Related Experiment Videos
Analyzing bivariate continuous data grouped into categories defined by empirical quantiles of marginal distributions
C B Borkowf1, M H Gail, R J Carroll
1National Cancer Institute, Division of Cancer Epidemiology and Genetics, Bethesda, Maryland 20892-7368, USA.
Biometrics
|September 18, 1997
Summary
Epidemiologists often analyze grouped exposure data, but standard methods assume incorrect distributions. This study introduces a new statistical theory for empirical bivariate quantile-partitioned (EBQP) data, improving confidence intervals for the kappa statistic.
Area of Science:
- Statistics
- Epidemiology
- Biostatistics
Background:
- Epidemiologists frequently analyze bivariate continuous exposure data by categorizing it using empirical quantiles.
- This grouping results in contingency tables, but the cell counts do not follow a multinomial distribution, a common assumption in statistical analysis.
- The joint distribution of counts in such tables is termed the empirical bivariate quantile-partitioned (EBQP) distribution.
Purpose of the Study:
- To correct the inaccurate asymptotic theory for EBQP distributions previously proposed by Blomqvist (1950).
- To develop a general asymptotic theory for EBQP tables of arbitrary dimensions.
- To apply the new theory for constructing accurate confidence intervals for the kappa statistic in epidemiological studies.
Main Methods:
- Developed a general asymptotic theory for empirical bivariate quantile-partitioned (EBQP) distributions.
- Applied the new asymptotic theory to derive methods for constructing confidence intervals for the kappa statistic.
- Conducted simulation studies to evaluate the performance of the proposed confidence interval procedures.
Main Results:
- Demonstrated that Blomqvist's (1950) asymptotic theory for EBQP data is incorrect except in specific cases.
- Proposed new confidence interval procedures for the kappa statistic derived from the general EBQP asymptotic theory.
- Simulation results showed that the proposed confidence intervals achieve near nominal coverage for sample sizes over 60 in 2x2 and 3x3 tables.
Conclusions:
- Existing methods for analyzing EBQP data, including those assuming multinomial distributions, can lead to inaccurate confidence intervals for the kappa statistic.
- The newly developed general asymptotic theory and associated confidence interval procedures provide more reliable statistical inference for EBQP data in epidemiology.
- The proposed methods offer improved accuracy and coverage for assessing agreement using the kappa statistic with empirically quantile-partitioned bivariate data.