PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure

Development of Risk Prediction Equations for Incident Chronic Kidney Disease

IMPORTANCE Early identification of individuals at elevated risk of developing chronic kidney disease (CKD) could improve clinical care through enhanced surveillance and better management of underlying health conditions.OBJECTIVE To develop assessment tools to identify individuals at increased risk of CKD, defined by reduced estimated glomerular filtration rate (eGFR).DESIGN, SETTING, AND PARTICIPANTS Individual-level data analysis of 34 multinational cohorts from the CKD Prognosis Consortium including 5 222 711 individuals from 28 countries. Data were collected from April 1970 through January 2017. A 2-stage analysis was performed, with each study first analyzed individually and summarized overall using a weighted average. Because clinical variables were often differentially available by diabetes status, models were developed separately for participants with diabetes and without diabetes. Discrimination and calibration were also tested in 9 external cohorts (n = 2 253 540).EXPOSURES Demographic and clinical factors.MAIN OUTCOMES AND MEASURES Incident eGFR of less than 60 mL/min/1.73 m(2).RESULTS Among 4 441 084 participants without diabetes (mean age, 54 years, 38% women), 660 856 incident cases (14.9%) of reduced eGFR occurred during a mean follow-up of 4.2 years. Of 781 627 participants with diabetes (mean age, 62 years, 13% women), 313 646 incident cases (40%) occurred during a mean follow-up of 3.9 years. Equations for the 5-year risk of reduced eGFR included age, sex, race/ethnicity, eGFR, history of cardiovascular disease, ever smoker, hypertension, body mass index, and albuminuria concentration. For participants with diabetes, the models also included diabetes medications, hemoglobin A(1c), and the interaction between the 2. The risk equations had a median C statistic for the 5-year predicted probability of 0.845 (interquartile range [IQR], 0.789-0.890) in the cohorts without diabetes and 0.801 (IQR, 0.750-0.819) in the cohorts with diabetes. Calibration analysis showed that 9 of 13 study populations (69%) had a slope of observed to predicted risk between 0.80 and 1.25. Discrimination was similar in 18 study populations in 9 external validation cohorts; calibration showed that 16 of 18 (89%) had a slope of observed to predicted risk between 0.80 and 1.25.CONCLUSIONS AND RELEVANCE Equations for predicting risk of incident chronic kidney disease developed from more than 5 million individuals from 34 multinational cohorts demonstrated high discrimination and variable calibration in diverse populations. Further study is needed to determine whether use of these equations to identify individuals at risk of developing chronic kidney disease will improve clinical care and patient outcomes.</p

The kidney failure risk equation:evaluation of novel input variables including eGFR estimated using the CKD-EPI 2021 equation in 59 cohorts

SIGNIFICANCE STATEMENT: The kidney failure risk equation (KFRE) uses age, sex, GFR, and urine albumin-to-creatinine ratio (ACR) to predict 2- and 5-year risk of kidney failure in populations with eGFR <60 ml/min per 1.73 m 2 . However, the CKD-EPI 2021 creatinine equation for eGFR is now recommended for use but has not been fully tested in the context of KFRE. In 59 cohorts comprising 312,424 patients with CKD, the authors assessed the predictive performance and calibration associated with the use of the CKD-EPI 2021 equation and whether additional variables and accounting for the competing risk of death improves the KFRE's performance. The KFRE generally performed well using the CKD-EPI 2021 eGFR in populations with eGFR <45 ml/min per 1.73 m 2 and was not improved by adding the 2-year prior eGFR slope and cardiovascular comorbidities. BACKGROUND: The kidney failure risk equation (KFRE) uses age, sex, GFR, and urine albumin-to-creatinine ratio (ACR) to predict kidney failure risk in people with GFR <60 ml/min per 1.73 m 2 . METHODS: Using 59 cohorts with 312,424 patients with CKD, we tested several modifications to the KFRE for their potential to improve the KFRE: using the CKD-EPI 2021 creatinine equation for eGFR, substituting 1-year average ACR for single-measure ACR and 1-year average eGFR in participants with high eGFR variability, and adding 2-year prior eGFR slope and cardiovascular comorbidities. We also assessed calibration of the KFRE in subgroups of eGFR and age before and after accounting for the competing risk of death. RESULTS: The KFRE remained accurate and well calibrated overall using the CKD-EPI 2021 eGFR equation. The other modifications did not improve KFRE performance. In subgroups of eGFR 45-59 ml/min per 1.73 m 2 and in older adults using the 5-year time horizon, the KFRE demonstrated systematic underprediction and overprediction, respectively. We developed and tested a new model with a spline term in eGFR and incorporating the competing risk of mortality, resulting in more accurate calibration in those specific subgroups but not overall. CONCLUSIONS: The original KFRE is generally accurate for eGFR <45 ml/min per 1.73 m 2 when using the CKD-EPI 2021 equation. Incorporating competing risk methodology and splines for eGFR may improve calibration in low-risk settings with longer time horizons. Including historical averages, eGFR slopes, or a competing risk design did not meaningfully alter KFRE performance in most circumstances

