Using ordinal logistic regression to evaluate the performance of laser-Doppler predictions of burn-healing time

Abstract

Background: Laser-Doppler imaging (LDI) of cutaneous blood flow is beginning to be used by burn surgeons to predict the healing time of burn wounds; predicted healing time is used to determine wound treatment as either dressings or surgery. In this paper, we do a statistical analysis of the performance of the technique.

Methods: We used data from a study carried out by five burn centers: LDI was done once between days 2 to 5 post burn, and healing was assessed at both 14 days and 21 days post burn. Random-effects ordinal logistic regression and other models such as the continuation ratio model were used to model healing-time as a function of the LDI data, and of demographic and wound history variables. Statistical methods were also used to study the false-color palette, which enables the laser-Doppler imager to be used by clinicians as a decision-support tool.

Results: Overall performance is that diagnoses are over 90% correct. Related questions addressed were what was the best blood flow summary statistic and whether, given the blood flow measurements, demographic and observational variables had any additional predictive power (age, sex, race, % total body surface area burned (%TBSA), site and cause of burn, day of LDI scan, burn center). It was found that mean laser-Doppler flux over a wound area was the best statistic, and that, given the same mean flux, women recover slightly more slowly than men. Further, the likely degradation in predictive performance on moving to a patient group with larger %TBSA than those in the data sample was studied, and shown to be small.

Conclusion: Modeling healing time is a complex statistical problem, with random effects due to multiple burn areas per individual, and censoring caused by patients missing hospital visits and undergoing surgery. This analysis applies state-of-the art statistical methods such as the bootstrap and permutation tests to a medical problem of topical interest. New medical findings are that age and %TBSA are not important predictors of healing time when the LDI results are known, whereas gender does influence recovery time, even when blood flow is controlled for.The conclusion regarding the palette is that an optimum three-color palette can be chosen 'automatically', but the optimum choice of a 5-color palette cannot be made solely by optimizing the percentage of correct diagnoses.

Figure 1

Picture of a laser-Doppler burn image.

Figure 2

Color photograph of the same burn area.

Figure 3

The coefficient $\hat{\beta }$ (vertical dotted line) and its permutation distribution under H₀ for gender, in the absence of a laser-Doppler measurement, with fitted normal distribution.

Figure 4

Model predictions for probabilities of slow, medium and fast healing for males and females under the PO model, as a function of mean laser-Doppler flux.

Figure 5

Observed and predicted proportions of females, under the proportional odds model.

Figure 6

Observed and predicted mean logged flux (PUs), under the proportional odds model.