title: Confidence intervals construction for difference of two means with incomplete correlated data.
abstract: BACKGROUND
  Incomplete data often arise in various clinical trials such as crossover trials, equivalence trials, and pre and post-test comparative studies. Various methods have been developed to construct confidence interval (CI) of risk difference or risk ratio for incomplete paired binary data. But, there is little works done on incomplete continuous correlated data. To this end, this manuscript aims to develop several approaches to construct CI of the difference of two means for incomplete continuous correlated data.
  
  
  METHODS
  Large sample method, hybrid method, simple Bootstrap-resampling method based on the maximum likelihood estimates (B 1) and Ekbohm's unbiased estimator (B 2), and percentile Bootstrap-resampling method based on the maximum likelihood estimates (B 3) and Ekbohm's unbiased estimator (B 4) are presented to construct CI of the difference of two means for incomplete continuous correlated data. Simulation studies are conducted to evaluate the performance of the proposed CIs in terms of empirical coverage probability, expected interval width, and mesial and distal non-coverage probabilities.
  
  
  RESULTS
  Empirical results show that the Bootstrap-resampling-based CIs B 1, B 2, B 4 behave satisfactorily for small to moderate sample sizes in the sense that their coverage probabilities could be well controlled around the pre-specified nominal confidence level and the ratio of their mesial non-coverage probabilities to the non-coverage probabilities could be well controlled in the interval [0.4, 0.6].
  
  
  CONCLUSIONS
  If one would like a CI with the shortest interval width, the Bootstrap-resampling-based CIs B 1 is the optimal choice.
authors.affiliation: Department of Statistics, Yunnan University, No.2 Cuihu North Road, Kunming, 650091, China. ynlhq08@163.com.
authors.forename: Hui-Qiong
authors.initials: HQ
authors.lastname: Li
authors.affiliation: Department of Statistics, Yunnan University, No.2 Cuihu North Road, Kunming, 650091, China.
authors.forename: Nian-Sheng
authors.initials: NS
authors.lastname: Tang
authors.affiliation: School of Statistics, Beijing Normal University, No. 19 XinJieKouWai St., HaiDian District, Beijing, China.
authors.forename: Jie-Yi
authors.initials: JY
authors.lastname: Yi
mesh_terms: D000280:Administration, Inhalation; D001249:Asthma / Q000175:diagnosis / Q000188:drug therapy* / Q000453:epidemiology; D016001:Confidence Intervals; D018592:Cross-Over Studies; D004305:Dose-Response Relationship, Drug; D004334:Drug Administration Schedule; D005260:Female; D000068759:Formoterol Fumarate / Q000008:administration & dosage*; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D015233:Models, Statistical; D016017:Odds Ratio; D012680:Sensitivity and Specificity
chemical_list: D000068759:Formoterol Fumarate
keywords: Bootstrap; Confidence interval; Correlated data; Incomplete data