Which treatment

[mmiguel]

You are a doctor in charge of a large hospital, and you have to decide which treatment should be used for a particular disease. You have the following data from last month: there were 390 patients with the disease. Treatment A was given to 160 patients of whom 100 were men and 60 were women; 20 of the men and 40 of the women recovered. Treatment B was given to 230 patients of whom 210 were men and 20 were women; 50 of the men and 15 of the women recovered.

A.) Which treatment is better for men?

B.) Which treatment is better for women?

C.) Which treatment is better for any person, regardless of gender?

[phil1882]

B for the first 2, A for the third. (weird!)

Edited September 4, 2012 by phil1882

[mmiguel]

B for the first 2, A for the third. (weird!)

So which treatment deserves further investment by the charities supporting people with this disease?

[jim]

B for men, B for women, so obviously B is the better treatment regardless of gender--although this might not be statistically significant.

But if you had only told me the overall numbers without a gender breakdown I would have picked A--but given the gender breakdown info I pick B.

[phil1882]

jim, try actually doing the math.

60/160 > 65/230

if you were to invest in a medicine, i would however recommend B. doctors are generally given the gender of their patient.

A would only be better where gender is not known.

[Pat22ryan]

Calculate the number of recoveries per 1,000 patients treated.

Test A:

Men = 250/1000

Women = 666/1000

Test B:

Men = 238/100

Women = 500/1000

Accordingly Treatment A is prefered for both sexes.

[phil1882]

pat, I'm not sure where you're getting those numbers.

390 patients treated.

160 given test A; 230 test B.

if 1000 patients treated, the ratios should be the same.

304 given test A; 696 test B

190 of test A male, with 38 recovering

114 of test A female, with 76 recovering.

635 of test B male, with 151 recovering.

61 of test B female, with 46 recovering.

again, test B is better if you know the gender of your patient, but if you don't test A is better.

Edited September 4, 2012 by phil1882

[phil1882]

edit: did my first calculation wrong! whoops.

if 1000 patients treated,

410 given test A; 590 test B

256 of test A male, with 51 recovering

154 of test A female, with 103 recovering.

539 of test B male, with 128 recovering.

64 of test B female, with 38 recovering.

again, test B is better if you know the gender of your patient, but if you don't test A is better.

[kbrdsk]

I give my funding to treatment B as long as they promise to stop testing such a disproportionately small number of women.

[Rob_Gandy]

Well it all depends on how you look at the data. If we think about totals 60/160 or 37.5% of the people taking A recovered and 65/230 or about 28.3% of the people taking B recovered, so A looks better. If we look at all four groups separately 20/100 or 20% of men recovered with A but 50/210 or 23.8% men recovered with B and 40/60 or 66.7% of women recovered with A but 15/20 or 75% or women recovered with B, so B looks better. I'd say B for now, but I'm still looking at the numbers.

[jim]

Perhaps this will help clarify things. Suppose we find the average height of college men is greater than it was 60 years ago, the average height of college women is also greater, but the average height of college students is less than it was 60 years ago. Would this suggest that people are taller or shorter than they were 60 years ago.

[superprismatic]

Arrr, mesmells a rat................Methinks Simpson's Paradox is rearing its ugly head!

[blubber]

1. b

2. a

3. b

[blubber]

oops

[blubber]

1. b

2. a

3. b

[plasmid]

Ah, the dangers of interpreting medical research. The way the OP is posed - looking at data in the hospital over the past month and seeing how patients who got treatment A did compared to those who got treatment B - is what's called a retrospective study. These are generally considered to be the least reliable studies for comparing the effects of two different treatments, and the biggest confounding factor in interpreting them tends to be that the physicians aren't randomly assigning patients to different therapies (although there are certainly other confounders).

For example: does having ICU level of care actually do people any good? If the survival of hospitalized patients who go to the ICU is 60%, and the survival of those who don't go to the ICU is 95%, a very simple minded interpretation would be that ICUs are no good and are actually harming patients. Of course, what's really going on is that doctors are sending patients to the ICU only if they look like they're in serious trouble and have a higher chance of dying in the first place. If you really wanted to find out if ICUs work, you'd have to do a randomized study - say anytime a doctor wants to send someone to the ICU, the study coordinator flips a coin and then either allows or prohibits sending them to the unit. (Of course, then you have to get informed consent from patients who are willing to sign up for a study that will randomize them to having or not having ICU availability; good luck getting people to sign up.)

In this case, the docs are more likely to give treatment A to a woman and B to a man, and within each gender patients who got treatment B were more likely to recover. If you ask the docs why they're doing that, they might be able to give you a good reason. (Maybe B is a better treatment for motion sickness but causes excessive facial hair growth?) So to answer the question posed of which treatment to select for the hospital - there's not enough information presented.

[Huruey]

A) Medicine B

B) Medicine B

C) Medicine B

Medicine A has a success rate of 20% for men, 67% for women, and 43% if the gender is unknown.

Medicine B has a success rate of 24% for men, 75% for women, and 49% if the gender is unknown.

Edited September 5, 2012 by Huruey

[Rox53]

I would say that the sample size of women is too small to make an accurate assessment, and that more female patients need to be assessed before a useful result can be found.