A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation

Rephrasing the backbone of two-dimensional percolation as a monochromatic path crossing problem, we investigate the latter by a transfer matrix approach. Conformal invariance links the backbone dimension D_b to the highest eigenvalue of the transfer matrix T, and we obtain the result D_b=1.6431 \pm 0.0006. For a strip of width L, T is roughly of size 2^{3^L}, but we manage to reduce it to \sim L!. We find that the value of D_b is stable with respect to inclusion of additional ``blobs'' tangent to the backbone in a finite number of points.Comment: 19 page

Finite average lengths in critical loop models

A relation between the average length of loops and their free energy is obtained for a variety of O(n)-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number) averaged loop length L stays finite for all non-zero fugacities n, and in particular it does not diverge upon entering the critical regime n -> 2+. Fully packed loop (FPL) models with n=2 seem to obey the simple relation L = 3 L_min, where L_min is the smallest loop length allowed by the underlying lattice. We demonstrate this analytically for the FPL model on the honeycomb lattice and for the 4-state Potts model on the square lattice, and based on numerical estimates obtained from a transfer matrix method we conjecture that this is also true for the two-flavour FPL model on the square lattice. We present in addition numerical results for the average loop length on the three critical branches (compact, dense and dilute) of the O(n) model on the honeycomb lattice, and discuss the limit n -> 0. Contact is made with the predictions for the distribution of loop lengths obtained by conformal invariance methods.Comment: 20 pages of LaTeX including 3 figure

Maintenance of response with atypical antipsychotics in the treatment of schizophrenia: a post-hoc analysis of 5 double-blind, randomized clinical trials

<p>Abstract</p> <p>Background</p> <p>How long an antipsychotic is effective in maintaining response is important in choosing the correct treatment for people with schizophrenia. This post-hoc analysis describes maintenance of response over 24 or 28 weeks in people treated for schizophrenia with olanzapine, risperidone, quetiapine, ziprasidone, or aripiprazole.</p> <p>Methods</p> <p>This was a post-hoc analysis using data from 5 double-blind, randomized, comparative trials of 24 or 28 weeks duration in which olanzapine was compared to risperidone (1 study; N = 339), quetiapine (1 study; N = 346), ziprasidone (2 studies; N = 548 and 394) or aripiprazole (1 study; N = 566) for treatment of schizophrenia. For each study, time to loss of response in patients who met criteria for response at Week 8 and the proportion of patients who lost response following Week 8 were compared by treatment group. The number needed to treat (NNT) with olanzapine rather than comparator to avoid loss of one additional responder over 24 or 28 weeks of treatment was calculated for each study.</p> <p>Results</p> <p>Time maintained in response was significantly longer (p < .05) for olanzapine compared to risperidone, quetiapine, and ziprasidone. Olanzapine did not significantly differ from aripiprazole. The proportion of patients who lost response was significantly lower for olanzapine versus risperidone, quetiapine, and ziprasidone (p < .05). NNTs to avoid one additional patient with loss of response with olanzapine versus risperidone, quetiapine and ziprasidone were favourable, ranging from 5 to 9.</p> <p>Conclusion</p> <p>During 24 and 28 weeks of treatment, the antipsychotics studied differed in the time that treated patients with schizophrenia remained in response and the proportion of patients who lost response. Olanzapine treatment resulted in a consistent and statistically significant advantage in maintenance of response compared to treatment with risperidone, quetiapine and ziprasidone; but not compared to treatment with aripiprazole.</p

Identification of early changes in specific symptoms that predict longer-term response to atypical antipsychotics in the treatment of patients with schizophrenia

<p>Abstract</p> <p>Background</p> <p>To identify a simple decision tree using early symptom change to predict response to atypical antipsychotic therapy in patients with (Diagnostic and Statistical Manual, Fourth Edition, Text Revised) chronic schizophrenia.</p> <p>Methods</p> <p>Data were pooled from moderately to severely ill patients (n = 1494) from 6 randomized, double-blind trials (N = 2543). Response was defined as a ≥30% reduction in Positive and Negative Syndrome Scale (PANSS) Total score by Week 8 of treatment. Analyzed predictors were change in individual PANSS items at Weeks 1 and 2. A decision tree was constructed using classification and regression tree (CART) analysis to identify predictors that most effectively differentiated responders from non-responders.</p> <p>Results</p> <p>A 2-branch, 6-item decision tree was created, producing 3 distinct groups. First branch criterion was a 2-point score decrease in at least 2 of 5 PANSS positive items (Week 2). Second branch criterion was a 2-point score decrease in the PANSS excitement item (Week 2). "Likely responders" met the first branch criteria; "likely non-responders" did not meet first or second criterion; "not predictable" patients did not meet the first but did meet the second criterion. Using this approach, response to treatment could be predicted in most patients (92%) with high positive predictive value (79%) and high negative predictive value (75%). Predictive findings were confirmed through analysis of data from 2 independent trials.</p> <p>Conclusions</p> <p>Using a data-driven approach, we identified decision rules using early change in the scores of selected PANSS items to accurately predict longer-term treatment response or non-response to atypical antipsychotic therapy. This could lead to development of a simple quantitative evaluation tool to help guide early treatment decisions.</p> <p>Trial Registration</p> <p>This is a retrospective, non-intervention study in which pooled results from 6 previously published reports were analyzed; thus, clinical trial registration is not required.</p

