Statistical analyses of the relative risk.

Area of Science:

• Epidemiology
• Biostatistics
• Statistical Modeling

Background:

• Relative risk (R) compares disease probabilities (P1/P2) between populations.
• Retrospective and prospective studies present unique challenges in risk analysis.
• Accurate statistical methods are crucial for valid epidemiological research.

Purpose of the Study:

• To develop and illustrate statistical methods for analyzing relative risk in epidemiological studies.
• To explore the relationship between relative risk and odds ratio in retrospective designs.
• To provide methods for prospective studies, particularly with small probabilities and large sample sizes.

Main Methods:

• Developed the relationship between relative risk and odds ratio for retrospective studies.
• Utilized exponential models with sufficient statistics for exact significance tests and confidence intervals.
• Extended methods to account for misclassification, matching, stratification, and combining results across strata.
• Applied Poisson distribution for prospective studies with small probabilities and large sample sizes.
• Adjusted for covariates like sex and age in comparative population analyses.

Main Results:

• Established exact conditional tests and confidence intervals for relative risk analysis.
• Demonstrated the application of these methods using case-control studies (e.g., HL-A frequencies and cancer).
• Provided examples of prospective study analyses, including comparisons of skin cancer risks across latitudes and cancer risks in fluoridated vs. non-fluoridated cities.

Conclusions:

• The proposed statistical methods offer robust tools for relative risk estimation and hypothesis testing in diverse epidemiological settings.
• Accurate analysis requires careful consideration of study design, potential biases (e.g., misclassification), and covariates.
• The methods are applicable to both retrospective and prospective studies, enhancing the reliability of disease risk comparisons.