less than 10%"
"RR=a/(a+c)/b/(b+d)"
Expected headings
"Risk ratios"
"Rate ratios"
"Odds ratios"
"Rare disease assumption"
"In 1956, Doll and Hill published a cohort study in the British Medical Journal comparing the death rates of smokers and non-smokers from lung cancer after 53 months of follow-up in male physicians ≥35 years of age 4. Among smokers, (the exposed), there were 83 lung cancer deaths during 98,090 person-years, for an incidence rate of 83/98,090 or 0.84 lung cancer deaths/1,000 person-years. Among the non-smokers (the unexposed), there was 1 lung cancer death during 15,107 person-years, for an incidence rate of 1/15,107 or 0.07 lung cancer deaths/1,000 person-years. The rate ratio for the “Doctor’s study” as published in 1956 is IR exposed/IR unexposed = 0.84/0.07 = 12. This means that smokers died of lung cancer at 12 times the rate of non-smokers."
"In 1950, Doll and Hill published a case-control study in the British Medical Journal comparing the exposure to smoking in subjects with lung cancer to hospitalised controls without lung cancer 6. There were 688 exposed cases (cell “a”), 21 unexposed controls (cell “b”), 650 exposed controls (cell “c”), and 59 unexposed controls (cell ”d”), resulting in an odds ratio = (ad) / (bc) = (688x59) / (650x21) = 40,592/13,650 = 2.97. In words, the odds of smoking among the subjects with lung cancer (cases) were 2.97 times greater than the odds of smoking among the subjects without lung cancer (controls). This study was one of the earliest that showed an association between smoking and lung cancer."
"In 1956, Doll and Hill published a cohort study in the British Medical Journal comparing the death rates of smokers and non-smokers from lung cancer after 53 months of follow-up in male physicians ≥35 years of age 4. Among smokers, (the exposed), there were 83 lung cancer deaths during 98,090 person-years, for an incidence rate of 83/98,090 or 0.84 lung cancer deaths/1,000 person-years. Among the non-smokers (the unexposed), there was 1 lung cancer death during 15,107 person-years, for an incidence rate of 1/15,107 or 0.07 lung cancer deaths/1,000 person-years. The rate ratio for the “Doctor’s study” as published in 1956 is IR exposed/IR unexposed = 0.84/0.07 = 12. This means that smokers died of lung cancer at 12 times the rate of non-smokers."
"In 1950, Doll and Hill published a case-control study in the British Medical Journal comparing the exposure to smoking in subjects with lung cancer to hospitalised controls without lung cancer 6. There were 688 exposed cases (cell “a”), 21 unexposed controls (cell “b”), 650 exposed controls (cell “c”), and 59 unexposed controls (cell ”d”), resulting in an odds ratio = (ad) / (bc) = (688x59) / (650x21) = 40,592/13,650 = 2.97. In words, the odds of smoking among the subjects with lung cancer (cases) were 2.97 times greater than the odds of smoking among the subjects without lung cancer (controls). This study was one of the earliest that showed an association between smoking and lung cancer."
"In 1950, Doll and Hill published a case-control study in the British Medical Journal comparing the exposure to smoking in subjects with lung cancer to hospitalised controls without lung cancer 6. There were 688 exposed cases (cell “a”), 21 unexposed controls (cell “b”), 650 exposed controls (cell “c”), and 59 unexposed controls (cell ”d”), resulting in an odds ratio = (ad) / (bc) = (688x59) / (650x21) = 40,592/13,650 = 2.97. In words, the odds of smoking among the subjects with lung cancer (cases) were 2.97 times greater than the odds of smoking among the subjects without lung cancer (controls). This study was one of the earliest that showed an association between smoking and lung cancer."