Help: Paired Proportions

Aim: To test significant difference in paired proportions.

Formula Used: for 2 tailed hypothesis

P10 = Proportion of Pairs with condition 1 positive and condition 2 negative, amongst all pairs in the study

P01 = Proportion of Pairs with condition 1 negative and condition 2 positive, amongst all pairs in the study

Example 1:
Suppose a dietary regimen is to be introduced to test its effect on weight. A similar study amongst 100 persons is available in literature, in which, initially, 25 were obese and 75 were non-obese. After a period of 1 year, it reported that out of 25 obese persons 10 have reduced weight (are now in non-obese group), and remaining 15 remained obese. However, amongst 75 non-obese subjects, 5 have become obese and remaining 70 remained non-obese. This is a before-after study involving proportions.
How can we calculate sample size required for similar study to test the significance at 95% confidence and 80% power?

	After dietary regimen
		Obese	Non-Obese	Total
Before dietary regimen	Obese	15	10	25
	Non-Obese	5	70	75
	Total	20	80	100

Please study carefully above table, which shows 15 persons are obese for both the times, 70 persons non-obese for both the times. These "time pairs" are concordant, meaning no change in result.

Similarly, there are 10 persons who were obese before but turned non-obese after the dietary regimen. Similarly, there are 5 persons who were non-obese before but turned obese after the dietary regimen.
These 10 and 5 are discordant pairs, meaning different results at two times. Thus, 10 is the number of persons who have condition 1 (before regimen) positive and condition 2 negative.
Similarly, 5 is the number of persons who have condition 1 (before regimen) negative and condition 2 positive. For details of the McNemar test, please click here.
So, 10% is the first input and 5% is the second input. After putting these values, and confidence of 95% and power of 80%, the required sample size is 469. For this example, 469 "time pairs" we must have. So 469 people must be included in the study and weights are taken for two times.

Example 2:
Suppose a pair matched case-control study is to be conducted to test the association of Oral Cancer and tobacco chewing. Cases and controls are matched for age, gender and smoking status. Following are the results of a pilot study.

	Controls Exposed
		Yes	No	Total
Cases Exposed	Yes	10	20	30
	No	7	23	30
	Total	17	43	60

In above table a pair is formed of a case and a control. This pilot study shows 20 pairs with condition 1 positive (case exposed to tobacco chewing: +ve) and condition 2 negative(control exposed: -ve). There are 7 pairs with condition 1 negative (case exposed: -ve) and condition 2 positive(control exposed: +ve). These 20 and 7 are discordant pairs, meaning different results for two persons in pair. There are a total of 60 pairs. So, 20*100/60 = 33.34% is the first input and 7*100/60 = 11.67% is the second input. After putting these values, and confidence of 95% and power of 80%, the required sample size is 73 pairs (means 73 cases and 73 controls).

@ Sachin Mumbare