A study considered the effect of prednisolone on severe hypercalcemia in women w
ID: 3354899 • Letter: A
Question
A study considered the effect of prednisolone on severe hypercalcemia in women with metastatic breast cancer (B. Kristensen et al., J. Intern. Med. 232: 237-245, 1992). Of 30 patients, 15 were randomly selected to receive prednisolone. The other 15 formed a control group. Normalization in their level of serum-ionized calciunm was achieved by 7 of the treated patients and none of the control group. Obtain a 95% confidence interval for the odds ratio using (a) the Wald interval and (b) the profile likelihood. In each case, note the effect of the zero cell count.Explanation / Answer
3.6.
TRADITIONAL METHOD
given that,
possibile chances (x)=7
sample size(n)=15
success rate ( p )= x/n = 0.467
I.
sample proportion = 0.467
standard error = Sqrt ( (0.467*0.533) /15) )
= 0.129
II.B9
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.129
= 0.252
III.
CI = [ p ± margin of error ]
confidence interval = [0.467 ± 0.252]
= [ 0.214 , 0.719]
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DIRECT METHOD
given that,
possibile chances (x)=7
sample size(n)=15
success rate ( p )= x/n = 0.467
CI = confidence interval
confidence interval = [ 0.467 ± 1.96 * Sqrt ( (0.467*0.533) /15) ) ]
= [0.467 - 1.96 * Sqrt ( (0.467*0.533) /15) , 0.467 + 1.96 * Sqrt ( (0.467*0.533) /15) ]
= [0.214 , 0.719]
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interpretations:
1. We are 95% sure that the interval [ 0.214 , 0.719] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
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