Isomorphism Testing for Graphs Excluding Small Minors

We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments

Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search

We generalize the monotone local search approach of Fomin, Gaspers,Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection betweenparameterized approximation and exponential-time approximation algorithms formonotone subset minimization problems. In a monotone subset minimizationproblem the input implicitly describes a non-empty set family over a universeof size $n$ which is closed under taking supersets. The task is to find aminimum cardinality set in this family. Broadly speaking, we use approximatemonotone local search to show that a parameterized $\alpha$-approximationalgorithm that runs in $c^k \cdot n^{O(1)}$ time, where $k$ is the solutionsize, can be used to derive an $\alpha$-approximation randomized algorithm thatruns in $d^n \cdot n^{O(1)}$ time, where $d$ is the unique value in $d \in(1,1+\frac{c-1}{\alpha})$ such that$\mathcal{D}(\frac{1}{\alpha}\|\frac{d-1}{c-1})=\frac{\ln c}{\alpha}$ and$\mathcal{D}(a \|b)$ is the Kullback-Leibler divergence. This running timematches that of Fomin et al. for $\alpha=1$, and is strictly better when$\alpha >1$, for any $c > 1$. Furthermore, we also show that this result can bederandomized at the expense of a sub-exponential multiplicative factor in therunning time. We demonstrate the potential of approximate monotone local search by derivingnew and faster exponential approximation algorithms for Vertex Cover,$3$-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback VertexSet, Directed Odd Cycle Transversal and Undirected Multicut. For instance, weget a $1.1$-approximation algorithm for Vertex Cover with running time $1.114^n\cdot n^{O(1)}$, improving upon the previously best known $1.1$-approximationrunning in time $1.127^n \cdot n^{O(1)}$ by Bourgeois et al. [DAM 2011].<br

Effects of canagliflozin compared with placebo on major adverse cardiovascular and kidney events in patient groups with different baseline levels of HbA<inf>1c</inf>, disease duration and treatment intensity: results from the CANVAS Program

Aims/hypothesis: Type 2 diabetes mellitus can manifest over a broad clinical range, although there is no clear consensus on the categorisation of disease complexity. We assessed the effects of canagliflozin, compared with placebo, on cardiovascular and kidney outcomes in the CANagliflozin cardioVascular Assessment Study (CANVAS) Program over a range of type 2 diabetes mellitus complexity, defined separately by baseline intensity of treatment, duration of diabetes and glycaemic control. Methods: We performed a post hoc analysis of the effects of canagliflozin on major adverse cardiovascular events (MACE) according to baseline glucose-lowering treatments (0 or 1, 2 or 3+ non-insulin glucose-lowering treatments, or insulin-based treatment), duration of diabetes (16 years) and HbA1c (≤53.0 mmol/mol [53.0 to 58.5 mmol/mol [>7.0% to 7.5%], >58.5 to 63.9 mmol/mol [>7.5 to 8.0%], >63.9 to 69.4 mmol/mol [8.0% to 8.5%], >69.4 to 74.9 mmol/mol [>8.5 to 9.0%] or >74.9 mmol/mol [>9.0%]). We analysed additional secondary endpoints for cardiovascular and kidney outcomes, including a combined kidney outcome of sustained 40% decline in eGFR, end-stage kidney disease or death due to kidney disease. We used Cox regression analyses and compared the constancy of HRs across subgroups by fitting an interaction term (p value for significance 74.9 mmol/mol (9.0%) and the median duration of diabetes was 12.6 years (interquartile interval 8.0–18 years). Canagliflozin reduced MACE (HR 0.86 [95% CI 0.75, 0.97]) with no evidence that the benefit differed between subgroups defined by the number of glucose-lowering treatments, the duration of diabetes or baseline HbA1c (all p-heterogeneity >0.17). Canagliflozin reduced MACE in participants receiving insulin with no evidence that the benefit differed from other participants in the trial (HR 0.85 [95% CI 0.72, 1.00]). Similar results were observed for other cardiovascular outcomes and for the combined kidney outcome (HR for combined kidney outcome 0.60 [95% CI 0.47, 0.77]), with all p-heterogeneity >0.37. Conclusions/interpretation: In people with type 2 diabetes mellitus at high cardiovascular risk, there was no evidence that cardiovascular and renal protection with canagliflozin differed across subgroups defined by baseline treatment intensity, duration of diabetes or HbA1c. Graphical abstract: [Figure not available: see fulltext.

