What\u27s missing in missing data? Omissions in survey responses among parents of children with advanced cancer

Background: Missing data is a common phenomenon with survey-based research; patterns of missing data may elucidate why participants decline to answer certain questions. Objective: To describe patterns of missing data in the Pediatric Quality of Life and Evaluation of Symptoms Technology (PediQUEST) study, and highlight challenges in asking sensitive research questions. Design: Cross-sectional, survey-based study embedded within a randomized controlled trial. Setting: Three large children\u27s hospitals: Dana-Farber/Boston Children\u27s Cancer and Blood Disorders Center (DF/BCCDC); Children\u27s Hospital of Philadelphia (CHOP); and Seattle Children\u27s Hospital (SCH). Measurements: At the time of their child\u27s enrollment, parents completed the Survey about Caring for Children with Cancer (SCCC), including demographics, perceptions of prognosis, treatment goals, quality of life, and psychological distress. Results: Eighty-six of 104 parents completed surveys (83% response). The proportion of missing data varied by question type. While 14 parents (16%) left demographic fields blank, over half (n=48; 56%) declined to answer at least one question about their child\u27s prognosis, especially life expectancy. The presence of missing data was unrelated to the child\u27s diagnosis, time from progression, time to death, or parent distress (p>0.3 for each). Written explanations in survey margins suggested that addressing a child\u27s life expectancy is particularly challenging for parents. Conclusions and Relevance: Parents of children with cancer commonly refrain from answering questions about their child\u27s prognosis, however, they may be more likely to address general cure likelihood than explicit life expectancy. Understanding acceptability of sensitive questions in survey-based research will foster higher quality palliative care research. © Copyright 2014, Mary Ann Liebert, Inc. 2014

Structure of the vacuum states in the presence of isovector and isoscalar pairing correlations

The long standing problem of proton-neutron pairing and, in particular, the limitations imposed on the solutions by the available symmetries, is revisited. We look for solutions with non-vanishing expectation values of the proton, the neutron and the isoscalar gaps. For an equal number of protons and neutrons we find two solutions where the absolute values of proton and neutrons gaps are equal but have the same or opposite sign. The behavior and structure of these solutions differ for spin saturated (single l-shell) and spin unsaturared systems (single j-shell). In the former case the BCS results are checked against an exact calculation.Comment: 19 pages, 5 postscript figure

Neutron-proton pairing in the BCS approach

We investigate the BCS treatment of neutron-proton pairing involving time-reversed orbits. We conclude that an isospin-symmetric hamiltonian, treated with the help of the generalized Bogolyubov transformation, fails to describe the ground state pairing properties correctly. In order for the np isovector pairs to coexist with the like-particle pairs, one has to break the isospin symmetry of the hamiltonian by artificially increasing the strength of np pairing interaction above its isospin symmetric value. We conjecture that the np isovector pairing represents part (or most) of the congruence energy (Wigner term) in nuclear masses.Comment: 9 pages, RevTex, submitted to Phys. Rev.

Neutron-Proton Correlations in an Exactly Solvable Model

We examine isovector and isoscalar neutron-proton correlations in an exactly solvable model based on the algebra SO(8). We look particularly closely at Gamow-Teller strength and double beta decay, both to isolate the effects of the two kinds of pairing and to test two approximation schemes: the renormalized neutron-proton QRPA (RQRPA) and generalized BCS theory. When isoscalar pairing correlations become strong enough a phase transition occurs and the dependence of the Gamow-Teller beta+ strength on isospin changes in a dramatic and unfamiliar way, actually increasing as neutrons are added to an N=Z core. Renormalization eliminates the well-known instabilities that plague the QRPA as the phase transition is approached, but only by unnaturally suppressing the isoscalar correlations. Generalized BCS theory, on the other hand, reproduces the Gamow-Teller strength more accurately in the isoscalar phase than in the usual isovector phase, even though its predictions for energies are equally good everywhere. It also mixes T=0 and T=1 pairing, but only on the isoscalar side of the phase transition.Comment: 13 pages + 11 postscript figures, in RevTe

Collective quadrupole excitations in the 50<Z,N<82 nuclei with the generalized Bohr Hamiltonian

The generalized Bohr Hamiltonian is applied to a description of low-lying collective excitations in even-even isotopes of Te, Xe, Ba, Ce, Nd and Sm. The collective potential and inertial functions are determined by means of the Strutinsky method and the cranking model, respectively. A shell-dependent parametrization of the Nilsson potential is used. An approximate particle-number projection is performed in treatment of pairing correlations. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameter.Comment: Latex2e source, 20 pages, 14 figures in EPS format, tar gzipped fil

Solutions of the Bohr hamiltonian, a compendium

The Bohr hamiltonian, also called collective hamiltonian, is one of the cornerstone of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the $V(\beta,\gamma)$ potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in $\gamma-$unstable and $\gamma-$stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments, and an appendix on the analysis of a few interesting numerical sequences appearing in this context. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.Comment: 48 pages, 28 figures, 6 table

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page

An Algebraic Pairing Model with Sp(4) Symmetry and its Deformation

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0^+ ground states, they also have a large effect on the energies of excited states, including especially excited 0^+ states. In this article we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp_{(q)}(4) to different realizations of u_{(q)}(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0^{+} states of even-even and odd-odd nuclei in the 1d_{3/2}, 1f_{7/2}, and 1f_{5/2}2p_{1/2}2p_{3/2}1g_{9/2} shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Sp_{q}(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with non-linear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0^{+} energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking, and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher-order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.Comment: 19 pages, 5 figures minor changes; improvements to achieve a better and clearer presentation of our messages and idea