Question

Question 3 In a hospital, patients admitted with lung cancer in the previous month were queried about their residency (urban, rural) and gender. During the same period, th e researchers also studied the residency and gender of a non-cancer control patient admitted in the same hospital. The observed frequencies are tabulated below Lung cancer (Y) Residency (Z) Gender (X) Cases Controls Male Female Male Female 505 100 32 Rural 10 16 4 Urban a. [2 marks] Identify the response and the explanatory variables. b.) [I mark] Identify the type of study this was. c.) B marks] Can you use these data to compare gender with lung cancer in terms of the proportion who suffered lung cancer? Why or why not? d. [ 4 marks] Find the conditional and marginal odds ratios and interpret the associations e. [4 marks] Explain why the conditional and marginal odds ratios gives different conclusions

Answer 1

Answers :

b)The study was observational examination as the specialist did not force any trial conditions.The patients were simply watched for their smoking status.

c)We can contrast smokers and non smokers regarding the extent who endured lung disease as the all out number of patients with lung malignancy and the quantity of individuals in control bunch are given.

Residency	Gender	Cases	Control
Rural	Male	5	50
	Female	10	100
Urban	Male	16	32
	Female	4	8

From the given data :

Proportion of lung cancer in Rurals cases = 5 / 15

= 0.333

Proportion of lung cancer in Rurals cases = 10 / 15

= 0.67

Proportion of lung cancer in Rurals control = 50 / 150

0.333

Proportion of lung cancer in Rurals cases = 100 / 150

=0.67

Proportion of lung cancer in Urban cases = 16 / 20

= 0.8

Proportion of lung cancer in Urban cases = 4 / 20

=0.2

Proportion of lung cancer in Urban control = 32 / 40

= 0.8

Proportion of lung cancer in Urban cases = 8 / 40

0.2

Odds ratio of rural and urban = [0.333(1 - 0.333) ] / [0.8(1 - 0.8)]

= [ 0.333( 0.667) ] / 0.8(0.2)

= 0.222111 / 0.16

= 1.38819375

It is the ratio of probability of event in exposed group vs unexpected group

RR = 0.333 / 0.8

= 0.41625

Odds ratio of rural and urban = 1.38819375 > 1

Female as will be 1 time more than the to develop lung cancer than the Males

Proportion of smokers lung cancer in Rurals cases = 5 / 15

= 0.333

Proportion of non smokers lung cancer in Rurals control = 50 / 150

= 0.333

RR = 0.333 / 0.333

= 1

So here the females lung cancer will be equal to males