Project delves into a classic case study of Simpson's Paradox, a statistical phenomenon where a trend apparent in several different groups of data disappears or reverses when these groups are combined. Utilizing a dataset from a 1986 study by a group of urologists in London, we examine the effectiveness of two kidney stone treatments: Treatment A (open surgery) and Treatment B (percutaneous nephrolithotomy). This analysis reveals how subgroup analysis can lead to different conclusions about treatment effectiveness, underscoring the importance of careful data interpretation in medical research.
Original paper: Charig CR, Webb DR, Payne SR, Wickham JE. Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy. Br Med J (Clin Res Ed). 1986 Mar 29;292(6524):879-82. doi: 10.1136/bmj.292.6524.879.
RPubs: https://rpubs.com/irfanezi/1145839
The dataset comprises 700 patients who underwent treatments for kidney stones. It includes the following variables:
Treatment: Type of treatment (A: open surgery, B: percutaneous nephrolithotomy)Stone Size: Size of the kidney stone (large, small)Success: Outcome of the treatment (1: success, 0: failure)
- To compare the overall success rates of Treatment A and Treatment B.
- To analyze the success rates of treatments by kidney stone size.
- To demonstrate Simpson's Paradox in the context of treatment effectiveness.
The analysis involves:
- Descriptive statistics to summarize the overall and subgroup success rates.
- Chi-squared tests to examine the association between treatment type and success rates.
- Logistic regression to model the probability of treatment success, considering treatment type and stone size.
- Visualizations to illustrate the distribution of treatment outcomes and the impact of Simpson's Paradox.
Our analysis confirmed the presence of Simpson's Paradox in the dataset. While Treatment B showed a higher overall success rate, subgroup analysis revealed that Treatment A was more effective for both large and small kidney stones. This paradox highlights the critical role of stone size in determining the best treatment option and the necessity of subgroup analysis in medical research.
The insights drawn from the analysis of the kidney stone treatment dataset can be summarized as follows:
The analysis showed significant differences in success rates depending on the size of the kidney stone. Small stones had higher success rates compared to large stones across treatments, which is consistent with medical expectations. The logistic regression model confirmed that stone size significantly affects treatment success, with large stones being less likely to result in a successful outcome.
The logistic regression analysis did not find a statistically significant difference in success rates between Treatment A and Treatment B when controlling for stone size. This suggests that, overall, neither treatment has a superior effectiveness over the other across all stone sizes. However, the lack of significance could also be due to sample size, variability in the data, or other factors not accounted for in this simple model.
The Chi-squared test provided strong evidence of an association between the type of treatment administered and the size of the kidney stone. This might indicate that treatment decisions could be influenced by stone size or that certain treatments are preferred for specific stone sizes, which could have implications for clinical practice.
The negative coefficient for stone size in the logistic regression model highlights the importance of stone size as a predictor of treatment success. This insight is crucial for medical professionals when advising patients about the expected outcomes of their treatment options.
The project emphasizes the importance of careful data analysis in healthcare, particularly when making treatment decisions. It also serves as a practical example of Simpson's Paradox, illustrating how aggregated data can mask important subgroup differences. Future research should consider additional factors that may influence treatment outcomes, such as patient health status and specific treatment protocols.
Code runs on R.