Missing observations are common in medical research and health survey research. Several statistical methods to handle the missing data problem have been proposed. The EM algorithm (Expectation-Maximization algorithm) is one of the ways of efficiently handling the missing data problem based on sufficient statistics. In this paper, we developed statistical models and methods for survey data with multivariate missing observations. Especially, we adopted the Em algorithm to handle the multivariate missing observations. We assume that the multivariate observations follow a multivariate normal distribution, where the mean vector and the covariance matrix are primarily of interest. We applied the proposed statistical method to analyze data from a health survey. The data set we used came from a physician survey on Resource-Based Relative Value Scale(RBRVS). In addition to the EM algorithm, we applied the complete case analysis, which used only completely observed cases, and the available case analysis, which utilizes all available information. The residual and normal probability plots were evaluated to access the assumption of normality. We found that the residual sum of squares from the EM algorithm was smaller than those of the complete-case and the available-case analyses.
Biostatistics ; Dataset ; Health Surveys* ; Models, Statistical ; Relative Value Scales

BACKGROUND: There have been a number of studies on mitral valve replacement and repeated percutaneous mitral balloon valvotomy for mitral valve restenosis after percutaneous mitral balloon valvotomy. However, studies on mitral valve repair for these patients are rare. In this study, we analyzed postoperative outcomes of mitral valve repair for mitral valve restenosis after percutaneous mitral balloon valvotomy. METHODS: In this study, we assessed 15 patients (mean age, 47.7+/-9.7 years; 11 female and 4 male) who underwent mitral valve repair between August 2008 and March 2013 for symptomatic mitral valve restenosis after percutaneous mitral balloon valvotomy. The mean interval between the initial percutaneous mitral balloon valvotomy and the mitral valve repair was 13.5+/-7 years. The mean preoperative Wilkins score was 9.4+/-2.6. RESULTS: The mean mitral valve area obtained using planimetry increased from 1.16+/-0.16 cm2 to 1.62+/-0.34 cm2 (p=0.0001). The mean pressure half time obtained using Doppler ultrasound decreased from 202.4+/-58.6 ms to 152+/-50.2 ms (p=0.0001). The mean pressure gradient obtained using Doppler ultrasound decreased from 9.4+/-4.0 mmHg to 5.8+/-1.5 mmHg (p=0.0021). There were no early or late deaths. Thromboembolic events or infective endocarditis did not occur. Reoperations such as mitral valve repair or mitral valve replacement were not performed during the follow-up period (39+/-16 months). The 5-year event-free survival was 56.16% (95% confidence interval, 47.467-64.866). CONCLUSION: On the basis of these results, we could not conclude that mitral valve repair could be an alternative for patients with mitral valve restenosis after percutaneous balloon mitral valvotomy. However, some patients presented with results similar to those of mitral valve replacement. Further studies including more patients with long-term follow-up are necessary to determine the possibility of this application of mitral valve repair.
Balloon Valvuloplasty ; Disease-Free Survival ; Endocarditis ; Female ; Follow-Up Studies ; Humans ; Mitral Valve* ; Ultrasonography