Development of Risk Prediction Equations for Incident Chronic Kidney Disease

IMPORTANCE ‐ Early identification of individuals at elevated risk of developing chronic kidney disease  could improve clinical care through enhanced surveillance and better management of underlying health  conditions.  OBJECTIVE – To develop assessment tools to identify individuals at increased risk of chronic kidney  disease, defined by reduced estimated glomerular filtration rate (eGFR).  DESIGN, SETTING, AND PARTICIPANTS – Individual level data analysis of 34 multinational cohorts from  the CKD Prognosis Consortium including 5,222,711 individuals from 28 countries. Data were collected  from April, 1970 through January, 2017. A two‐stage analysis was performed, with each study first  analyzed individually and summarized overall using a weighted average. Since clinical variables were  often differentially available by diabetes status, models were developed separately within participants  with diabetes and without diabetes. Discrimination and calibration were also tested in 9 external  cohorts (N=2,253,540). EXPOSURE Demographic and clinical factors.  MAIN OUTCOMES AND MEASURES – Incident eGFR <60 ml/min/1.73 m2.  RESULTS – In 4,441,084 participants without diabetes (mean age, 54 years, 38% female), there were  660,856 incident cases of reduced eGFR during a mean follow‐up of 4.2 years. In 781,627 participants  with diabetes (mean age, 62 years, 13% female), there were 313,646 incident cases during a mean follow‐up of 3.9 years. Equations for the 5‐year risk of reduced eGFR included age, sex, ethnicity, eGFR, history of cardiovascular disease, ever smoker, hypertension, BMI, and albuminuria. For participants  with diabetes, the models also included diabetes medications, hemoglobin A1c, and the interaction  between the two. The risk equations had a median C statistic for the 5‐year predicted probability of  0.845 (25th – 75th percentile, 0.789‐0.890) in the cohorts without diabetes and 0.801 (25th – 75th percentile, 0.750‐0.819) in the cohorts with diabetes. Calibration analysis showed that 9 out of 13 (69%) study populations had a slope of observed to predicted risk between 0.80 and 1.25. Discrimination was  similar in 18 study populations in 9 external validation cohorts; calibration showed that 16 out of 18 (89%) had a slope of observed to predicted risk between 0.80 and 1.25. CONCLUSIONS AND RELEVANCE – Equations for predicting risk of incident chronic kidney disease developed in over 5 million people from 34 multinational cohorts demonstrated high discrimination and  variable calibration in diverse populations

Serum potassium and adverse outcomes across the range of kidney function: a CKD Prognosis Consortium meta-analysis.

Aims: Both hypo- and hyperkalaemia can have immediate deleterious physiological effects, and less is known about long-term risks. The objective was to determine the risks of all-cause mortality, cardiovascular mortality, and end-stage renal disease associated with potassium levels across the range of kidney function and evaluate for consistency across cohorts in a global consortium. Methods and results: We performed an individual-level data meta-analysis of 27 international cohorts [10 general population, 7 high cardiovascular risk, and 10 chronic kidney disease (CKD)] in the CKD Prognosis Consortium. We used Cox regression followed by random-effects meta-analysis to assess the relationship between baseline potassium and adverse outcomes, adjusted for demographic and clinical characteristics, overall and across strata of estimated glomerular filtration rate (eGFR) and albuminuria. We included 1 217 986 participants followed up for a mean of 6.9 years. The average age was 55 ± 16 years, average eGFR was 83 ± 23 mL/min/1.73 m2, and 17% had moderate- to-severe increased albuminuria levels. The mean baseline potassium was 4.2 ± 0.4 mmol/L. The risk of serum potassium of >5.5 mmol/L was related to lower eGFR and higher albuminuria. The risk relationship between potassium levels and adverse outcomes was U-shaped, with the lowest risk at serum potassium of 4-4.5 mmol/L. Compared with a reference of 4.2 mmol/L, the adjusted hazard ratio for all-cause mortality was 1.22 [95% confidence interval (CI) 1.15-1.29] at 5.5 mmol/L and 1.49 (95% CI 1.26-1.76) at 3.0 mmol/L. Risks were similar by eGFR, albuminuria, renin-angiotensin-aldosterone system inhibitor use, and across cohorts. Conclusions: Outpatient potassium levels both above and below the normal range are consistently associated with adverse outcomes, with similar risk relationships across eGFR and albuminuria

Using a Health Economic Framework to Prioritize Quality Indicators: An Example With Smoking Cessation in Chronic Obstructive Pulmonary Disease

