Asymptotic Relative Risk Results from a Simplified Armitage and Doll Model of Carcinogenesis.

We examine basic asymptotic properties of relative risk for two families of generalized Erlang processes (where each one is based off of a simplified Armitage and Doll multistage model) in order to predict relative risk data from cancer. The main theorems that we are able to prove are all corroborated by large clinical studies involving relative risk for former smokers and transplant recipients. We then show that at least some of these theorems do not extend to other Armitage and Doll multistage models. We conclude with suggestions for lifelong increased cancer screening for both former smoker and transplant recipient subpopulations of individuals and possible future directions of research.

Patterns of glycaemic control in patients with type 2 diabetes mellitus initiating second-line therapy after metformin monotherapy: Retrospective data for 10 256 individuals from the United Kingdom and Germany.

AIM: To investigate determinants of change in glycated haemoglobin (HbA1c) in patients with type 2 diabetes mellitus (T2DM) at 6 months after initiating uninterrupted second-line glucose-lowering therapies. MATERIALS AND METHODS: This cohort study utilized retrospective data from 10 256 patients with T2DM who initiated second-line glucose-lowering therapy (switch from or add-on to metformin) between 2011 and 2014 in Germany and the UK. Effects of pre-specified patient characteristics on 6-month HbA1c changes were assessed using analysis of covariance. RESULTS: Patients had a mean (standard error [SE]) baseline HbA1c of 8.68% (0.02); 28.5% of patients discontinued metformin and switched to an alternative therapy and the remainder initiated add-on therapy. Mean (SE) unadjusted 6-month HbA1c change was -1.27% (0.02). When adjusted for baseline HbA1c, 6-month changes depended markedly on the magnitude of the baseline HbA1c (HbA1c <9%, -0.45% per unit increase in HbA1c; HbA1c ≥9%, -0.87% per unit increase in HbA1c). Adjusted mean 6-month HbA1c reductions showed slight treatment differences (range, 0.92-1.09%; P < .001). Greater reductions in HbA1c were associated with second-line treatment initiation within 6 months of T2DM diagnosis (1.36% vs 1.03% [P < .001]) and advanced age (≥70 years, 1.13%; <70 years, 1.02% [P < .001]). CONCLUSIONS: Many patients with T2DM have very high HbA1c levels when initiating second-line therapy, indicating the need for earlier treatment intensification. Patient-specific factors merit consideration when making treatment decisions.

Characteristic patterns of cancer incidence: Epidemiological data, biological theories, and multistage models.

We investigate and classify several patterns in cancer incidence and relative risk data which persist across different countries and multiple published studies. We then explore biological hypotheses as well as many mathematical models in the literature that attempt to explain these patterns. A general modeling framework is presented which is general enough to model most of observed behaviors. It is our belief that this model has sufficient flexibility to be adapted to new information as it is discovered. As one application of this framework, we give a model for the effect of aging on the process of carcinogenesis.

Clinical and Patient-Related Variables Associated with Initiating GLP-1 Receptor Agonist Therapy in Type 2 Diabetes Patients in Primary Care in Germany.

AIMS: To investigate real-world clinical and patient-related variables associated with initiating GLP-1 receptor agonist (GLP-1RA) treatment relative to initiation of other glucose-lowering therapies in type 2 diabetes (T2D) patients of primary care in Germany. METHODS: Data for 938 T2D patients who started therapy with a GLP-1RA within 823 practices of primary care throughout Germany were retrospectively analyzed (Disease Analyser: 01/2011-03/2014). 5,197 T2D patients who initiated other non-GLP-1RA antidiabetic therapies were selected as controls. Multivariate logistic regression analyses were applied to identify factors associated with GLP-1RA initiation in primary care. RESULTS: Mean age (SD) of GLP-1RA users was 57.8 (11.8) years (males: 55.5%) and the average BMI was 36.1 (6.7) kg/m2. 22.8% were in diabetologist care and 12.0% had private health insurance. In multivariate regression, choice of GLP-1RA therapy instead of a different glucose-lowering drug class was associated with obesity (odds ratio: 1.68; 95% CI: 1.34-2.10), private health insurance (2.42; 1.89-3.09), younger age (0.94; 0.93-0.95 per year), male sex (0.85; 0.73-0.99), diabetologist care (2.11; 1.73-2.57), and geographic practice location (East vs. West-Germany; 1.25; 1.05-1.49). Among co-medication, angiotensin II antagonists (increased) and non-steroidal antirheumatic agents (decreased) were related to GLP-1RA prescriptions (both p<0.001). CONCLUSIONS: Consistent with German guidelines, GLP-1RA is mainly prescribed preferentially in T2D patients who are obese. GLP-1RA drugs were more frequently used than other options in privately health insured patients and in patients seeing a diabetologist.