On a geometric approach to the structural identifiability problem and its application in a water quality case study

Abstract¿We present and apply an alternative method for the investigation of the well-known parameter identifiability question for non-linear system models. The method is based on a geometric analysis of the parametric output sensitivities and is, in fact, an application of the tools that are available in non-linear control theory to an augmented system, including the parametric output sensitivities. Accessibility Lie algebras are calculated that yield insight (through a simple rank test) in the controllability of this augmented system. The method is demonstrated in an example that is due to Dochain et al [4]. Results are confirmed by the method that has certain advantages in comparison to, for example, the Taylor series approach that seeks for identifiable combinations of parameters through inspection of the individual terms in a Taylor series expansion of the output signal, i.e. application of the well-known method of Pohjanpalo [15]. Parametric output sensitivities (as already noted by D¨otsch and Van den Hof [5] and Peeters and Hanzon [13]) play a crucial role in identifiability analysis and we further elaborate on this insight in the current paper. Our goals are (i) to present an interesting method for addressing the (local) identifiability question for non-linear systems and (ii) to gain better understanding in the role of parametric state- and output sensitivities in the identifiability question that stems from an alternative perspective, and that has not been presented in the identification literature. Of course, we are aware of other algorithms and software that establishes an answer to the identifiability question, albeit from a different perspective, e.g. [19], but seek in the current paper mainly for another interpretation and computational framework to address the question of local identifiability, shedding some new light on the problem

Validity of the Patient Experiences and Satisfaction with Medications (PESaM) Questionnaire

Background: This study assessed the validity and reliability of the generic module of the recently developed Patient Experiences and Satisfaction with Medications (PESaM) questionnaire in a sample of patients in the Netherlands. Methods: The generic module of the PESaM questionnaire consists of 18 items related to the domains effectiveness, side effects and ease of use of medications. It assesses patients’ experiences regarding the impact of the medication on daily life, health and satisfaction. In 2017, the PESaM questionnaire was sent out to idiopathic pulmonary fibrosis patients using pirfenidone or nintedanib, atypical haemolytic uraemic syndrome patients receiving eculizumab and patients using tacrolimus after kidney transplantation. Mean scores for each domain were calculated applying a scoring algorithm. Construct validity and reliability were assessed using recommended methods. Results: 188 participants completed the generic module, of whom 48% used pirfenidone, 36% nintedanib, 11% tacrolimus and 5% eculizumab. The generic module has good structural properties. Internal consistency values of the domains were satisfactory (i.e. Cronbach’s coefficient alpha above 0.7). Confirmatory factor analysis provided further evidence for construct validity, with good convergent and discriminant validity. The PESaM questionnaire also showed different scores for patients using different medications, in line with expectations, and was therefore able to differentiate between patient groups. Test–retest reliability of the items and domains were rated as moderate to fair (i.e. intraclass coefficients ranged between 0.18 and 0.76). Conclusions: The PESaM questionnaire is a unique patient-reported outcome measure evaluating patient experiences and satisfaction with medications. It has been developed in conjunction with patients, ensuring coverage of domains and issues relevant from the patient’s perspective. This study has shown promising validity of the generic module of the PESaM questionnaire. Further research is recommended to assess reliability in greater detail as well as the responsiveness of the measure. Trial registration: The study

Author Correction: The messy death of a multiple star system and the resulting planetary nebula as observed by JWST

Stars and planetary system