Penalized Poisson model for network meta-analysis of individual patient time-to-event data

Network meta-analysis (NMA) allows the combination of direct and indirect evidence from a set of randomized clinical trials. Performing NMA using individual patient data (IPD) is considered as a gold standard approach as it provides several advantages over NMA based on aggregate data. For example, it allows to perform advanced modelling of covariates or covariate-treatment interactions. An important issue in IPD NMA is the selection of influential parameters among terms that account for inconsistency, covariates, covariate-by-treatment interactions or non-proportionality of treatments effect for time to event data. This issue has not been deeply studied in the literature yet and in particular not for time-to-event data. A major difficulty is to jointly account for between-trial heterogeneity which could have a major influence on the selection process. The use of penalized generalized mixed effect model is a solution, but existing implementations have several shortcomings and an important computational cost that precludes their use for complex IPD NMA. In this article, we propose a penalized Poisson regression model to perform IPD NMA of time-to-event data. It is based only on fixed effect parameters which improve its computational cost over the use of random effects. It could be easily implemented using existing penalized regression package. Computer code is shared for implementation. The methods were applied on simulated data to illustrate the importance to take into account between trial heterogeneity during the selection procedure. Finally, it was applied to an IPD NMA of overall survival of chemotherapy and radiotherapy in nasopharyngeal carcinoma

Chemical sensitivity to the ratio of the cosmic-ray ionization rates of He and H2 in dense clouds

Aim: To determine whether or not gas-phase chemical models with homogeneous and time-independent physical conditions explain the many observed molecular abundances in astrophysical sources, it is crucial to estimate the uncertainties in the calculated abundances and compare them with the observed abundances and their uncertainties. Non linear amplification of the error and bifurcation may limit the applicability of chemical models. Here we study such effects on dense cloud chemistry. Method: Using a previously studied approach to uncertainties based on the representation of rate coefficient errors as log normal distributions, we attempted to apply our approach using as input a variety of different elemental abundances from those studied previously. In this approach, all rate coefficients are varied randomly within their log normal (Gaussian) distribution, and the time-dependent chemistry calculated anew many times so as to obtain good statistics for the uncertainties in the calculated abundances. Results: Starting with so-called ``high-metal'' elemental abundances, we found bimodal rather than Gaussian like distributions for the abundances of many species and traced these strange distributions to an extreme sensitivity of the system to changes in the ratio of the cosmic ray ionization rate zeta\_He for He and that for molecular hydrogen zeta\_H2. The sensitivity can be so extreme as to cause a region of bistability, which was subsequently found to be more extensive for another choice of elemental abundances. To the best of our knowledge, the bistable solutions found in this way are the same as found previously by other authors, but it is best to think of the ratio zeta\_He/zeta\_H2 as a control parameter perpendicular to the ''standard'' control parameter zeta/n\_H.Comment: Accepted for publicatio

Maple procedures for the coupling of angular momenta. VI. LS-jj transformations

Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open-shell atoms and ions. While, for instance, relativistic computations are traditionally carried out in jj-coupling, a LSJ coupling notation often occurs much more appropriate for classifying the valence-shell structure of atoms. Apart from the (known) transformation of single open shells, however, further demand on proper transformation coefficients has recently arose from the study of open d- and f-shell elements, the analysis of multiple--excited levels, or the investigation on inner-shell phenomena. Therefore, in order to facilitate a simple access to LS jj transformation matrices, here we present an extension to the Racah program for the set-up and the transformation of symmetry-adapted functions. A flexible notation is introduced for defining and for manipulating open-shell configurations at different level of complexity which can be extended also to other coupling schemes and, hence, may help determine an optimum classification of atomic levels and processes in the future

On the master equation approach to diffusive grain-surface chemistry: the H, O, CO system

We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO2), formaldehyde (H2CO), and methanol (CH3OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.Comment: 13 pages, 5 figure

On the ionisation fraction in protoplanetary disks III. The effect of X-ray flares on gas-phase chemistry

Context. Recent observations of the X-ray emission from T Tauri stars in the Orion nebula have shown that they undergo frequent outbursts in their X-ray luminosity. These X-ray flares are characterised by increases in luminosity by two orders of magnitude, a typical duration of less than one day, and a significant hardening of the X-ray spectrum. Aims. It is unknown what effect these X-ray flares will have on the ionisation fraction and dead-zone structure in protoplanetary disks. We present the results of calculations designed to address this question. Methods. We have performed calculations of the ionisation fraction in a standard $\alpha$-disk model using two different chemical reaction networks. We include in our models ionisation due to X-rays from the central star, and calculate the time-dependent ionisation fraction and dead--zone structure for the inner 10 AU of a protoplanetary disk model. Results. We find that the disk response to X-ray flares depends on whether the plasma temperature increases during flares and/or whether heavy metals (such as magnesium) are present in the gas phase. Under favourable conditions the outer disk dead--zone can disappear altogether,and the dead-zone located between 0.5 < R < 2 AU can disappear and reappear in phase with the X-ray luminosity. Conclusions. X-ray flares can have a significant effect on the dead-zone structure in protoplanetary disks. Caution is required in interpreting this result as the duration of X-ray bursts is considerably shorter than the growth time of MHD turbulence due to the magnetorotational instability.Comment: 12 pages, 8 figures, accepted by A &

On the Ionisation Fraction in Protoplanetary Disks II: The Effect of Turbulent Mixing on Gas--phase Chemistry

