On the consistency of multiclass classification methods

Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that not all generalizations preserve the nice property of Bayes consistency. We provide a necessary and sufficient condition for consistency which applies to a large class of multiclass classification methods. The approach is illustrated by applying it to some multiclass methods proposed in the literature.

On the consistency of multiclass classification methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Identification of area-level influences on regions of high cancer incidence in Queensland, Australia : a classification tree approach

Background: Strategies for cancer reduction and management are targeted at both individual and area levels. Area-level strategies require careful understanding of geographic differences in cancer incidence, in particular the association with factors such as socioeconomic status, ethnicity and accessibility. This study aimed to identify the complex interplay of area-level factors associated with high area-specific incidence of Australian priority cancers using a classification and regression tree (CART) approach. Methods: Area-specific smoothed standardised incidence ratios were estimated for priority-area cancers across 478 statistical local areas in Queensland, Australia (1998-2007, n=186,075). For those cancers with significant spatial variation, CART models were used to identify whether area-level accessibility, socioeconomic status and ethnicity were associated with high area-specific incidence. Results: The accessibility of a person’s residence had the most consistent association with the risk of cancer diagnosis across the specific cancers. Many cancers were likely to have high incidence in more urban areas, although male lung cancer and cervical cancer tended to have high incidence in more remote areas. The impact of socioeconomic status and ethnicity on these associations differed by type of cancer. Conclusions: These results highlight the complex interactions between accessibility, socioeconomic status and ethnicity in determining cancer incidence risk.

Utility of routine data sources for feedback on the quality of cancer care: an assessment based on clinical practice guidelines

Background Not all cancer patients receive state-of-the-art care and providing regular feedback to clinicians might reduce this problem. The purpose of this study was to assess the utility of various data sources in providing feedback on the quality of cancer care. Methods Published clinical practice guidelines were used to obtain a list of processes-of-care of interest to clinicians. These were assigned to one of four data categories according to their availability and the marginal cost of using them for feedback. Results Only 8 (3%) of 243 processes-of-care could be measured using population-based registry or administrative inpatient data (lowest cost). A further 119 (49%) could be measured using a core clinical registry, which contains information on important prognostic factors (e.g., clinical stage, physiological reserve, hormone-receptor status). Another 88 (36%) required an expanded clinical registry or medical record review; mainly because they concerned long-term management of disease progression (recurrences and metastases) and 28 (11.5%) required patient interview or audio-taping of consultations because they involved information sharing between clinician and patient. Conclusion The advantages of population-based cancer registries and administrative inpatient data are wide coverage and low cost. The disadvantage is that they currently contain information on only a few processes-of-care. In most jurisdictions, clinical cancer registries, which can be used to report on many more processes-of-care, do not cover smaller hospitals. If we are to provide feedback about all patients, not just those in larger academic hospitals with the most developed data systems, then we need to develop sustainable population-based data systems that capture information on prognostic factors at the time of initial diagnosis and information on management of disease progression.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

What We Have Here is a Failure to Communicate! Improving Communication between Tertiary to Primary Care for Chronic Heart Failure Patients

Background:  The aims of this study were to determine the documentation of pharmacotherapy optimization goals in the discharge letters of patients with the principal diagnosis of chronic heart failure. Methods:  A retrospective practice audit of 212 patients discharged to the care of their local general practitioner from general medical units of a large tertiary hospital. Details of recommendations regarding ongoing pharmacological and non-pharmacological management were reviewed. The doses of medications on discharge were noted and whether they met current guidelines recommending titration of angiotensin-converting enzyme inhibitors and beta-blockers. Ongoing arrangements for specialist follow up were also reviewed. Results:  The mean age of patients whose letters were reviewed was 78.4 years (standard deviation ± 8.6); 50% were men. Patients had an overall median of six comorbidities and eight regular medications on discharge. Mean length of stay for each admission was 6 days. Discharge letters were posted a median of 4 days after discharge, with 25% not posted at 10 days. No discharge letter was sent in 9.4% (20) of the cases. Only six (2.8%) letters had any recommendations regarding future titration of angiotensin-converting enzyme inhibitors and 6.6% (14) for beta-blockers. Recommendations for future non-pharmacological management, for example, diuretic action plans, regular weight monitoring and exercise plans were not found in the letters in this audit. Conclusion:  Hospital discharge is an opportunity to communicate management plans for treatment optimization effectively, and while this opportunity is spurned, implementation gaps in the management of cardiac failure will probably remain.

Randomised controlled trial of a supervised exercise rehabilitation program for colorectal cancer survivors immediately after chemotherapy: study protocol

Background Colorectal cancer (CRC) diagnosis and the ensuing treatments can have a substantial impact on the physical and psychological health of survivors. As the number of CRC survivors increases, so too does the need to develop viable rehabilitation programs to help these survivors return to good health as quickly as possible. Exercise has the potential to address many of the adverse effects of CRC treatment; however, to date, the role of exercise in the rehabilitation of cancer patients immediately after the completion of treatment has received limited research attention. This paper presents the design of a randomised controlled trial which will evaluate the feasibility and efficacy of a 12-week supervised aerobic exercise program (ImPACT Program) on the physiological and psychological markers of rehabilitation, in addition to biomarkers of standard haematological outcomes and the IGF axis. Methods/Design Forty CRC patients will be recruited through oncology clinics and randomised to an exercise group or a usual care control group. Baseline assessment will take place within 4 weeks of the patient completing adjuvant chemotherapy treatment. The exercise program for patients in the intervention group will commence a week after the baseline assessment. The program consists of three supervised moderate-intensity aerobic exercise sessions per week for 12 weeks. All participants will have assessments at baseline (0 wks), mid-intervention (6 wks), post-intervention (12 wks) and at a 6-week follow-up (18 wks). Outcome measures include cardio-respiratory fitness, biomarkers associated with health and survival, and indices of fatigue and quality of life. Process measures are participants' acceptability of, adherence to, and compliance with the exercise program, in addition to the safety of the program. Discussion The results of this study will provide valuable insight into the role of supervised exercise in improving life after CRC. Additionally, process analyses will inform the feasibility of implementing the program in a population of CRC patients immediately after completing chemotherapy.