An experimental design or experimental study must have an intervention, by definition. Case-control studies are observational studies, not experimental. This question is technically incorrect. They wanted to amke a point that case-control studies are time and cost efficient since they don't require following patients over time or any resources besides reviewing/gathering information. Case series could not test this hypothesis.

Also, the wording "associated wit an increased risk" somewhat alludes to case-control studies only having the ability to find odds of an associations between exposure and outcome, but not establish causal relationship.

I woud do a retrospective cohort here. I don't think this question is correct and provides too little information to get the correct answer. "Time efficient" is the operant word here but they simply didn't consider that retrospective cohort would be a better design here as long as the variables are coded.

I think something not mentioned yet is the fact that odds ratio can be used to estimate relative risk in RARE diseases as per the Rare Disease Assumption (where disease prevalence is <10%). Although the cancer in this question is described as "common," (common relative to other cancers), the cancer is still probably rare overall.

I think the key on this question is recognizing how much "most time-efficient" jumps out in the question stem - a pretty unique thing to be specifically asking. Going off that and the fact they want to look at exposure -> outcome, by far the fastest approach would be to find people who currently have the dz in question and then just ask them if they have a previous exposure aka case-control.

I think key here is they are investigating the hypothesis of ammount of arsenicin water increases RISK of cancer.... best way to measure risk is case control.

pretty good summary