The potential role of appetite in predicting weight changes during treatment with olanzapine

Background Clinically significant weight gain has been reported during treatment with atypical antipsychotics. It has been suggested that weight changes in patients treated with olanzapine may be associated with increased appetite. Methods Data were used from adult patients for whom both appetite and weight data were available from 4 prospective, 12- to 24-week clinical trials. Patients' appetites were assessed with Eating Behavior Assessment (EBA, Study 1), Platypus Appetite Rating Scale (PARS, Study 2), Eating Inventory (EI, Study 3), Food Craving Inventory (FCI, Study 3), and Eating Attitude Scale (EAS, Study 4). Results In Studies 1 (EBA) and 4 (EAS), patients who reported overall score increases on appetite scales, indicating an increase in appetite, experienced the greatest overall weight gains. However, in Studies 2 (PARS) and 3 (EI, FCI), patients who reported overall score increases on appetite scales did not experience greater weight changes than patients not reporting score increases. Early weight changes (2-4 weeks) were more positively correlated with overall weight changes than early or overall score changes on any utilized appetite assessment scale. No additional information was gained by adding early appetite change to early weight change in correlation to overall weight change. Conclusions Early weight changes may be a more useful predictor for long-term weight changes than early score changes on appetite assessment scales

Time to discontinuation of atypical versus typical antipsychotics in the naturalistic treatment of schizophrenia

BACKGROUND: There is an ongoing debate over whether atypical antipsychotics are more effective than typical antipsychotics in the treatment of schizophrenia. This naturalistic study compares atypical and typical antipsychotics on time to all-cause medication discontinuation, a recognized index of medication effectiveness in the treatment of schizophrenia. METHODS: We used data from a large, 3-year, observational, non-randomized, multisite study of schizophrenia, conducted in the U.S. between 7/1997 and 9/2003. Patients who were initiated on oral atypical antipsychotics (clozapine, olanzapine, risperidone, quetiapine, or ziprasidone) or oral typical antipsychotics (low, medium, or high potency) were compared on time to all-cause medication discontinuation for 1 year following initiation. Treatment group comparisons were based on treatment episodes using 3 statistical approaches (Kaplan-Meier survival analysis, Cox Proportional Hazards regression model, and propensity score-adjusted bootstrap resampling methods). To further assess the robustness of the findings, sensitivity analyses were performed, including the use of (a) only 1 medication episode for each patient, the one with which the patient was treated first, and (b) all medication episodes, including those simultaneously initiated on more than 1 antipsychotic. RESULTS: Mean time to all-cause medication discontinuation was longer on atypical (N = 1132, 256.3 days) compared to typical antipsychotics (N = 534, 197.2 days; p < .01), and longer on atypicals compared to typicals of high potency (N = 320, 187.5 days; p < .01), medium potency (N = 140, 213.5 days; p < .01), and low potency (N = 74, 208.7 days; p < .01). Among the atypicals, only clozapine, olanzapine, and risperidone had significantly longer time to all-cause medication discontinuation compared to typicals, regardless of potency level, and compared to haloperidol with prophylactic anticholinergic treatment. When compared to perphenazine, a medium-potency typical antipsychotic, only clozapine and olanzapine had a consistently and significantly longer time to all-cause medication discontinuation. Results were confirmed by sensitivity analyses. CONCLUSION: In the usual care of schizophrenia patients, time to medication discontinuation for any cause appears significantly longer for atypical than typical antipsychotics regardless of the typical antipsychotic potency level. Findings were primarily driven by clozapine and olanzapine, and to a lesser extent by risperidone. Furthermore, only clozapine and olanzapine therapy showed consistently and significantly longer treatment duration compared to perphenazine, a medium-potency typical antipsychotic