A total of 21 participants were recruited, but one participant did not record observations on two devices (see Table 1). On average, 302 valid respiratory rate measurements were recorded per device for all participants (between 192 and 385). Bland Altman diagrams were drawn showing the differences in respiratory rate from the mean (see Figures 1 and 2), with the match limits superimposed on mixed effects and the corresponding confidence intervals at 95%. Table 2 presents the (combined) standard deviations between participants and the total number of differences, both for the original mixed-effect model, including outliers, and for a revised analysis of mixed effects with outliers. In this table, the overall standard deviation represents the square root of the sum of variances within and between participants. Table 3 shows the corresponding 95% bootstrap confidence intervals around the compliance limits for the two mixed-effect model series. Respiratory rate was measured in 21 people with a series of COPD severities. Participants were asked to perform eleven different activities, representative of daily life, during a standardized protocol based on the 57-minute laboratory. A mixed effect agreement limit method was used to assess the compliance of five commercially available monitors (camera, photoplethysmography (PPG), impedance, accelerometer and mammary ligament) with the current gold standard device for measuring respiratory rate. To calculate the mixed effect limits of the chord, we analyzed the differences of each device from the gold standard using a regression model of mixed effects, including participants as a random effect and activity as a fixed effect, using the nlme package [13] in R-Software version 3.2.3 [14]. If Yij represents the jth-conjugate difference in breathing frequency between devices for patient i, which expresses the k-th activity, the differences in form are modeled: α being the constant interceptic term, the accidental effect of the i-patient, the fixed effect of the k-th activity and the error for the paired difference j on the i-ten.

Average distortion and compliance limits are displayed by dotted lines, while confidence intervals are displayed by pointed lines. (A) Camera: speed per second. (B) Camera: Rate per minute. (C) PPG: gross. (D) PPG: filtered median. The simple method of 95% compliance limits is based on the assumption that the mean and standard deviation of the differences are constant, i.e. they do not depend on the size of the measurement. In our original work, we described the usual situation, where the standard deviation is proportional to the size, and described a method using a logarithmic transformation of the data. In our 1999 overall work (Bland and Altman 1999), we described a method for managing each relationship between the mean and SD of differences and the size of the measure. (That was Doug Altman`s idea, I can`t borrow.) The limitations of the mixed effects of the compliance analysis allowed us to answer the question of which devices showed the highest compliance with the gold standard device with respect to the measurement of breathing rates. In particular, the participant-based estimation and general standard deviations of the differences easily obtained from the mixed effects model results clearly indicated that accelerometer and chest band devices performed best. To compare the measurement systems with the Bland Altman method, the differences between the different measurements of the two different measurement systems are calculated, and then the mean and standard deviation are calculated.

The 95% “concordance limits” are calculated as the mean of the two minus and plus values 1.96 standard deviation. This 95 percent limit should contain the difference between the two measurement systems for 95 percent of future measurement pairs. If we evaluate the approximate 95% match limits that ignore this relationship, we have a mean difference = 0.3625 mmol/L, SD = 1.2357 mmol/L Bland-Altman graphs are widely used to assess the concordance between two different instruments or two measurement techniques…