Chapter 5, Problem 5.7AYK

(a)

To determine

To find: the per cent of kidney stones and mention the procedure that had the higheroverall success rate

Answer to Problem 5.7AYK

The PCNL procedure had a higher success and the per cent of kidney stones are $82.6\%$

Explanation of Solution

Given:

  

Calculation:

One study looked at the success rate of both open surgery and percutaneous nephrolithotomy (PCNL), a minimally invasive technique, for the removal of kidney stones. The success or failure of both techniques for removing kidney stones is shown in the chart.

Small stones
	Open Surgery	PCNL	Total
Success	81	234	315
Failure	6	36	42
Total	87	270	357

Large stones
	Open Surgery	PCNL	Total
Success	192	55	247
Failure	71	25	96
Total	263	80	343

Table 1: Success and failure of open surgery and PCNL on kidney removal for both small (top) and large (bottom) stones

Based on these values, the percent of kidney stones that were removed for both procedures can be calculated. The total successes for each technique from both charts will be used. Open Surgery Successes: Begin by adding open surgery successes for both small and large stones.

  $81+192=273$

Then find the total number of all open surgeries.

  $87+263=350$

Divide the open surgery successes by the total number of open surgeries performed.

  $\begin{array}{l}\frac{273}{350}=0.78\\ =78\%\end{array}$

PCNL Successes:

Begin by adding the PCNL successes for both small and large stones.

  $234+55=289$

Then find the total number of all PCNL surgeries.

  $270+80=350$

Divide the open surgery successes by the total number of open surgeries performed.

  $\begin{array}{l}\frac{289}{350}=0.8257\\ \approx 0.826\\ =82.6\%\end{array}$

Thus, the PCNL procedure had a higher success rate when factoring in all the kidney stones removed for both open surgery and PCNL.

Conclusion:

Thus, the PCNL procedure had a higher success rate and the per cent of kidney stones are $82.6\%$

(b)

To determine

To find: thepercent of all small kidney stones and large kidney stonesthat were removedand mention which type of kidney stone are easier to treat

Answer to Problem 5.7AYK

It appears that smaller kidney stones are move easily removed when looking at this data The per cent of kidney stones are $72.01\%$ and the per cent of kidney stones are $88.2\%$

Explanation of Solution

Calculation:

In addition to the above information, the success of removing small vs. large kidney stones can be calculated.

Small stones:

Begin by adding the successes for removal of small stones.

  $81+234=315$

Then find the total number of all surgeries for small kidney stones.

  $81+234+6+36=357$

Divide the small kidney stone successes by the total number of surgeries performed.

  $\begin{array}{l}\frac{315}{357}=0.8824\\ \approx 88.2\%\end{array}$

The per cent of kidney stones are $88.2\%$

Large stones:

Begin by adding the successes for removal of large stones.

  $192+55=247$

Then find the total number of all surgeries for large kidney stones.

  $192+55+71+25=343$

Divide the large kidney stone successes by the total number of surgeries performed

  $\begin{array}{l}\frac{247}{343}=0.7201\\ \approx 72.01\%\end{array}$

The per cent of kidney stones are $72.01\%$

When trying to remove small kidney stones, $88\%$ were successfully removed as compared to $72\%$ for large kidney stones.

Conclusion:

Thus, it appears that smaller kidney stones are move easily removed when looking at this data.

The per cent of kidney stones are $72.01\%$ and the per cent of kidney stones are $88.2\%$

(c)

To determine

To find: the percent of successful procedures of each type for small and large kidney stones

Answer to Problem 5.7AYK

The percent of PCNL for small and large kidney stones are $86.7\%$ and $68.8\%$

The percent of open surgery for small and large kidney stones are $93.1\%$ and $73\%$

Explanation of Solution

Calculation:

Now, the per cent of successful open surgeries and PCNL for each of the small and large stones will be determined. To do this for small kidney stones, take the number of successes for open surgery divided by the total number of open surgeries. This is then repeated for small stones successfully removed by PCNL surgeries and again for both categories of large stones.

Small stones - open surgery:

  $\begin{array}{l}\frac{81}{87}=0.931\\ =93.1\%\end{array}$

Small stones - PCNL:

  $\frac{234}{270}=86.7\%$

Large stones - open surgery:

  $\frac{192}{263}=73\%$

Large stones - PCNL:

  $\frac{55}{80}=68.8\%$

These numbers indicate that PCNL surgery performed worse than open surgeries for both small and large stones. However, when combined, it performed better overall. The reasoning for this is that the size of the kidney stones could be a lurking variable that without including it in the evaluation could lead to misinterpretation of the data.

Here, the data is best evaluated separately in order to remove the likelihood of Simpson's paradox.

Conclusion:

Therefore,

The percent of PCNL for small and large kidney stones are $86.7\%$ and $68.8\%$

The percent of open surgeryfor small and large kidney stones are $93.1\%$ and $73\%$