It dawns on me that it might be helpful for me to give a more concrete example of what I'm talking about. Drawing on something in my own line of work, but which I think requires no specialized knowledge to understand, consider this example.
Hospitalization length of stay (the number of days from admission to discharge) is a variable of great importance to hospital administration. Because hospitals are mostly paid a flat fee for a hospitalization based on the final diagnoses, they can profit by taking actions that lead to shorter lengths of stay. That both enables them to recycle the beds to new patients more frequently and also reduces the costs associated with keeping the patient in the hospital longer. So administrations are often eager to find ways to reduce length of stay.
It turns out that length of stay has a very strange distribution in most general hospitals. There is a huge spike in the distribution at 0 (i.e. a stay that begins and ends the same day) and 1 day, followed by rapidly decreasing numbers of hospitalizations with each additional day. As a result, the median length of stay is 4 days: half of all patients are discharged within 4 days of admission. The 75th percentile is 7 days, and the 90th percentile is 14 days. Even the 99th percentile is just 46 days. Yet, there is a very long tail on this distribution that extends out to stays measured in years. There are very few of those, but they are very lengthy indeed.
Now, as you might guess, different medical situations are characterized by different distributions of length of stay. The shortest stays are typically for ambulatory surgery procedures, or treatment of acute conditions that respond quickly (e.g. an asthma attack often can be resolved in a matter of several hours). The typical admission for obstetrical care or treatment of a simple pneumonia will typically be somewhere in the 2-5 day range. Those very long stays in the right tail of the distribution mostly fall into two different categories. One is patients who are too ill to go home but who are, for various social or economic reasons, very difficult to place in a long-term care facility. They linger in the hospital until some suitable disposition can be arranged, and this can take many months or extend into years. The other group is patients with disastrous medical conditions who remain critically ill and on life support with failing organ systems, but who neither recover nor die, and just linger in this awful limbo state, punctuated by various crises that turn out not to be fatal, for the long term. As you might imagine, things that might be done to shorten the shorter stays are likely to have no impact on the longest ones, and vice versa.
So suppose I were to design a study to test the effect of some administrative (not medical*) intervention such as changes in staffing or acquisition of certain equipment, or acquiring a nursing home, or a hospice, and would like to assess its effect on length of stay. As already mentioned, it is unlikely that any such intervention is likely to have an across-the-board effect on length of stay at all scales. So in planning the analysis of that data, I would ask myself which group of stays would be most likely to be affected by that particular intervention. If, say, this particular intervention is most likely going to shorten the very lengthy stays, it is fair to say that this effect would not be detectable by looking at median length of stay in the intervention and control groups. A more suitable analysis would compare the means (which probably won't be affected very much, but at least they would budge a little bit, or, better, probably compare the 99th or 99.5th percentiles, something like that. I would also add that because the number of very long stays is small, the effect would have to be very large to be of much practical value to the hospital's bottom line.
By contrast, if the intervention were most likely to shave a day, on average, from the people who are in that middle group of 2-5 day stays, there are enough of these people that a modest effect would be economically important to the hospital. And, the median length of stay would be a very good statistic with which to look for an effect. The mean would surely show some difference as well, although perhaps less since the current mean is about 6.5 days which is slightly outside the typical range for this group of patients.
So I think this example shows how the choice of statistic to examine depends on the distribution of the outcome variable being measured, and also depends on the substance of the intervention and where and how it is likely to have an effect.
*I don't want to consider medical interventions here because they would be targeted at patients with specific diseases or conditions, and the effects would be measured only in that subset of patients. What I have in mind are broad-based interventions that would be implemented without regard to any patient's specific situation, and would be implemented hospital-wide (or, during the study, implemented on half of the hospital floors or departments, with the other half serving as a control group). These would constitute changes in the overall functioning of the hospital or its environment.
Hospitalization length of stay (the number of days from admission to discharge) is a variable of great importance to hospital administration. Because hospitals are mostly paid a flat fee for a hospitalization based on the final diagnoses, they can profit by taking actions that lead to shorter lengths of stay. That both enables them to recycle the beds to new patients more frequently and also reduces the costs associated with keeping the patient in the hospital longer. So administrations are often eager to find ways to reduce length of stay.
It turns out that length of stay has a very strange distribution in most general hospitals. There is a huge spike in the distribution at 0 (i.e. a stay that begins and ends the same day) and 1 day, followed by rapidly decreasing numbers of hospitalizations with each additional day. As a result, the median length of stay is 4 days: half of all patients are discharged within 4 days of admission. The 75th percentile is 7 days, and the 90th percentile is 14 days. Even the 99th percentile is just 46 days. Yet, there is a very long tail on this distribution that extends out to stays measured in years. There are very few of those, but they are very lengthy indeed.
Now, as you might guess, different medical situations are characterized by different distributions of length of stay. The shortest stays are typically for ambulatory surgery procedures, or treatment of acute conditions that respond quickly (e.g. an asthma attack often can be resolved in a matter of several hours). The typical admission for obstetrical care or treatment of a simple pneumonia will typically be somewhere in the 2-5 day range. Those very long stays in the right tail of the distribution mostly fall into two different categories. One is patients who are too ill to go home but who are, for various social or economic reasons, very difficult to place in a long-term care facility. They linger in the hospital until some suitable disposition can be arranged, and this can take many months or extend into years. The other group is patients with disastrous medical conditions who remain critically ill and on life support with failing organ systems, but who neither recover nor die, and just linger in this awful limbo state, punctuated by various crises that turn out not to be fatal, for the long term. As you might imagine, things that might be done to shorten the shorter stays are likely to have no impact on the longest ones, and vice versa.
So suppose I were to design a study to test the effect of some administrative (not medical*) intervention such as changes in staffing or acquisition of certain equipment, or acquiring a nursing home, or a hospice, and would like to assess its effect on length of stay. As already mentioned, it is unlikely that any such intervention is likely to have an across-the-board effect on length of stay at all scales. So in planning the analysis of that data, I would ask myself which group of stays would be most likely to be affected by that particular intervention. If, say, this particular intervention is most likely going to shorten the very lengthy stays, it is fair to say that this effect would not be detectable by looking at median length of stay in the intervention and control groups. A more suitable analysis would compare the means (which probably won't be affected very much, but at least they would budge a little bit, or, better, probably compare the 99th or 99.5th percentiles, something like that. I would also add that because the number of very long stays is small, the effect would have to be very large to be of much practical value to the hospital's bottom line.
By contrast, if the intervention were most likely to shave a day, on average, from the people who are in that middle group of 2-5 day stays, there are enough of these people that a modest effect would be economically important to the hospital. And, the median length of stay would be a very good statistic with which to look for an effect. The mean would surely show some difference as well, although perhaps less since the current mean is about 6.5 days which is slightly outside the typical range for this group of patients.
So I think this example shows how the choice of statistic to examine depends on the distribution of the outcome variable being measured, and also depends on the substance of the intervention and where and how it is likely to have an effect.
*I don't want to consider medical interventions here because they would be targeted at patients with specific diseases or conditions, and the effects would be measured only in that subset of patients. What I have in mind are broad-based interventions that would be implemented without regard to any patient's specific situation, and would be implemented hospital-wide (or, during the study, implemented on half of the hospital floors or departments, with the other half serving as a control group). These would constitute changes in the overall functioning of the hospital or its environment.
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