Optimal Classification of Respiratory Patterns From Manual Analyses Using Expectation-Maximization

Manual scoring (MS) of cardiorespiratory signals is the <italic>gold standard</italic> method for the analysis of respiratory data in sleep laboratories. In MS, trained, expert scorers characterize respiratory patterns by scrolling through a data record and visually identifying patterns. However, MS is limited by high intra- and inter-scorer variability and subjectivity. A strategy to mitigate this is to analyze the same respiratory data multiple times and generate a consensus. This consensus is generally determined by a majority vote (MV), where the most frequent pattern is selected as the <italic>true pattern</italic>. This paper presents expectation-maximization pattern sequence (EM-PSEQ), a novel method based on EM that estimates the <italic>true patterns</italic> optimally. A simulation study examined the accuracies of EM-PSEQ, MV, and individual scorers (IS) as a function of the number of analyses. Accuracy was measured with the Fleiss <italic>κ</italic> statistic, and is reported as <inline-formula> <tex-math notation="LaTeX">$[{\kappa _{{\rm{MDN}}}} = x;{\kappa _{{\rm{P5}}}} = y]$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">${\kappa _{{\rm{MDN}}}}$</tex-math></inline-formula>, the median value, is the expected accuracy, and <inline-formula><tex-math notation="LaTeX">${\kappa _{{\rm{P5}}}}$</tex-math> </inline-formula>, the 5th percentile value, gives the minimum accuracy for 95% confidence. IS accuracy remained constant at <inline-formula><tex-math notation="LaTeX">$[{\kappa _{{\rm{MDN}}}} = 0.67;{\kappa _{{\rm{P5}}}} = 0.60]$ </tex-math></inline-formula> as the number of analyses increased. MV accuracy increased slowly with the number of analyses and plateaued at <inline-formula><tex-math notation="LaTeX">$[{\kappa _{{\rm{MDN}}}} = 0.78;{\kappa _{{\rm{P5}}}} = 0.76]$</tex-math></inline-formula> after five analyses. In contrast, EM-PSEQ accuracy improved quickly, reaching an <italic>almost perfect</italic> value of <inline-formula><tex-math notation="LaTeX">$[{\kappa _{{\rm{MDN}}}} = 0.83;{\kappa _{{\rm{P5}}}} = 0.77]$</tex-math></inline-formula> with four analyses, and <italic> perfect</italic> accuracy <inline-formula><tex-math notation="LaTeX">$[{\kappa _{{\rm{MDN}}}} = 1.00;{\kappa _{{\rm{P5}}}} = 0.99]$</tex-math></inline-formula> after 25 analyses. EM-PSEQ performed much better than either MV or IS, and required only modest computational effort. Consequently, we believe EM-PSEQ will be a very valuable tool for clinical studies, as it can dramatically improve the accuracy of manual respiratory analysis with minimal additional cost.