Introduction {#s1}
============

There has been increasing interest in the use of 'decision aids' [@pone.0004705-OConnor1], defined as adjuncts to the discussions clinicians have with patients during deliberations about decisions: these aids provide information about options and help clarify personal values [@pone.0004705-OConnor2]. These adjuncts range from leaflets through face to face methods such as coaching or counselling to interactive multimedia websites. To describe this generic family of clinician-patient interventions we will use the term *decision support technologies* (DSTs) [@pone.0004705-OConnor3], corresponding with the internationally recognised need to assess the impact of 'health technologies' [@pone.0004705-Banta1]. DSTs are complex interventions which require detailed assessment to ensure safe use in healthcare contexts [@pone.0004705-OConnor3] because they help make options explicit, provide information about harms and benefits, clarify patient values\' and provide structured means to help people deliberate when making decisions. Although there are published methods to assess the quality of clinical practice guidelines [@pone.0004705-Cluzeau1], DSTs go further and address issues of equipoise for which patients need to deliberate about difficult choices [@pone.0004705-Elwyn1]. However, as yet, there are no reliable methods to assure the quality of DSTs development process, content, potential bias, and method of field testing and evaluation -- a gap which we address in this study. We did not intend to develop methods to assess how DSTs are used in practice, in the clinical encounter, although we recognise that this is an important area that requires further work.

There are reports that DSTs have achieved a 'tipping point' in the US and are widely accessed by increasing numbers of patients [@pone.0004705-OConnor1]. The ability of DSTs to improve the quality of decisions and enable reductions in discretionary surgery and invasive procedures without adverse effects on health outcomes has been demonstrated in clinical trials [@pone.0004705-OConnor2], [@pone.0004705-Coulter1]. The central role that these technologies will play in future healthcare systems is increasingly recognised [@pone.0004705-OConnor1], [@pone.0004705-OConnor4]--[@pone.0004705-Godlee1]. Over the last decade, the interest in developing DSTs has moved beyond research groups and has entered the commercial world. A global interest in developing DSTs has emerged among both for-profit and not-for-profit organisations. It is therefore essential to have a set of internationally accepted standards to assess their quality, to assess whether interests are declared and whether they are unduly biased [@pone.0004705-OConnor4], [@pone.0004705-HolmesRovner1].

The International Patient Decision Aid Standards (IPDAS) Collaboration produced a checklist for the assessment of DSTs [@pone.0004705-Elwyn2]. The checklist was rigorously developed in a two stage web-based Delphi process using online rating process to enable international collaboration. A total of 122 individuals from four stakeholder groups (researchers, practitioners, patients, policy makers) representing 14 countries reviewed background evidence summaries, and rated the importance of 80 criteria in 12 quality dimensions. Second round participants received feedback from the first round and repeated their assessment of the 80 criteria plus three new ones. The IPDAS checklist enabled broad assessments in 12 dimensions: systematic development process, providing information about options; presentation of probabilities; clarification of values; use of patient stories; information about guiding or coaching; disclosure of interests; providing internet access; balanced presentation of options; use of plain language; use of up-to-date evidence; and effectiveness. The IPDAS checklist allows users, developers and others to assess whether these technologies contain the suggested components and judge whether they underwent rigorous development and evaluation. It has been used in updating the Cochrane systematic review of DSTs and to guide the development of DSTs [@pone.0004705-Evans1], [@pone.0004705-OConnor5].

However, the checklist was not designed to provide precise, quantitative assessments, such that judgements could be made about the quality of DSTs, either at item, dimension or global levels. In addition, because not all checklist items were applicable to every DST, comparability, even at the checklist level, was not possible. Given interest in being able to assess these DSTs at a more precise level of detail --- in terms of how they were developed and field tested, whether their content was valid and whether effectiveness had been evaluated with patients facing relevant decisions --- the IPDAS Collaboration agreed that achieving this objective would require an instrument capable of quantitatively assessing the quality of DSTs. The aim of this article is to describe the development, validation and inter-rater reliability of an IPDAS instrument (IPDASi), built on the existing framework.

Methods {#s2}
=======

IPDASi was developed in four stages.

Stage 1 Refinement and preparation of instrument (IPDASi v1) {#s2a}
------------------------------------------------------------

The published IPDAS checklist required transformation into a quantitative instrument, although we agreed to adopt the dimension-item framework. As part of this preparation, a group of researchers (GE, DS, RT, CB, SB, TW) used the existing checklist and dimension-item framework to score three purposefully selected DSTs, representing different design approaches and where our prior overall assessments indicated variable quality. These were Healthwise\'s Breast Cancer Surgery (BCS), web-based information, Bastian&McBrides Hormone Replacement Therapy (HRT), an illustrated booklet, and Wolf et al\'s Prostate Specific Antigen (PSA) screening, a brief text-based script. A binary (yes/no) and 'not applicable' scale was proposed; comments were collected on item applicability. Tabulations and qualitative analyses were performed but inter-rater correlations were not calculated.

