Spectral synthesis and topologies on ideal spaces for Banach *-algebras

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G).

Can we improve the statistical analysis of stroke trials? Statistical re-analysis of functional outcomes in stroke trials

Background: Most large acute stroke trials have been neutral. Functional outcome is usually analysed using a yes or no answer, e.g. death or dependency vs. independence. We assessed which statistical approaches are most efficient in analysing outcomes from stroke trials. Methods: Individual patient data from acute, rehabilitation and stroke unit trials studying the effects of interventions which alter functional outcome were assessed. Outcomes included modified Rankin Scale, Barthel Index, and ‘3 questions’. Data were analysed using a variety of approaches which compare two treatment groups. The results for each statistical test for each trial were then compared. Results: Data from 55 datasets were obtained (47 trials, 54,173 patients). The test results differed substantially so that approaches which use the ordered nature of functional outcome data (ordinal logistic regression, t-test, robust ranks test, bootstrapping the difference in mean rank) were more efficient statistically than those which collapse the data into 2 groups (chi square) (ANOVA p<0.001). The findings were consistent across different types and sizes of trial and for the different measures of functional outcome. Conclusions: When analysing functional outcome from stroke trials, statistical tests which use the original ordered data are more efficient and more likely to yield reliable results. Suitable approaches included ordinal logistic regression, t-test, and robust ranks test.

Can we improve the statistical analysis of stroke trials? Statistical reanalysis of functional outcomes in stroke trials

Background and Purpose—Most large acute stroke trials have been neutral. Functional outcome is usually analyzed using a yes or no answer, eg, death or dependency versus independence. We assessed which statistical approaches are most efficient in analyzing outcomes from stroke trials. Methods—Individual patient data from acute, rehabilitation and stroke unit trials studying the effects of interventions which alter functional outcome were assessed. Outcomes included modified Rankin Scale, Barthel Index, and “3 questions”. Data were analyzed using a variety of approaches which compare 2 treatment groups. The results for each statistical test for each trial were then compared. Results—Data from 55 datasets were obtained (47 trials, 54 173 patients). The test results differed substantially so that approaches which use the ordered nature of functional outcome data (ordinal logistic regression, t test, robust ranks test, bootstrapping the difference in mean rank) were more efficient statistically than those which collapse the data into 2 groups (2; ANOVA, P0.001). The findings were consistent across different types and sizes of trial and for the different measures of functional outcome. Conclusions—When analyzing functional outcome from stroke trials, statistical tests which use the original ordered data are more efficient and more likely to yield reliable results. Suitable approaches included ordinal logistic regression, test, and robust ranks test.

Effect of telmisartan on functional outcome, recurrence, and blood pressure in patients with acute mild ischemic stroke: a PRoFESS subgroup analysis

Background and Purpose—High blood pressure (BP) is common in acute ischemic stroke and associated independently with a poor functional outcome. However, the management of BP acutely remains unclear because no large trials have been completed. Methods—The factorial PRoFESS secondary stroke prevention trial assessed BP-lowering and antiplatelet strategies in 20 332 patients; 1360 were enrolled within 72 hours of ischemic stroke, with telmisartan (angiotensin receptor antagonist, 80 mg/d, n647) vs placebo (n713). For this nonprespecified subgroup analysis, the primary outcome was functional outcome at 30 days; secondary outcomes included death, recurrence, and hemodynamic measures at up to 90 days. Analyses were adjusted for baseline prognostic variables and antiplatelet assignment. Results—Patients were representative of the whole trial (age 67 years, male 65%, baseline BP 147/84 mm Hg, small artery disease 60%, NIHSS 3) and baseline variables were similar between treatment groups. The mean time from stroke to recruitment was 58 hours. Combined death or dependency (modified Rankin scale: OR, 1.03; 95% CI, 0.84–1.26; P0.81; death: OR, 1.05; 95% CI, 0.27–4.04; and stroke recurrence: OR, 1.40; 95% CI, 0.68–2.89; P0.36) did not differ between the treatment groups. In comparison with placebo, telmisartan lowered BP (141/82 vs 135/78 mmHg, difference 6 to 7 mmHg and 2 to 4 mmHg; P0.001), pulse pressure (3 to 4 mmHg; P0.002), and rate-pressure product (466 mmHg.bpm; P0.0004). Conclusion—Treatment with telmisartan in 1360 patients with acute mild ischemic stroke and mildly elevated BP appeared to be safe with no excess in adverse events, was not associated with a significant effect on functional dependency, death, or recurrence, and modestly lowered BP.