Analysis of variance of communication latencies in anesthesia: comparing means of multiple log-normal distributions

Anesthesiologists rely on communication over periods of minutes. The analysis of latencies between when messages are sent and responses obtained is an essential component of practical and regulatory assessment of clinical and managerial decision-support systems. Latency data including times for anesthesia providers to respond to messages have moderate (> n = 20) sample sizes, large coefficients of variation (e.g., 0.60 to 2.50), and heterogeneous coefficients of variation among groups. Highly inaccurate results are obtained both by performing analysis of variance (ANOVA) in the time scale or by performing it in the log scale and then taking the exponential of the result. To overcome these difficulties, one can perform calculation of P values and confidence intervals for mean latencies based on log-normal distributions using generalized pivotal methods. In addition, fixed-effects 2-way ANOVAs can be extended to the comparison of means of log-normal distributions. Pivotal inference does not assume that the coefficients of variation of the studied log-normal distributions are the same, and can be used to assess the proportional effects of 2 factors and their interaction. Latency data can also include a human behavioral component (e.g., complete other activity first), resulting in a bimodal distribution in the log-domain (i.e., a mixture of distributions). An ANOVA can be performed on a homogeneous segment of the data, followed by a single group analysis applied to all or portions of the data using a robust method, insensitive to the probability distribution.