Question

You are given results on a case control study on alcoholism and breast cancer, 200m participants with Breast cancer and 200 participants without cancer were selected and questioned on previous alcohol use.

	Breast Cancer (+)	Breast Cancer (-)	Total
Heavy alcohol use	40	20	60
No/low alcohol use	160	180	340
total	200	200	400

1. Calculate and interpret the appropriate measure of association for this study?
2. You later learn that 15 of the controls [Breast CANCER (-)] did not remember their previous heavy alcohol use and incorrectly reported that they were low alcohol users. By comparison all the breast cancer (+) cases correctly remembered their alcohol use. Please compare appropriate measure of association. (HINT: create a new 2x2 table below)
3. Was there evidence of Bias in this study? If so what type of Bias?

Answer 1

Yule’s coefficient of Association ‘Q’ is given by

0.384615385=Q₁(say) (using table 1)

(AB (ab)-(Ab (aB) (AB) (ab)+(Ab)(aB)

As Q is >0 implies there is a positive association between 'Breast cancer' and "use of alcohol'

Table 1

	Breast Cancer (+) denoted 'A'	Breast Cancer (-) denoted 'a'	Total
Heavy alcohol use denoted 'B'	40 (AB)	20 (aB)	60 (B)
No/low alcohol use denoted 'b'	160 (Ab)	180 (ab)	340 (b)
total	200 (A)	200 (a)	400 (N)

As it is reported that 15 of the controls [Breast CANCER (-)] did not remember their previous heavy alcohol use and incorrectly reported that they were low alcohol users. So corrected frequency table is shown in Table 2:

   0.081967213 =Q₂ (corrected) (using table 2)

(AB (ab)-(Ab (aB) (AB) (ab)+(Ab)(aB)

Table 2

	Breast Cancer (+) denoted 'A'	Breast Cancer (-) denoted 'a'	Total
Heavy alcohol use denoted 'B'	40 (AB)	35 (aB)	60 (B)
No/low alcohol use denoted 'b'	160 (Ab)	180 (ab)	340 (b)
total	200 (A)	165 (a)	400 (N)

Obviously there exists a Bias in this study as Q₁ and Q₂ are not same and this types of bias is called misclassification bias. Misclassification bias is a types of bias that appear due to negligence of data collection.