In developing regression models, data analysts are often faced with many predictor variables that may influence an outcome variable. After more than half a century of research, the 'best' way of selecting a multivariable model is still unresolved. It is generally agreed that subject matter knowledge, when available, should guide model building. However, such knowledge is often limited, and data-dependent model building is required. We limit the scope of the modelling exercise to selecting important predictors and choosing interpretable and transportable functions for continuous predictors. Assuming linear functions, stepwise selection and all-subset strategies are discussed; the key tuning parameters are the nominal P-value for testing a variable for inclusion and the penalty for model complexity, respectively. We argue that stepwise procedures perform better than a literature-based assessment would suggest. Concerning selection of functional form for continuous predictors, the principal competitors are fractional polynomial functions and various types of spline techniques. We note that a rigorous selection strategy known as multivariable fractional polynomials (MFP) has been developed. No spline-based procedure for simultaneously selecting variables and functional forms has found wide acceptance. Results of FP and spline modelling are compared in two data sets. It is shown that spline modelling, while extremely flexible, can generate fitted curves with uninterpretable 'wiggles', particularly when automatic methods for choosing the smoothness are employed. We give general recommendations to practitioners for carrying out variable and function selection. While acknowledging that further research is needed, we argue why MFP is our preferred approach for multivariable model building with continuous covariates.

During early embryogenesis, microglia arise from yolk sac progenitors that populate the developing central nervous system (CNS), but how the tissue-resident macrophages are maintained throughout the organism's lifespan still remains unclear. Here, we describe a system that allows specific, conditional ablation of microglia in adult mice. We found that the microglial compartment was reconstituted within 1 week of depletion. Microglia repopulation relied on CNS-resident cells, independent from bone-marrow-derived precursors. During repopulation, microglia formed clusters of highly proliferative cells that migrated apart once steady state was achieved. Proliferating microglia expressed high amounts of the interleukin-1 receptor (IL-1R), and treatment with an IL-1R antagonist during the repopulation phase impaired microglia proliferation. Hence, microglia have the potential for efficient self-renewal without the contribution of peripheral myeloid cells, and IL-1R signaling participates in this restorative proliferation process.

BackgroundIn network meta-analyses, several treatments can be compared by connecting evidence from clinical trials that have investigated two or more treatments. The resulting trial network allows estimating the relative effects of all pairs of treatments taking indirect evidence into account. For a valid analysis of the network, consistent information from different pathways is assumed. Consistency can be checked by contrasting effect estimates from direct comparisons with the evidence of the remaining network. Unfortunately, one deviating direct comparison may have side effects on the network estimates of others, thus producing hot spots of inconsistency.MethodsWe provide a tool, the net heat plot, to render transparent which direct comparisons drive each network estimate and to display hot spots of inconsistency: this permits singling out which of the suspicious direct comparisons are sufficient to explain the presence of inconsistency. We base our methods on fixed-effects models. For disclosure of potential drivers, the plot comprises the contribution of each direct estimate to network estimates resulting from regression diagnostics. In combination, we show heat colors corresponding to the change in agreement between direct and indirect estimate when relaxing the assumption of consistency for one direct comparison. A clustering procedure is applied to the heat matrix in order to find hot spots of inconsistency.ResultsThe method is shown to work with several examples, which are constructed by perturbing the effect of single study designs, and with two published network meta-analyses. Once the possible sources of inconsistencies are identified, our method also reveals which network estimates they affect.ConclusionOur proposal is seen to be useful for identifying sources of inconsistencies in the network together with the interrelatedness of effect estimates. It opens the way for a further analysis based on subject matter considerations.

AimsAircraft noise disturbs sleep, and long-term exposure has been shown to be associated with increases in the prevalence of hypertension and an overall increased risk for myocardial infarction. The exact mechanisms responsible for these cardiovascular effects remain unclear.Methods and resultsWe performed a blinded field study in 75 healthy volunteers (mean age 26 years), who were exposed at home, in random order, to one control pattern (no noise) and two different noise scenarios [30 or 60 aircraft noise events per night with an average maximum sound pressure level (SPL) of 60 dB(A)] for one night each. We performed polygraphy during each study night. Noise caused a worsening in sleep quality (P < 0.0001). Noise60, corresponding to equivalent continuous SPLs of 46.3 dB (Leq) and representing environmental noise levels associated with increased cardiovascular events, caused a blunting in FMD (P = 0.016). As well, although a direct comparison among the FMD values in the noise groups (control: 10.4 ± 3.8%; Noise30: 9.7 ± 4.1%; Noise60: 9.5 ± 4.3%, P = 0.052) did not reach significance, a monotone dose-dependent effect of noise level on FMD was shown (P = 0.020). Finally, there was a priming effect of noise, i.e. the blunting in FMD was particularly evident when subjects were exposed first to 30 and then to 60 noise events (P = 0.006). Noise-induced endothelial dysfunction (ED) was reversed by the administration of Vitamin C (P = 0.0171). Morning adrenaline concentration increased from 28.3 ± 10.9 to 33.2 ± 16.6 and 34.1 ± 19.3 ng/L (P = 0.0099). Pulse transit time, reflecting arterial stiffness, was also shorter after exposure to noise (P = 0.003).ConclusionIn healthy adults, acute nighttime aircraft noise exposure dose-dependently impairs endothelial function and stimulates adrenaline release. Noise-induced ED may be in part due to increased production in reactive oxygen species and may thus be one mechanism contributing to the observed association of chronic noise exposure with cardiovascular disease.

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