Association between TNF Receptors and KIM-1 with Kidney Outcomes in Early-Stage Diabetic Kidney Disease

Background and objectives Clinical trials in nephrology are enriched for patients with micro-or macroalbuminuria to enroll patients at risk of kidney failure. However, patients with normoalbuminuria can also progress to kidney failure. TNF receptor-1, TNF receptor-2, and kidney injury marker-1 (KIM-1) are known to be associated with kidney disease progression in patients with micro-or macroalbuminuria. We assessed the value of TNF receptor-1, TNF receptor-2, and KIM-1 as prognostic biomarkers for CKD progression in patients with type 2 diabetes and normoalbuminuria. Design, setting, participants, & measurements TNF receptor-1, TNF receptor-2, and KIM-1 were measured using immunoassays in plasma samples from patients with type 2 diabetes at high cardiovascular risk participating in the Canagliflozin Cardiovascular Assessment Study trial. We used multivariable adjusted Cox proportional hazards analyses to estimate hazard ratios per doubling of each biomarker for the kidney outcome, stratified the population by the fourth quartile of each biomarker distribution, and assessed the number of events and event rates. Results In patients with normoalbuminuria (n=2553), 51 kidney outcomes were recorded during a median follow-up of 6.1 (interquartile range, 5.8–6.4) years (event rate, 3.5; 95% confidence interval, 2.6 to 4.6 per 1000 patient-years). Each doubling of baseline TNF receptor-1 (hazard ratio, 4.2; 95% confidence interval, 1.8 to 9.6) and TNF receptor-2 (hazard ratio, 2.3; 95% confidence interval, 1.5 to 3.6) was associated with a higher risk for the kidney outcome. Baseline KIM-1, urinary albumin-creatinine ratio, and eGFR were not associated with kidney outcomes. The event rates in the highest quartile of TNF receptor-1 (≥2992 ng/ml) and TNF receptor-2 (≥11,394 ng/ml) were 5.6 and 7.0 events per 1000 patient-years, respectively, compared with 2.8 and 2.3, respectively, in the lower three quartiles. Conclusions TNF receptor-1 and TNF receptor-2 are associated with kidney outcomes in patients with type 2 diabetes and normoalbuminuria

Cardiovascular and renal outcomes with canagliflozin according to baseline diuretic use:a post hoc analysis from the CANVAS Program

