Two Prop Z Test (AIDS Example)

Introduction to Confidence Intervals and Hypothesis Testing

  • Focus on learning confidence intervals and hypothesis testing for two samples.

  • These procedures are frequently utilized in real-world scenarios.

Case Example: AIDS Vaccine Development

Historical Context

  • Prior to COVID-19, significant efforts were directed at creating a vaccine for AIDS/HIV.

  • Attention shifted to COVID-19 vaccine development, but interest in an AIDS vaccine remains relevant.

Previous Vaccine Attempts

  • Sanofi Vaccine (ALVAC-HIV):

    • Used a canary pox virus with three AIDS virus genes.

    • Tested in multiple countries, found to be safe but not protective.

  • AIDSVAX by Genentech:

    • Contained a protein from the AIDS virus, grew in hamster ovary cell culture.

    • Failed trials in various demographics including Thai drug users and gay men in 2002/2003.

Experimental Design for New Vaccine

Combining Vaccines

  • Concept: Combine two previously unsuccessful vaccines to create a potentially effective option.

  • Initial considerations include:

    • Ensuring safety through preliminary trials.

    • Testing on small human subject batches after animal trials to gauge safety further.

Controlled Randomized Experiment

  • Key features:

    • Split participants into treatment group (receives vaccine) and control group (receives placebo).

    • Monitor participants over time based on their natural lifestyles rather than direct exposure to HIV.

Data Collection

  • Track the number of participants who contract HIV (x) and the number in each group (n).

  • Focus on calculating proportions (p hat) for both groups:

    • p hat = x/n.

Statistical Analysis of Data

Measurement of Effectiveness

  • Hypothesis testing will quantify vaccine effectiveness.

  • This involves a two-sample test to compare proportions:

    • Safe but not protective means past vaccines did not risk participants but failed to prevent infection.

    • Aim is to determine if combined vaccine is statistically significant in reducing infection rates.

Analytical Steps

Define Parameters

  • Null Hypothesis (H0):

    • The percentage of infection in the vaccinated group = percentage in the control group.

  • Alternative Hypothesis (H1):

    • The percentage of infection in the vaccinated group is less than that in the control group.

Experiment Setup

    • Assign groups of volunteers into treatment and control groups (e.g., 8,201 each).

    • Monitor long-term outcomes, likely spanning several years.

Hypothesis Testing Process

Two-Proportion Z-Test

  • Gather data:

    • Treatment group: 51 infections.

    • Control group: 74 infections.

  • Calculate proportions, p hats for each group to assess the effectiveness of the vaccine.

Statistical Significance

  • P-value analysis will guide decisions:

    • Comparing p-values to an alpha level (suggested α = 0.01 for conservative results).

  • Higher confidence is required in medical trials due to ethical considerations.

Conclusion of Experiment

Interpretation of Results

  • The p-value indicates how convincing the results are regarding vaccination efficacy.

  • If p-value < alpha level, reject null hypothesis, affirming vaccine efficacy.

  • If p-value > alpha level, fail to reject null hypothesis, suggesting lack of proof for the vaccine's protective effect.

Consideration of Adjusting Alpha Levels

  • Depending on the situation and test subject demographics, the alpha level may be adjusted to ensure ethical treatment.

    • Example: In the context of Alzheimer's drugs, a higher alpha can be justified due to lack of existing treatments.

Ethical Considerations in Test Design

  • Ensuring a fair experiment requires considering ethical implications, focusing on both participant safety and scientific integrity.

    • Better outcomes could result from focusing on higher-risk groups even if this is cost-prohibitive.