I. SAS OUTPUT INTERPRETATION

SCENARIO: A study of smoking and colon cancer recruited $48$ men who have been diagnosed with colon cancer in the past $3$ years $($prevalent and incident cases$)$ and a random sample of $52$ colon cancer$-$free men who received a colonoscopy within the past month at the same U$.$S$.$ hospital where the cases are being treated. Participants were asked about their smoking history in the past $5$ years. For smoking, participants were categorized as $$exposed$$ if they reported smoking at least an average of one pack per day over the $5-$year period, and $$unexposed$$ otherwise.

Researchers suspected several other variables as possible confounders, or effect modifiers of the smoking $-$ colon cancer relationship, and so they collected information about the following variables over the past $5$ years: alcohol consumption $($dichotomized as $>=2$ vs$.<2$ drinks per day$),$ aspirin consumption $($dichotomized as $>=0\mathrm{.}75$ vs$.<0\mathrm{.}75$ mg per day$),$ coffee consumption $(>=2$ vs$.<2$ cups per day$)$ and exercise $(>=3$ vs$.<3$ times per week$).$ The SAS syntax and its output are on Blackboard, along with the dataset if you wish to run the analyses yourself. The codebook for variables is below:

Alphabetic List of Variables and Attributes

# Variable Type Length Original Format Recoding Label

$2$ alcohol Num $80=$ Unexposed $/$ No

$1=$ Exposed $/$ Yes $2$

$1$ Average $>=2$ alcoholic drinks per day

$5$ aspirin Num $80=$ No

$1=$ Yes $2$

$1$ Average $>=0\mathrm{.}75$mg aspirin per day

$3$ cancer Num $80=$ Control

$1=$ Case $2$

$1$ Has colon cancer

$7$ coffee Num $80=$ No

$1=$ Yes $2$

$1$ Average of $>=2$ cups of coffee per day

$6$ exercise Num $80=$ No

$1=$ Yes $2$

$1$ Physically active $(>=3$ times per week$)$

$1$ id Num $8$ Study ID

$4$ smoking Num $80=$ No

$1=$ Yes $2$

$1$ Totaled $>=5$ pack$-$years $($average of $>=1$ pack per day$)$

Note: All you need to answer the following questions is the SAS output that has been provided in PDF form on Blackboard. The SAS syntax is provided to give you a sense of some of the analyses performed before arriving at the final outputs; not all the syntax has associated output provided.

$(1)$ Create a table $($not directly copy from SAS output file$)$ to display the distribution of the exposure and other variables, stratified by colon cancer status $($e$.$g$.,$ describe the proportion of participants who smoked, drank alcohol, etc., among cases and controls$)$ and summarize the findings $(1-2$ sentences$)[2$ point$].$

$(2)$ Use a table $($not directly copy from SAS output file$)$ to present the study findings. The table should start with the unadjusted model, then move to assessment of confounding and effect modification, and should finally present and label the correct and final results. Describe and interpret only the final and relevant results in detail, briefly mentioning why you chose these particular results to present $($short paragraph, ~$4-5$ sentences$).[4$ points$]$

$(3)$ Discuss limitations and potential sources of bias in this study. How might these issues have affected the results and causal inferences that can be drawn from them? $($short paragraph, ~$4-5$ sentences$)[3$ points$]$

$(4)$ Suggest an alternate study design $($be specific, including details like exposure$/$outcome assessment and measure of association$)$ for this research question that would address some of the limitations that you described in Q$3.$ How could your proposal improve internal$/$external validity and the causal inferences that can be made? Does your proposal have any drawbacks? $($short paragraph, ~$4-5$ sentences$)[4$ points$]$