Statistical inferences for a twin correlation with multinomial outcomes

Current methods for statistical analysis of twin studies focus on continuous and dichotomous data, while only limited methodology exists for analysing multinomial data. As a consequence, investigators are often tempted to collapse multinomial data into two categories simply to facilitate the analysis. We address this problem by developing and evaluating two approaches to the assessment of twin correlation for an outcome variable having more than two nominal categories. One method developed is an extension of the goodness-of-fit approach, while the other method is based on large sample normal theory. Procedures for confidence interval construction are developed and compared using Monte Carlo simulation. The results show that either method may be safely used for confidence interval construction provided the number of twin pairs is large (> or =100) but that in smaller sample sizes the goodness-of-fit procedure is to be preferred on the grounds of validity. Other inference problems are also discussed, including point estimation, hypothesis testing and sample size estimation. An example is included.