On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

Overview of data assimilation methods

We present the data assimilation approach, which provides a framework for combining observations and model simulations of the climate system, and has led to a new field of applications for paleoclimatology. The three subsequent articles explore specific applications in more detail.

Role of diuretics, blockers, and statins in increasing the risk of diabetes in patients with impaired glucose tolerance: reanalysis of data from the NAVIGATOR study

OBJECTIVE To examine the degree to which use of β blockers, statins, and diuretics in patients with impaired glucose tolerance and other cardiovascular risk factors is associated with new onset diabetes. DESIGN Reanalysis of data from the Nateglinide and Valsartan in Impaired Glucose Tolerance Outcomes Research (NAVIGATOR) trial. SETTING NAVIGATOR trial. PARTICIPANTS Patients who at baseline (enrolment) were treatment naïve to β blockers (n=5640), diuretics (n=6346), statins (n=6146), and calcium channel blockers (n=6294). Use of calcium channel blocker was used as a metabolically neutral control. MAIN OUTCOME MEASURES Development of new onset diabetes diagnosed by standard plasma glucose level in all participants and confirmed with glucose tolerance testing within 12 weeks after the increased glucose value was recorded. The relation between each treatment and new onset diabetes was evaluated using marginal structural models for causal inference, to account for time dependent confounding in treatment assignment. RESULTS During the median five years of follow-up, β blockers were started in 915 (16.2%) patients, diuretics in 1316 (20.7%), statins in 1353 (22.0%), and calcium channel blockers in 1171 (18.6%). After adjusting for baseline characteristics and time varying confounders, diuretics and statins were both associated with an increased risk of new onset diabetes (hazard ratio 1.23, 95% confidence interval 1.06 to 1.44, and 1.32, 1.14 to 1.48, respectively), whereas β blockers and calcium channel blockers were not associated with new onset diabetes (1.10, 0.92 to 1.31, and 0.95, 0.79 to 1.13, respectively). CONCLUSIONS Among people with impaired glucose tolerance and other cardiovascular risk factors and with serial glucose measurements, diuretics and statins were associated with an increased risk of new onset diabetes, whereas the effect of β blockers was non-significant.

A reconstruction of radiocarbon production and total solar irradiance from the Holocene ¹⁴C and CO₂ records: implications of data and model uncertainties

Radiocarbon production, solar activity, total solar irradiance (TSI) and solar-induced climate change are reconstructed for the Holocene (10 to 0 kyr BP), and TSI is predicted for the next centuries. The IntCal09/SHCal04 radiocarbon and ice core CO2 records, reconstructions of the geomagnetic dipole, and instrumental data of solar activity are applied in the Bern3D-LPJ, a fully featured Earth system model of intermediate complexity including a 3-D dynamic ocean, ocean sediments, and a dynamic vegetation model, and in formulations linking radiocarbon production, the solar modulation potential, and TSI. Uncertainties are assessed using Monte Carlo simulations and bounding scenarios. Transient climate simulations span the past 21 thousand years, thereby considering the time lags and uncertainties associated with the last glacial termination. Our carbon-cycle-based modern estimate of radiocarbon production of 1.7 atoms cm−2 s−1 is lower than previously reported for the cosmogenic nuclide production model by Masarik and Beer (2009) and is more in-line with Kovaltsov et al. (2012). In contrast to earlier studies, periods of high solar activity were quite common not only in recent millennia, but throughout the Holocene. Notable deviations compared to earlier reconstructions are also found on decadal to centennial timescales. We show that earlier Holocene reconstructions, not accounting for the interhemispheric gradients in radiocarbon, are biased low. Solar activity is during 28% of the time higher than the modern average (650 MeV), but the absolute values remain weakly constrained due to uncertainties in the normalisation of the solar modulation to instrumental data. A recently published solar activity–TSI relationship yields small changes in Holocene TSI of the order of 1 W m−2 with a Maunder Minimum irradiance reduction of 0.85 ± 0.16 W m−2. Related solar-induced variations in global mean surface air temperature are simulated to be within 0.1 K. Autoregressive modelling suggests a declining trend of solar activity in the 21st century towards average Holocene conditions.