Modelling physiological deterioration in post-operative patient vital-sign data

Patients who undergo upper-gastrointestinal surgery have a high incidence of post-operative complications, often requiring admission to the intensive care unit several days after surgery. A dataset comprising observational vital-sign data from 171 post-operative patients taking part in a two-phase clinical trial at the Oxford Cancer Centre, was used to explore the trajectory of patients’ vital-sign changes during their stay in the post-operative ward using both univariate and multivariate analyses. A model of normality based vital-sign data from patients who had a “normal” recovery was constructed using a kernel density estimate, and tested with “abnormal” data from patients who deteriorated sufficiently to be re-admitted to the intensive care unit. The vital-sign distributions from “normal” patients were found to vary over time from admission to the post-operative ward to their discharge home, but no significant changes in their distributions were observed from halfway through their stay on the ward to the time of discharge. The model of normality identified patient deterioration when tested with unseen “abnormal” data, suggesting that such techniques may be used to provide early warning of adverse physiological events

On sign-based regression quantiles

A sign-based (SB) approach suggests an alternative criterion for quantile regression fit. The SB criterion is a piecewise constant function, which often leads to a non-unique solution. We compare the mid-point of this SB solution with the least absolute deviations (LAD) method and describe asymptotic properties of SB estimators under a weaker set of assumptions as compared with the assumptions often used with the generalized method of moments. Asymptotic properties of LAD and SB estimators are equivalent; however, there are finite sample differences as we show in simulation studies. At small to moderate sample sizes, the SB procedure for modelling quantiles at longer tails demonstrates a substantially lower bias, variance, and mean-squared error when compared with the LAD. In the illustrative example, we model a 0.8-level quantile of hospital charges and highlight finite sample advantage of the SB versus LAD

On sign-based regression quantiles

A sign-based (SB) approach suggests an alternative criterion for quantile regression fit. The SB criterion is a piecewise constant function, which often leads to a non-unique solution. We compare the mid-point of this SB solution with the least absolute deviations (LAD) method and describe asymptotic properties of SB estimators under a weaker set of assumptions as compared with the assumptions often used with the generalized method of moments. Asymptotic properties of LAD and SB estimators are equivalent; however, there are finite sample differences as we show in simulation studies. At small to moderate sample sizes, the SB procedure for modelling quantiles at longer tails demonstrates a substantially lower bias, variance, and mean-squared error when compared with the LAD. In the illustrative example, we model a 0.8-level quantile of hospital charges and highlight finite sample advantage of the SB versus LAD