Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

ALVAC-AIDSVAX vaccine

  1. Sep 28, 2009 #1

    Borek

    User Avatar

    Staff: Mentor

    It hit the news in a last few days, you have probably heard about it. That's what I have found about the trial:

    And it makes me wonder - what is statistical significance of this diference? What is a confidence level that those that were given vaccine were in fact more immune? Or in other words - what is a confidence level that probability of contracting AIDS was lower in those that received vaccine? (Sure, we have to assume both group were otherwise identical).

    In theory I should know how to calculate it, but after 20 years of lying somewhere in the dark corner my statistics is so rusty I prefer not to touch it, as it may fall apart :grumpy:
     
  2. jcsd
  3. Sep 28, 2009 #2

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    There are two groups: control vs. experiment.

    If a group consists of N total individuals, n of whom were infected, then each individual within that group can be modeled as a Bernoulli trial with mean p = n/N and variance = p(1-p). A Bernoulli trial is an individual "experiment" with probability p of getting infected.

    N trials are distributed Binomial with mean = Np = n and variance = Np(1-p) for the group as a whole.

    Control group (m = 74, M = 8198):
    ...For an individual:
    ......Bernoulli probability: p = m/M = 0.00902659
    ...For the group:
    ......Binomial mean: m = 74
    ......Binomial variance: u = Mp(1-p) = 73.332.
    Experiment group (n = 51, N = 8197)
    ...For an individual:
    ......Bernoulli probability: q = n/N = 0.00622179
    ...For the group:
    ......Binomial mean: n = 51
    ......Binomial variance: v = Nq(1-q) = 50.6827.

    Unequal variances t-test:
    ...s = Sqrt[(Nu+Mv)/(MN)] = 0.122997
    ...t = (m - n)/s = 186.997
    ...d.f. = (u/M + v/N)^2 / ((u/M)^2/(M - 1) + (v/N)^2/(N - 1)) = 15,864.5
    ...The null hypothesis "true m = true n" can be rejected at a very high degree of statistical significance.

    Equal variance t-test:
    ...S = Sqrt[((M-1)u+(N-1)v)/(M+N-2)] = 7.8745
    ...s = S Sqrt[1/M + 1/N] = 0.122998
    ...t = (m - n)/s = 186.995
    ...d.f. = M + N - 2 = 16,393
    ...Again, the null hypothesis "true m = true n" can be rejected at a very high degree of statistical significance.
     
    Last edited: Sep 28, 2009
  4. Sep 28, 2009 #3

    Borek

    User Avatar

    Staff: Mentor

    Many thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook