NEED HELP ON TRYING TO SOLVE THIS. . /55 points)(public health) In 1972 a one-in

Question

NEED HELP ON TRYING TO SOLVE THIS.

. /55 points)(public health) In 1972 a one-in-six random survey of the electoral roll-largely concerned with studying heart disease and smoking _ was carried out in Whickham, a mixed urban and rural district near Newcastle upon Tyne in England. Twenty years later a follow-up study was conducted, with the results published in the journal Clinical Endocrinology in 1995 The dataset summarized below in this problem pertains to the subsample of 1,314 women in the study who were classified in the original survey either as current smokers or as never having smoked. There were relatively few women (162) who had smoked but stopped, and only 18 whose smoking habits were not recorded; these women are not included in the data here. The 20-year survival status was determined for all the women in the original survey The outcome variable Y of interest here was mortality, recorded as dead or alive in 1992; the re- searchers regarded X, smoking behavior in 1972 (current smoker or never smoked), as the supposedly causal factor (SCF), and they also measured the variable Z, age (18-64 or 65+) in 1972 Several definitions and conclusions from the field of erperimental design are relevant here o A controlled experiment is a study in which the investigators have control over X, in the sense that they assign participants to different groups defined by X (in this case, smoker (the so- called treatment group T) versus never-smoked (the control group C); controlled experiments become randomized controlled trials (RCTs) when the investigators assign the participants to T and C at random. Investigations in which the researchers have no control over who gets into T and C-typically because the participants themselves choose which group they're in are called observational studies. ·Two variables V and W are associated if as V increases W tends on average to increase or decrease, and vice versa; two variables that are not associated are independent. If both of the variables are binary i.e., if they each have only two possible values, which may without loss of generality be taken as 0 and 1-then {V and W are associated): {as V moves from 0 to 1, P(W = 1) increases or decreases) . A confounding factor (CF) is a third variable Z, distinct from Y and X, that satisfies two properties

Explanation / Answer

Part (a)

It is observational study because the researcher has no control over which woman participant would get into which group since it is automatically decided by her status in regard to her age, smoking habit and mortality. ANSWER

Part (b)

P(smoker)

= number of smokers/total number of participants = 582/1314 = 0.4429 ANSWER 1

P(smoker/18-64)

= number of smokers in 18-64/total number of participants in 18-64

= 533/1072 = 0.4972 ANSWER 2

P(smoker/65+)

= number of smokers in 65+/total number of participants in 65+

= 49/242 = 0.2025 ANSWER 3

There is a significant association between smoker and age. Probability of a young woman (18-64) being a smoker is more than double the probability of an old woman (18-64) being a smoker.

So, it may be fair to assume that as women get older they tend to leave smoking. ANSWER 4

Part (c)

P(Dead) = number of dead/ total number of participants = 369/1314 = 0.2808 ANSWER 1

P(Dead/smoker)

= number of dead who were smokers/ total number of participants who were smokers

= 139/582 = 0.2388 ANSWER 2

P(Dead/non-smoker)

= number of dead who were non-smokers/ total number of participants who were non-smokers

= 230/732 = 0.3142 ANSWER 3

Going strictly by the numbers, there is an apparently-odd relationship between mortality and smoking – non-smokers have greater chance of death than smokers which leads to an absurd conclusion that smoking improves longevity. [This is due to a hidden factor which is not considered so far. This is covered in Part (d)] ANSWER 4

Part (d)

The apparently odd conclusion derived in Part (c) is due to a relationship between mortality and age as commonly known and which is also confirmed by the figures that mortality rate rises with age.

P(Dead/18-64) = 162/1072 = 0.1511 and P(Dead/65+) = 207/242 = 0.8554, indicating an almost 5-fold increase in probability. This, in conjunction with the fact brought out in Part (b) that as women age, they tend to leave smoking leads to the apparent odd result. ANSWER

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