Sample description
A total of 254 patients met the inclusion criteria and were recorded at baseline (admission to the wound care centre and inpatients). Sixteen patients were lost to follow-up (deceased or dropped out due to other reasons, e.g. moved), which resulted in 237 study participants.
The mean age of the sample was 65.9 (SD 12.3) years. The proportion of female and male patients was 16.5% and 83.5%, respectively. Among all the patients, 31.6% (n = 75) had at least any-amputation (excluding lesser toes) and 12.2% (n = 29) underwent a major-amputation procedure.
Model diagnostics
We reviewed the Markov Chain Monte Carlo (MCMC) sampling procedure of the Bayesian logistic regression models for convergence, autocorrelation, effective sample size (ESS) and collinearity. The chain of each coefficient converged, lacked autocorrelation and showed a large effective sample size (> 10,000) for all the model coefficients. The covariate matrix revealed an absence of collinearity (see online-appendix). Univariate models, which were calculated to explore the relationships, showed that perfusion, extent and depth had an impact on the outcome while infection and sensation were unconnected with the outcome (see appendix). Based on the MCMC sample, we were able to compute the posterior coefficient distributions, posterior AUC distributions as well as distribution of the predictions.
Models without prior knowledge
The any-amputation risk model provided significant evidence of a positive effect of perfusion status, ulcer extent and ulcer depth as their 95% HDI excluded the null value (Table 3). In contrast, the 95% HDI of infection status and loss of sensation covered the null value and thus indicated no impact.
The major-amputation risk model lacked significant evidence of an effect of any PEDIS risk factor as their 95% HDIs included the null value. However, the proportion of posterior coefficient values below zero for perfusion, extent and depth was 2.7%, 2% and 2.2%, respectively, which hints at a positive relationship as most posterior values cluster above zero (Figure 1 and Table 3).
Concerning the prognostic value, the receiver operating characteristic analysis of the posterior AUC distributions showed a posterior median estimate of 0.793 (95% HDI 0.778-0.801) for any-amputation and 0.765 (95% HDI 0.725-0.779) for major-amputation. Comparing both AUC values (Δ=0.031), the former model revealed a higher predictive value.
Models including prior knowledge
To evaluate the impliact of informative priors, we compared the Bayesian models, which used a neutral prior and were presented in the last sections, with models which incorporated external, a priori available scientific knowledge.
The informative priors had an impact on the major-amputation risk model, which mainly led to a decreased variance in the posterior coefficient distribution (Table 3). As a result, the informed model revealed three non-null predictors: perfusion status, ulcer extent and depth. The decreased variance also affected the predictive value of the informed model for the outcome major-amputation: Yielding a large effect size (Cohen’s d = 2.217), the difference between both AUC values (Δ=0.029) suggested that the informed model outperformed the uninformed counterpart (AUC: 0.765 vs 0.790).
Opposed to the major-amputation models, the bottom-line finding for the any-amputation models remained the same: the 95% HDI of perfusion, extent and depth excluded the neutral value of zero (which corresponds to the neutral odds ratio of 1 when exponentiated), whereas those for infection and sensation did not (Table 3 and Figure 2). The posterior median estimates for the coefficients and the AUC remained nearly constant, e.g. AUC: 0.793 vs 0.790 (Cohen’s d = 0.224, Δ=0.003).
Model application for decision support
The results of these models can be visualised for clinical use to support decision making. Figure 3 shows the distributions of the predicted probabilities for any-amputation using the informed model for two hypothetical ulcers classified according to the PEDIS system. In the first case, the PEDIS classification describes a rather moderate ulcer. In this first example, the patient has a peripheral arterial disease but no critical limb ischaemia (stage 2/3), an ulcer extent ranging between one and five cm2 (stage 2/3), but just a superficial ulcer (stage 1/3), no signs of infection (stage 1/4) and the presence of protective sensation (stage 1/2). In this case, the model computes a median posterior amputation risk of 4.4% (95% HDI 0.2% - 13%). The second example describes a more severe ulcer, i.e. the limb perfusion is critical due to ischaemia (stage 3/3), the ulcer extends > five cm2 (stage 3/3) and it reaches deep tissues (stage 3/3), and infection (stage 1/4) and sensation status (stage 1/2) are less concern (Table 1). In this case, the median posterior risk estimate was 63% (95% HDI 37.2%-85.9%).
The model clearly discriminates between both diabetic ulcers predicting a lower risk for the former compared to the latter which is not only indicated by the median risk prediction but also in the non-overlapping HDIs. Furthermore, the posterior variability quantified by the HDI expresses the associated uncertainty of the predicted risk: The range of the 95% HDI of the former example is nearly four times narrower than that of the latter and, therefore, the model is more confident in its former prediction.