We calculate the ionisation fraction in protostellar disk models using two different gas-phase chemical networks, and examine the effect of turbulent mixing by modelling the diffusion of chemical species vertically through the disk. The aim is to determine in which regions of the disk gas can couple to a magnetic field and sustain MHD turbulence. We find that the effect of diffusion depends crucially on the elemental abundance of heavy metals (magnesium) included in the chemical model. In the absence of heavy metals, diffusion has essentially no effect on the ionisation structure of the disks, as the recombination time scale is much shorter than the turbulent diffusion time scale. When metals are included with an elemental abundance above a threshold value, the diffusion can dramatically reduce the size of the magnetically decoupled region, or even remove it altogther. For a complex chemistry the elemental abundance of magnesium required to remove the dead zone is 10(-10) - 10(-8). We also find that diffusion can modify the reaction pathways, giving rise to dominant species when diffusion is switched on that are minor species when diffusion is absent. This suggests that there may be chemical signatures of diffusive mixing that could be used to indirectly detect turbulent activity in protoplanetary disks. We find examples of models in which the dead zone in the outer disk region is rendered deeper when diffusion is switched on. Overall these results suggest that global MHD turbulence in protoplanetary disks may be self-sustaining under favourable circumstances, as turbulent mixing can help maintain the ionisation fraction above that necessary to ensure good coupling between the gas and magnetic field.Comment: 11 pages, 7 figures; accepted for publication in A &

Time-dependent H2 formation and protonation

Methods: The microscopic equations of H2-formation and protonation are integrated numerically over time in such a manner that the overall structures evolve self-consistently under benign conditions. Results: The equilibrium H2 formation timescale in an H I cloud with N(H) ~ 4x10^{20}/cm^2 is 1-3 x 10^7 yr, nearly independent of the assumed density or H2 formation rate constant on grains, etc. Attempts to speed up the evolution of the H2-fraction would require densities well beyond the range usually considered typical of diffuse gas. The calculations suggest that, under benign, quiescent conditions, formation of H2 is favored in larger regions having moderate density, consistent with the rather high mean kinetic temperatures measured in H2, 70-80 K. Formation of H3+ is essentially complete when H2-formation equilibrates but the final abundance of H3+ appears more nearly at the very last instant. Chemistry in a weakly-molecular gas has particular properties so that the abundance patterns change appreciably as gas becomes more fully molecular, either in model sequences or with time in a single model. One manifestation of this is that the predicted abundance of H3+ is much more weakly dependent on the cosmic-ray ionization rate when n(H2)/n(H) < 0.05. In general, high abundances of H3+ do not enhance the abundances of other species (e.g. HCO+) but late-time OH formation proceeds most vigourously in more diffuse regions having modest density, extinction and H2 fraction and somewhat higher fractional ionization, suggesting that atypically high OH/H2 abundance ratios might be found optically in diffuse clouds having modest extinction

The chemistry of compact planetary nebulae

We report high-sensitivity millimetre observations of several molecular species (13CO, HCN, HNC, CN, HCO+ and N2H+) in a sample of compact planetary nebulae. Some species such as HCO+ and CN are particularly abundant compared to envelopes around AGB stars or even interstellar clouds. We have estimated the following average values for the column densities ratios: CN/HCN~2.6, HCO+/HCN~0.5, and HNC/HCN~0.4. Thus, the chemical composition of the molecular envelopes in these compact PNe appears somewhat intermediate between the composition of proto-PNe (such as CRL 2688 or CRL 618) and well evolved PNe (such as the Ring, M4--9, or the Helix). From observations of the CO isotopomers, we have estimated that the 12C/13C ratio is in the range 10 ~< 12C/13C ~< 40. These values are below those expected from standard asymptotic giant branch models and suggest non-standard mixing processes. The observed molecular abundances are compared to very recent modelling work, and we conclude that the observations are well explained, in general terms, by time-dependent gas-phase chemical models in which the ionization rate is enhanced by several orders of magnitude with respect to the average interstellar value. Thus, our observations confirm that the chemistry in the neutral shells of PNe is essentially governed by the high energy radiation from the hot central stars. The complexity of the chemical processes is increased by numerous factors linked to the properties of the central star and the geometry and degree of clumpiness of the envelope. Several aspects of the PN chemistry that remains to be understood are discussed within the frame of the available chemical models.Comment: 9 pages, 3 figures. "In press" in Astronomy and Astrophysic

Molecular dark matter in galaxies

Clouds containing molecular dark matter in quantities relevant for star formation may exist in minihaloes of the type of cold dark matter included in many cosmological simulations or in the regions of some galaxies extending far beyond their currently known boundaries. We have systematically explored parameter space to identify conditions under which plane-parallel clouds contain sufficient column densities of molecular dark matter that they could be reservoirs for future star formation. Such clouds would be undetected or at least appear by current observational criteria to be uninteresting from the perspective of star formation. We use a time-dependent PDR code to produce theoretical models of the chemistry and emission arising in clouds for our chosen region of parameter space. We then select a subset of model clouds with levels of emission that are low enough to be undetectable or at least overlooked by current surveys. The existence of significant column densities of cold molecular dark matter requires that the background radiation field be several or more orders of magnitude weaker than that in the solar neighbourhood. Lower turbulent velocities and cosmic ray induced ionization rates than typically associated with molecular material within a kpc of the Sun are also required for the molecular matter to be dark. We find that there is a large region within the parameter space that results in clouds that might contain a significant mass of molecular gas whilst remaining effectively undetectable or at least not particularly noticeable in surveys. We note briefly conditions under which molecular dark matter may contain a dynamically interesting mass.Comment: 9 pages, 2 figures, accepted for publication in A&A; additional concluding paragraph added at proof stag