Question

Bob reported that the patients suffering from the “Mad Man Disease” who used his “magic dust” elixir properly resulted in an odds-ratio = .6 relative to controls who did not use his elixir, whose probability of suffering from the “Mad Man Disease” was only p = .3.

(a) Describe the meaning of the odds-ratio for elixir users in words.

(b) What was the probability of suffering from the “Mad Man Disease” for the elixir group?

Answer 1

Answer:

a)

Odds-ratio for elixir :

Here we can say that the Odds-ratio for elixir is defined as the ratio of the chance of elixir users suffering from mad man disease to that of the chance of non-users suffering from the mad man disease.

i.e.,

Odds-ratio for elixir = Probability of elixir users suffering from mad man disease / Probability of non-users suffering from the mad man disease.

b)

Now to determine the probability of suffering from the “Mad Man Disease” for the elixir group

i.e.,

Given,

Odds-ratio elixir = 0.5

Non-users likelyhood = 0.3

Let us assume X be the Probability of elixir users suffering from mad man disease

Now consider,

Odds-ratio for elixir = Probability of elixir users suffering from mad man disease / Probability of non-users suffering from the mad man disease.

substitute given values in above formula

0.6 = X / 0.3

X = 0.3*0.6

X = 0.18

Hence the probability of elixir users suffering from mad man disease is 0.18