Quantile Regression: A Statistical Tool for Out-of-hospital Research

The performance of out-of-hospital systems is frequently evaluated based on the times taken to respond to emergency requests and to transport patients to hospital. The 90th percentile is a common statistic used to measure these indicators, since they reflect performance for most patients. Traditional regression models, which assess how the mean of a distribution varies with changes in patient or system characteristics, are thus of limited use to researchers in out-of-hospital care. In contrast, quantile regression models estimate how specified quantiles (or percentiles) of the distribution of the outcome variable vary with patient or system characteristics. The authors examined the performance of traditional linear regression vs. that of quantile regression to assess the association between hospital transport interval and patient and system characteristics. They demonstrate that richer inferences can be drawn from the data using quantile regression, utilizing data drawn from a study of ambulance diversion and out-of-hospital delay. The results demonstrate that the effect of ambulance diversion upon out-of-hospital transport intervals is not uniform, but is worse on the right tail of the distribution of transport intervals. In other words, ambulance diversion disproportionately affects those patients who already have longer transport intervals. Second, the distribution of transport intervals, conditional on a given set of variables, is positively skewed, and not uniformly or symmetrically distributed. The flexibility of quantile regression models makes them particularly well suited to out-of-hospital research, and they may allow for more relevant evaluation of out-of-hospital system performance.