Background Physical Frailty Phenotype (PFP) is the most used frailty instrument among kidney transplant recipients, classifying patients as pre-frail if they have 1–2 criteria and as frail if they have ≥ 3. However, different definitions of robustness have been used among renal patients, including only those who have 0 criteria, or those with 0–1 criteria. Our aim was to determine the impact of one PFP criterion on transplant outcomes. Methods We underwent a retrospective study of 296 kidney transplant recipients who had been evaluated for frailty by PFP at the time of evaluating for transplantation. Results Only 30.4% of patients had 0 criteria, and an additional 42.9% showed one PFP criterion. As PFP score increased, a higher percentage of women and cerebrovascular disease were found. Recipients with 0–1 criteria had lower 1 year-mortality after transplant than those with ≥ 2 (1.8% vs. 10.1%), but this difference was already present when we only considered those who scored 0 (mortality 1.1%) and 1 (mortality 2.4%) separately. The multivariable analysis confirmed that one PFP criterion was associated to a higher risk of patient death after kidney transplantation (HR 3.52 [1.03–15.9]). Conclusions Listed kidney transplant candidates frequently show only one PFP frailty criterion. This has an independent impact on patient survival after transplantation.

The purpose of this paper is to complete the classification of almost involutive Hopf algebras up to dimension 23. For this, we first present a brief survey of these algebras, showing that most of them can be obtained by iterated Hopf-Ore extensions. Then the classification follows using a technique we developed for determining when a Hopf-Ore extension is almost involutive.

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