Aims The CANVAS Program identified the effect of canagliflozin on major adverse cardiovascular events (MACE) differed according to whether participants were using diuretics at study commencement. We sought to further evaluate this finding related to baseline differences, treatment effects, safety, and risk factor changes.Methods and results The CANVAS Program enrolled 10 142 participants with type 2 diabetes mellitus and high cardiovascular risk. Participants were randomized to canagliflozin or placebo and followed for a mean of 188 weeks. The primary outcome was major cardiovascular events, a composite of cardiovascular death, nonfatal myocardial infarction, or nonfatal stroke. Secondary outcomes included multiple cardiovascular, renal, and safety events. In this post hoc subgroup analysis, participants were categorized according to baseline use of any diuretic. The effect on outcomes was compared using Cox proportional hazards models, while risk factor changes were compared using mixed-effect models. At baseline, 4490 (44.3%) participants were using a diuretic. Compared with those not using a diuretic, participants using a diuretic were more likely to be older (mean age +/- standard deviation, 64.3 +/- 8.0 vs. 62.5 +/- 8.3), be female (38.9% vs. 33.4%), and have heart failure (19.6% vs. 10.3%) (all P-difference &lt; 0.0001). The effect of canagliflozin on major cardiovascular events was greater for those using diuretic at baseline than for those who were not [adjusted hazard ratio 0.65 (95% confidence interval 0.54-0.78) vs. adjusted hazard ratio 1.13 (95% confidence interval 0.93-1.36), P-heterogeneity &lt; 0.0001]. Changes in most risk factors, including blood pressure, body weight, and urine albumin-to-creatinine ratio, were similar between groups (all P-difference &gt; 0.11), although the effect of canagliflozin on haemoglobin A1c reduction was slightly weaker in participants using compared with not using diuretics at baseline (-0.52% vs. -0.64%, P-heterogeneity = 0.0007). Overall serious adverse events and key safety outcomes, including adverse renal events, were also similar (all P-heterogeneity &gt; 0.07).Conclusions Participants on baseline diuretics derived a greater benefit for major cardiovascular events from canagliflozin, which was not fully explained by differences in participant characteristics nor risk factor changes.</p

Sodium-Glucose Cotransporter 2 Inhibitors and Risk of Hyperkalemia in People With Type 2 Diabetes: A Meta-Analysis of Individual Participant Data From Randomized, Controlled Trials

Background: Hyperkalemia increases risk of cardiac arrhythmias and death and limits the use of renin-angiotensin-aldosterone system (RAAS) inhibitors and mineralocorticoid receptor antagonists (MRAs), which improve clinical outcomes in people with chronic kidney disease (CKD) and/or systolic heart failure. Sodium-glucose cotransporter 2 (SGLT2) inhibitors reduce the risk of cardiorenal events in people with type 2 diabetes at high cardiovascular risk or with CKD. However, their effect on hyperkalemia has not been systematically evaluated. / Methods: A meta-analysis was conducted using individual participant data from randomized, double-blind, placebo-controlled clinical outcome trials with SGLT2 inhibitors in people with type 2 diabetes at high cardiovascular risk and/or with CKD, in which serum potassium levels were routinely measured. The primary outcome was time to serious hyperkalemia, defined as central laboratory determine serum potassium ≥6.0 mmol/L, with other outcomes including investigator-reported hyperkalemia events and hypokalemia (serum potassium ≤3.5 mmol/L). Cox regression analyses were performed to estimate treatment effects from each trial with hazards ratios (HR) and corresponding 95% CI pooled using random effects models to obtain summary treatment effects, overall and across key subgroups. / Results: Results from six trials were included comprising 49,875 participants assessing four SGLT2 inhibitors. 1,754 participants developed serious hyperkalemia and an additional 1,119 investigator-reported hyperkalemia events were recorded. SGLT2 inhibitors reduced the risk of serious hyperkalemia (HR 0.84, 95% CI 0.76-0.93), an effect consistent across studies (P-heterogeneity=0.71). The incidence of investigator-reported hyperkalemia was also lower with SGLT2 inhibitors (HR 0.80, 95% CI 0.68-0.93; P-heterogeneity=0.21). Reductions in serious hyperkalemia were observed across a range of subgroups including baseline kidney function, history of heart failure, RAAS inhibitor, diuretic and MRA use. SGLT2 inhibitors did not increase the risk of hypokalemia (HR 1.04, 95% CI 0.94-1.15; P-heterogeneity=0.42). / Conclusions: SGLT2 inhibitors reduce the risk of serious hyperkalemia in people with type 2 diabetes at high cardiovascular risk and/or with CKD, without increasing the risk of hypokalemia

Blood pressure effects of canagliflozin and clinical outcomes in type 2 diabetes and chronic kidney disease: Insights from the CREDENCE trial