Background. Health care performance monitoring is a major focus of the modern quality movement, resulting in widespread development of quality indicators and making prioritizations an increasing focus. Currently, few prioritization methods of performance measurements give serious consideration to the association of performance with expected health benefits and costs. We demonstrate a proof-of-concept application of using a health economic framework to prioritize quality indicators by expected variations in population health and costs, using smoking cessation in chronic obstructive pulmonary disease (COPD) as an example. Methods. We developed a health state transition, microsimulation model to represent smoking cessation practices for adults with COPD from the health care payer perspective in Ontario, Canada. Variations in life years, quality-adjusted life years (QALYs), and lifetime costs were associated with changes in performance. Incremental net health benefit (INHB) was used to represent the joint variation in mortality, morbidity, and costs associated with the performance of each quality indicator. Results. Using a value threshold of $50,000/QALY, the indicators monitoring assessment of smoking status and smoking cessation interventions were associated with the largest INHBs. Combined performance variations among groups of indicators showed that 81% of the maximum potential INHB could be represented by three out of the six process indicators. Conclusions. A health economic framework can be used to bring dimensions of population health and costs into explicit consideration when prioritizing quality indicators. However, this should not preclude policymakers from considering other dimensions of quality that are not part of this framework

Impact of limited sample size and follow-up on single event survival extrapolation for health technology assessment: a simulation study

Abstract Introduction Extrapolation of time-to-event data from clinical trials is commonly used in decision models for health technology assessment (HTA). The objective of this study was to assess performance of standard parametric survival analysis techniques for extrapolation of time-to-event data for a single event from clinical trials with limited data due to small samples or short follow-up. Methods Simulated populations with 50,000 individuals were generated with an exponential hazard rate for the event of interest. A scenario consisted of 5000 repetitions with six sample size groups (30–500 patients) artificially censored after every 10% of events observed. Goodness-of-fit statistics (AIC, BIC) were used to determine the best-fitting among standard parametric distributions (exponential, Weibull, log-normal, log-logistic, generalized gamma, Gompertz). Median survival, one-year survival probability, time horizon (1% survival time, or 99th percentile of survival distribution) and restricted mean survival time (RMST) were compared to population values to assess coverage and error (e.g., mean absolute percentage error). Results The true exponential distribution was correctly identified using goodness-of-fit according to BIC more frequently compared to AIC (average 92% vs 68%). Under-coverage and large errors were observed for all outcomes when distributions were specified by AIC and for time horizon and RMST with BIC. Error in point estimates were found to be strongly associated with sample size and completeness of follow-up. Small samples produced larger average error, even with complete follow-up, than large samples with short follow-up. Correctly specifying the event distribution reduced magnitude of error in larger samples but not in smaller samples. Conclusions Limited clinical data from small samples, or short follow-up of large samples, produce large error in estimates relevant to HTA regardless of whether the correct distribution is specified. The associated uncertainty in estimated parameters may not capture the true population values. Decision models that base lifetime time horizon on the model’s extrapolated output are not likely to reliably estimate mean survival or its uncertainty. For data with an exponential event distribution, BIC more reliably identified the true distribution than AIC. These findings have important implications for health decision modelling and HTA of novel therapies seeking approval with limited evidence

Comparison of Goals of Care Between Hemodialysis Patients and Their Health Care Providers

Background: Patient-centered care requires knowledge of patients’ goals of care (GoC) on the part of health care providers (HCPs). Whether HCPs caring for in-center hemodialysis patients meet this criterion is uncertain. Objective: We designed and conducted a GoC survey among patients and HCPs within a single in-center hemodialysis (ICHD) program to determine whether HCPs have an understanding of their patients’ GoC. Design: This was a prospective comparative quantitative survey study. Setting: The study included a single Canadian maintenance ICHD center. Participants: These included hemodialysis patients and their primary nephrologists, nurses, social workers, pharmacists, and dietitians. Methods and Measurements: Two surveys, one for patients and another for primary HCPs, were designed, piloted, and administered. For each participating patient, HCPs consisted of the primary nephrologist, nurse, social worker, pharmacist, and dietitian. Surveys included questions pertaining to 7 GoC themes. Patient-HCP agreement on the importance of each domain individually and the most important domain overall was assessed with kappa statistics. Factors influencing agreement were assessed with logistic regression in a secondary analysis. Results: A total of 173 patients were invited to participate, of whom 137 (79%) completed surveys. Fifty HCPs completed 623 corresponding surveys: 132 by physicians, 112 by nurses, 126 by pharmacists, 127 by social workers, and 126 by dietitians. A total of 70.1% and 78.8% of patients agreed with the importance of and would feel comfortable having GoC discussions, respectively, with their HCPs; 42.7% of physicians reported not having provided prognostic information to the corresponding patient. Patient-HCP agreement regarding GoC was poor (all κ .05). In adjusted analyses, only patients choosing “Be Cured” as the most important GoC was significantly associated with poorer HCP-patient agreement than expected (odds ratio, 0.04; 95% confidence interval, 0.01-0.18). Limitations: This is a single-center study involving only ICHD patients. Conclusions: HCP perceptions of GoC did not agree with patients’ reported GoC. This study suggests the need for the design and validation of interventions to improve HCPs’ understanding of their patients’ GoC