Study design and sample
We conducted an observational, prospective single-centre, open cohort study, including Diabetes Mellitus (DM) patients with a diabetic foot ulcer (DFU).
The study pursued a prospective study design, as the data collection and analysis were planned before the eligible subjects were studied. The investigation was conducted at a specialised wound care centre as part of the traumatic surgery unit of Klinikum Melle in Germany, which is a partner in a local learning health system. Data capture started on 1 June 2013 and ended on 1 July 2019. We recruited male and female type 1 and 2 diabetes patients who were over 18 years old. The exclusion criteria were traumatic wounds, tumour-induced ulcers and patients without DM. GH screened all inpatient and outpatient subjects with DFU before study entry.
At baseline, GH, JHe, and SW assessed all the included patients according to the PEDIS classification (IWGDF) as described by Schaper . To obtain the perfusion status, for which different methods are described , e.g. assessing the tcoO2 value, we used the blood pressure as an indicator, i.e., the Ankle Brachial Pressure Index (ABPI) and systolic ankle pressure. To obtain the sensation, we used 10g-monofilament (on three sites of the plantar foot) and a 128 Hz tuning fork on the hallux. When a patient had more than one ulcer, we chose the one with the highest PEDIS score as the index ulcer. Gender and age at baseline were collected s demographic variables. After the baseline assessment, patients were treated in the wound care centre according to the national clinical guidelines  by an interdisciplinary team of physicists (surgeons, diabetologists, cardiologists), specialised nurses, physiotherapists, podiatrists. To ensure an optimal healing situation, an external orthopaedic technician supplied patients with individual offloading systems on-site in close collaboration with the wound care centre. Six months after each patient's baseline assessment, we determined the final treatment outcomes as any-amputation (ICD‐9 CM code: 84.13‐84.19 and 84.11‐84.12) and major-amputation (amputations above the ankle ICD‐9 CM code 84.11‐84.12), however, as in accordance with Pickwell et al. , excluding the lesser toes.
To answer the first two research questions, Bayesian models were fitted using the five PEDIS risk factors as the predictors as well as age and gender as the covariates. Each of the clinical outcomes served as the criterion. With regard to the third research question, focusing on the effect of prior knowledge, we followed a twofold strategy. First, we created models for both outcomes waiving prior knowledge. Second, we fitted the same models, but in this step, we incorporated the available information.
We used prior information for three main reasons: First, prior knowledge helps to make more reliable inferences when only a small amount of data is available. Second, as prior knowledge mainly represents external scientific knowledge, it is especially useful for our risk models as we utilised data from a single wound care centre. Third, as the role of the PEDIS risk factors is established in clinical care and research, a models waiving prior information neglect existing knowledge and would stand against the Bayesian reasoning, encouraging the use of the available knowledge in these situations [24, 32].
The priors were designed with Cauchy distributions as proposed by Gelman et al. . In the first approach, i.e. modelling without prior information, we assigned a zero-centred Cauchy distribution with a broad scale of 1 to each predictor, spanning a vast range of prior plausible model coefficients. In the second case, i.e. with knowledge, odds ratios and corresponding confidence intervals (CI) were derived from the published data in the study of Pickwell et al.  which were then pooled and further adjusted by subtracting the standard error twice (see appendix). Thereby, the odds ratios were designed as conservative prior estimates reflecting the general pattern of external knowledge. The log-transformed odds ratios were then integrated as parameters into informative Cauchy distributions for the Bayesian logistic regression. Figure 1 illustrates the implemented prior distributions.
The Monte Carlo Markov Chain (MCMC) sampling procedure was used to fit the Bayesian models, and for the computation of the posterior distributions, the open-source R-package rstanarm (version 2.19.2) was used . For each model, we generated four MCMC chains with 8,500 steps and set the burn-in period to 500 iterations, yielding 30,000 sample MCMC steps for each model.
To make inferences about the effect of the risk factors on the outcome, 95% Highest Density Intervals (HDI) were computed as credible intervals, which are common in Bayesian statistics [24, 35]. Any value within the interval has a higher density than the values outside, and the total mass of values inside is 95%. As the HDI contains the 95% most credible posterior values of the predictor, it is considered to be associated with the outcome when the HDI excludes the null value [35, 36]. For beta-coefficients, the null value is zero, but it is also common to exponentiate beta coefficients in logistic regression, whereby they can be interpreted as odds ratios . In this case, the null value is one.
We used the programming language R (version 3.6.2) and additional open-source R-packages for all the statistical analyses [34, 38–40].