Question

The following is an excerpt from a paper published in BMJ (formerly the British Medical Journal) in 1994: Charig et al undertook a historical comparison of success rates in removing kidney stones. Open surgery had a success rate of 78% (273/350) while a minimally invasive procedure called percutaneous nephrolithotomy had a success rate of 83% (289/350), an improvement over the use of open surgery. However, the success rates looked rather different when stone diameter was taken into account. This showed that, for stones of <2 cm, 93% (81/87) of cases of open surgery were successful compared with just 83% (234/270) of cases of percutaneous nephrolithotomy. Likewise, for stones of >/=2 cm, success rates of 73% (192/263) and 69% (55/80) were observed for open surgery and percutaneous nephrolithotomy respectively. The main reason why the success rate reversed is because the probability of having open surgery or percutaneous nephrolithotomy varied according to the diameter of the stones. In observational (nonrandomised) studies comparing treatments it is likely that the initial choice of treatment would have been influenced by patients' characteristics such as age or severity of condition; so any difference between treatments could be accounted for by these original factors. Such a situation may arise when a new treatment is being phased in over time. Randomised trials are therefore necessary to demonstrate any treatment effect. This is an example of Simpson's paradox because: when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them). when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them). when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them). when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).

Answer 1

From the given question we understand that

There is an observation taken into account . It is related to Kidney operations.success rates in removing kidney stones. Following observations are made.

1. Traditionally It is seen that open surgery had a success rate of 78% (273/350) while a minimally invasive procedure called percutaneous nephrolithotomy had a success rate of 83% (289/350).

2. However, the success rates looked rather different when stone diameter was taken into account. For stones of size<2 cm, It was observed that

93% (81/87) of cases of open surgery were successful compared and just 83% (234/270) of cases of percutaneous nephrolithotomy.

3. Likewise, for stones of size >/=2 cm, success rates of 73% (192/263) and 69% (55/80) were observed for open surgery and percutaneous nephrolithotomy respectively.

It was understood that the above mentioned trends and reverse trends respectively were observed because

the probability of having open surgery or percutaneous nephrolithotomy varied according to

1. the diameter of the stones.

Now when we do observational study to validate the above inferences by comparing treatments it is likely that the initial choice of treatment would have been influenced by

a. Patients' characteristics such as age or severity of condition; so any difference between treatments could be accounted for by these original factors.

Now this is an observed Simpson's paradox which states that

In probability and statistics, we can see a particular trend appearing in several different groups of data

These trends disappears or reverses completely when these groups are combined.

Now we have been given the observation and we need to justify as to what is the reason for observing Simpson's paradox in our case.

This is an example of Simpson's paradox because:

1.when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).

2. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).

3. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).

4.when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).

Now lets us draw the table of the observations made so far .

(Here Treatment A =Open Surgery, Treatment B =Percutaneous Nephrolithotomy Surgery)

First of all we need to define and identify the lurking variable in this case .

A Lurking Variable is a variable that influences both the dependent variable and independent variable, causing a spurious association.

In our case, Observe what is this variable ?

Clearly the severity of the case is the variable which is influencing the choice of treatment.

Hence our lurking variable is the severity of the case (Stone size).

Now Think !!!!

Why does Simpson's paradox, happen??

because two effects occur together:

1. The sizes of the groups, which are combined when the lurking variable is ignored, are very different. Doctors tend to give the severe cases (large stones) the better treatment (A), and the milder cases (small stones) the inferior treatment (B). Therefore, the totals are dominated by groups 3 and 2, and not by the two much smaller groups 1 and 4.
2. The lurking variable has a large effect on the ratios; i.e., the success rate is more strongly influenced by the severity of the case than by the choice of treatment. Therefore, the group of patients with large stones using treatment A (group 3) does worse than the group with small stones (groups 1 and 2), even if the latter used the inferior treatment B (group 2).

Based on these effects, the paradoxical result is seen to arise due to

1. suppression of the causal effect of the severity of the case on successful treatment.

Hence when the less effective treatment (B) is applied more frequently to less severe cases, it can appear to be a more effective treatment.

Hence Option (C)