Question

A study commissioned by the power company shows that of 9,848 persons residing within 500 yards of high voltage lines, 600 have developed one of the cancers in question. Of 13,112 living more than 500 yards from such lines, 550 contracted one of the cancers. a. Calculate the point estimate of odds ratio b. Calculated 95% confidence interval of the odds ratio. Does the odds ratio significantly different from 1?

Answer 1

Solution:

From given information, we have following table:

		Within 500 yards of high voltage lines
Cancer		Yes	No	Total
	Yes	600	550	1150
	No	9248	12562	21810
	Total	9848	13112	22960

We have a=600, b=550, c=9248, d=12562

Odds Ratio = OR = ad/bc = (600*12562)/(550*9248) = 1.48183391

Confidence interval = exp(log(OR) ± Zα/2­*sqrt(1/a + 1/b + 1/c + 1/d)

Confidence level = 95%

α = 0.05

Zα/2 = 1.96 (by using z-table)

Confidence interval = exp(log(1.48183391) ± 1.96*sqrt(1/600 + 1/550 + 1/9248 + 1/12562)

Confidence interval = exp(log(1.48183391) ± 1.96* 0.060602

Confidence interval = exp(log(1.48183391) ± 0.11878

Confidence interval = 1.186253 ± 0.11878

Lower limit = 1.186253 - 0.11878 = 1.067473

Upper limit = 1.186253 + 0.11878 = 1.305033

Confidence interval = (1.067473, 1.305033)

Odds Ratio is significantly different from 1 because the value 1 is not lies within above confidence interval.