Background: People with type 2 diabetes mellitus (T2DM) and chronic kidney disease (CKD) experience a high burden of hypertension but the magnitude and consistency of blood pressure (BP) lowering with canagliflozin in this population is uncertain. Whether the effects of canagliflozin on kidney and cardiovascular outcomes vary by baseline BP or BP lowering therapy is also unknown. Methods: The CREDENCE trial randomized people with T2DM and CKD to canagliflozin or placebo. Post-hoc, we investigated the effect of canagliflozin on systolic BP across subgroups defined by baseline systolic BP, number of BP lowering drug classes, and history of apparent treatment-resistant hypertension (BP ≥130/80 mmHg while receiving ≥3 classes of BP lowering drugs, including a diuretic). We also assessed whether effects on clinical outcomes differed across these subgroups. Results: The trial included 4,401 participants of whom 3,361 (76.4%) had baseline systolic BP ≥130 mmHg, and 1371 (31.2%) had resistant hypertension. By week 3, canagliflozin reduced systolic BP by 3.50mmHg (95% CI, -4.27 to -2.72), an effect maintained over the duration of the trial, with similar reductions across BP and BP lowering therapy subgroups (all P-interaction ≥0.05). Canagliflozin also reduced the need for initiation of additional BP lowering agents during the trial (HR 0.68, 95% CI 0.61-0.75). The effect of canagliflozin on kidney failure, doubling of serum creatinine, or death due to kidney or cardiovascular disease (HR 0.70, 95% CI 0.59-0.82) was consistent across BP and BP lowering therapy subgroups (all P-interaction ≥0.35), as were effects on other key kidney, cardiovascular and safety outcomes. Conclusions: In people with T2DM and CKD, canagliflozin lowers systolic BP across all BP defined subgroups and reduces the need for additional BP lowering agents. These findings support use of canagliflozin for end-organ protection and as an adjunct BP lowering therapy in people with CKD. Clinical Trial Registration: URL: https://clinicaltrials.gov. Unique Identifier: NCT02065791

Evaluation of Variation in the Performance of GFR Slope as a Surrogate End Point for Kidney Failure in Clinical Trials that Differ by Severity of CKD

BACKGROUND: The GFR slope has been evaluated as a surrogate end point for kidney failure in meta-analyses on a broad collection of randomized controlled trials (RCTs) in CKD. These analyses evaluate how accurately a treatment effect on GFR slope predicts a treatment effect on kidney failure. We sought to determine whether severity of CKD in the patient population modifies the performance of GFR slope. METHODS: We performed Bayesian meta-regression analyses on 66 CKD RCTs to evaluate associations between effects on GFR slope (the chronic slope and the total slope over 3 years, expressed as mean differences in ml/min per 1.73 m2/yr) and those of the clinical end point (doubling of serum creatinine, GFR &lt;15 ml/min per 1.73 m2, or kidney failure, expressed as a log-hazard ratio), where models allow interaction with variables defining disease severity. We evaluated three measures (baseline GFR in 10 ml/min per 1.73 m2, baseline urine albumin-to-creatinine ratio [UACR] per doubling in mg/g, and CKD progression rate defined as the control arm chronic slope, in ml/min per 1.73 m2/yr) and defined strong evidence for modification when 95% posterior credible intervals for interaction terms excluded zero. RESULTS: There was no evidence for modification by disease severity when evaluating 3-year total slope (95% credible intervals for the interaction slope: baseline GFR [-0.05 to 0.03]; baseline UACR [-0.02 to 0.04]; CKD progression rate [-0.07 to 0.02]). There was strong evidence for modification in evaluations of chronic slope (95% credible intervals: baseline GFR [0.02 to 0.11]; baseline UACR [-0.11 to -0.02]; CKD progression rate [0.01 to 0.15]). CONCLUSIONS: These analyses indicate consistency of the performance of total slope over 3 years, which provides further evidence for its validity as a surrogate end point in RCTs representing varied CKD populations.</p