Type a Using the analysis below answer the following questions: Do…

Question Type a Using the analysis below answer the following questions: Do… Type aUsing the analysis below answer the following questions: Do you agree with the authors’ final conclusion regarding when to apply Treatment A and when to apply Treatment B? Explain why or why not, either referencing the original data directly or the arguments made by the authors.How did the authors address Simpson’s Paradox in their response?Identify one passage (you may quote it) that is particularly striking to you as readers. This passage can be something you vigorously agree or disagree with, something you find surprising or confusing. Explain why this passage stands out to you and your teammates.Identify one or more elements of the authors’ report (such as the formatting, the structure, the style of writing, etc.) that you think will influence your group’s writing submissions in the future.The analysisTo whom it may concern:This memo has been written to give guidance to our surgeons about when it is better to use Open Surgery (OS) and when it is better to use Nephrolithotomy (N) in treating kidney stones. Let’s first give an overview of kidney stone removal procedures at our hospital, overall. We analyzed 700 procedures and for each one recorded the size of kidney stones removed (large or small) whether the procedure was successful (yes or no) and which procedure was applied (OS or N). We found that our hospital does a pretty good job of removing kidney stones, with a 562/700= 80.29% marginal success rate. We treat approximately equal number of cases where kidney stones are categorized as small (n = 357) vs. where they are categorized as large (n = 343). Additionally, we appear to implement the two treatment procedures at equal rates: half of our patients received open surgery and half received nephrolithotomy. Now, if you consider Table 1, it appears that treatment N, with an 82.57% success rate, outperforms treatment OS, which was only successful 78% of the time. This makes N about 4.57% better than OS. Equivalently, we calculated an odds ratio for a successful outcome and found that the odds of the surgery being successful were 33.62% higher for N treatment compared to OS treatment. You can see these results displayed in the mosaic plot to the right, where the proportion of the N column labeled ‘Success’ is slightly higher than it is in the OS column. Because N is both cheaper and less invasive and performs better overall, this might lead doctors to recommend it anytime a patient arrives for kidney stone treatment.However, the careful observer will notice a surprising results when they analyze the small stone and large stone cases separately. Treatment N was less successful at successfully removing kidney stones than Treatment OS for both cases where stones were small and where stones were large. The table on the next page summarizes this contradiction: Small stonesLarge stonesN success rate234/270 = 0.86755/80 = 0.688OS success rate81/87 = 0.931192/263 = 0.73Difference in conditional proportions of success-0.063-0.042O.R. comparing N to OS0.48150.8135O.R. comparing OS to N2.0771.229 As hospital administrators, we were initially confused by the finding that N treatment appeared to be about 4.57% better than OS treatment overall, but between 4% and 6% worse for all subgroups of patients. The table above shows that the odds-ratio for a successful outcome flips from being above 1 overall (which means that N treatment is better) to below 1 for both sizes of stones (meaning N treatment is worse). To further explore this idea, we made mosaic plots of just the small and large stone cases, shown below:Image transcription textOverall results Small stone resultsLarge stone results NepholithotomyOpenSurgery Nepholitho… Show more… Show moreThese plots really helped us realize that Simpson’s Paradox was at play here. Simpson’s Paradox describes a situation where a third, confounding variable changes the association between two other variables. In this case, we believe the size of the kidney stone confounds the relationship between treatment type and the patient’s outcome and that it is therefore inadvisable to blindly apply treatment N in all cases. Simpson’s Paradox is shown in the mosaic plots first because they show that small stones are just easier to treat than large stones – the success rate is higher in the middle plot for small stones than the right plot for large stones. This is also shown in the mosaic plots above because the proportion of successes for N treatment is higher in the overall results but lower for both small and large stone cases. In short, these plots also show us that, although the hospital appears to administer an equal number of OS and N treatments overall, it does not apply these procedures evenly to small and large stone cases. If a patient has small kidney stones that need to be removed, they are much more likely to get N treatment than OS treatment. If the patient has large kidney stones, open surgery is much more likely. We believe a good way to think about these mosaic plots is interpret the overall results on the left as the sum of the two other mosaic plots. Even though open surgery is always the better option in terms of success rates, it is less successful on large stones (where most open surgeries are) than nephrolithotomy is on small stones (where most nephrolithotomies are performed). This is why nephrolithotomy appears to be better overall, even when it is not.This leads us to our final recommendation. In general, open surgery is always the better procedure with the higher success rate. That said, it is more invasive and more expensive and so should be reserved for cases when the kidney stones are severe (i.e., large). In cases where the kidney stones to be removed are small and the work to be done is easier, we might recommend going for the less invasive procedure. Again, in the case of large kidney stones, open surgery is always recommended. I would like a detailed explanation. Thank you.  Math Statistics and Probability STA 227 Share QuestionEmailCopy link Comments (0)