Valid statistical inference methods for incomplete contingency table with three-category missing data

Abstract

Missing observations in r × c contingency tables often occur in medical, bio-pharmaceutical and epidemiological researches. The most common method to analyze incomplete contingency tables simply removes the non-response counts from both variables or depends on an independence assumption, which may be improper and could result in unreliable conclusions because of the under-estimation of the uncertainty. In this article, we first derive the valid sampling distribution of the observed counts by taking three categories missing data into consideration under the assumption of missing at random and the assumption of the total number of observations being fixed. Next, based on the new sampling distribution, the Fisher scoring algorithm for calculating the maximum likelihood estimates of parameters is developed, and the small-sample bootstrap confidence interval method is also provided. In addition, we theoretically compare the proposed sampling distribution with two existing sampling distributions, and conduct some simulations to investigate the performance of the three different sampling distributions in statistical inferences. Finally, two real data sets are analyzed to illustrate the newly proposed sampling distribution and corresponding statistical methods.

Keywords:

• Bootstrap methods
• Categorical random variable
• Incomplete contingency tables
• Missing at random
• Valid sampling distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H17 Contingency tables

Additional information

Funding

Xifen Huang and Guo-Liang Tian’s researches are partially supported by the National Natural Science Foundation of China (11901515, 11771199), respectively. Jiajuan Liang’s research is partially supported by United International College (UIC) Start-up Research Fund R72021106.