Stage 2 IPDASi Confirmation of items (IPDASi v2) {#s2b}
------------------------------------------------

On the basis of the results of Stage 1, a refined version IPDAS instrument (IPDASi v2) was designed and used in Stage 2. The non-applicable option was removed, and in this and all subsequent versions, a 4-point rating scale was used for each item, with possible responses as follows: strongly agree = score 4 (the issue is addressed clearly and comprehensively); agree = score 3 (the issue is addressed but with room for improvement); disagree = score 2 (the DST fails to clearly address the issue); strongly disagree = score 1 (the DST totally fails to address the issue). In common with the binary (yes/no) scale it replaced, the scale intentionally does not include a midpoint expressing neutrality. Items in the 'balance' dimension were integrated into the 'information' dimension. The web dimension was not applicable to all DSTs, therefore removed. A website was created for data collection (<http://www.ipdasi.org/>). Scale anchor point descriptions were developed for all items.

Five raters, two in the UK (MA-D and SS, Cardiff) and three in North America (ED and SK in Ottawa and MP in Providence) were familiarised with IPDASi v2, prior to using it to score the three previously selected DSTs, and asked to comment on item phrasing. Members of the IPDASi development group were asked to view the IPDASi instrument online and comment on item phrasing. For IPDASi v2 and subsequent versions, item scores were rescaled to be 0 to 100. At Stage 2, only an unweighted average of all items was calculated, as our focus was not on dimension scores. Analysis included inter-rater reliability using intraclass correlations for two way random effects at item and global score levels [@pone.0004705-Yaffee1].

Stage 3 IPDASi Validation Study {#s2c}
-------------------------------

Based on the results of Stage 2, a third version, IPDASi v3 was designed. This retained the majority of items from Stage 2, albeit with changes to phrasing. It comprised 47 items representing 10 dimensions. 9 dimensions applicable to all DSTs relate to Information (8 items); Probabilities (8 items); Values (4 items); Decision Guidance (2 items); Development (6 items); Evidence (5 items); Disclosure (2 items); Plain language (1 item); Evaluation (2 items). One additional dimension (9 items) relates to decisions based around tests or screening. Feedback from the comments resulted in more detailed anchor scale descriptions and standardization of descriptions.

IPDASi v3 was then used in a validation study to assess the quality of a sample of DSTs. Two approaches were used to achieve a sample of DSTs. First, five major producers of publically available DSTs were identified (The Foundation for Informed Medical Decision Making, Healthwise, Mayo Clinic, Midwives Information and Resource Service (MIDIRS) and Ottawa Health Decision Centre (OHDeC). Three DSTs from each producer were chosen at random, giving a total of 15. Second, 66 English-language DSTs, for which contact details were available, were chosen at random from the Cochrane inventory maintained by the University of Ottawa (<http://decisionaid.ohri.ca/cochinvent.php>), and their developers were approached and asked:

1.  Whether the DST was in current use and free of charge to clients;

2.  For consent to assess the DST using IPDASi; and

3.  For copies or information about documentation (published reports or peer reviewed articles) about the development or evaluation of the DST.

Each DST included in the sample was prepared for assessment in a standardised way. Background documents (relevant publications, reports) and all DST content were made available online (either in pdf or html formats; videos were converted into Windows Media Video format) for raters to assess. [Table 1](#pone-0004705-t001){ref-type="table"} provides details of the DSTs that were included in the sample, and the results of the IPDASi assessments.

10.1371/journal.pone.0004705.t001

###### Thirty sampled decision support technologies: sample characteristics and adjusted full IPDASi (v3) [\*](#nt101){ref-type="table-fn"} and SF scores based on duplicate assessment, with 95% confidence limits.

![](pone.0004705.t001){#pone-0004705-t001-1}

  ID\#    Raters       Developer                                                                       Title                                                                                Topic Area                                            Format                                    Length \# Pages/Duration           IPDASi Scores
  ------ --------- ------------------ ---------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------- --------------------------------------------------------------- ------------------------------------- ------------------- -------------------
  32      NJ, ED     Wakefield, MU     Genetic testing for breast cancer ovarian cancer risk: A decision aid for people with a family history of breast and/or ovarian cancer    Breast and ovarian cancer screening                             Text (paper)                                    v1 40 pp, v2 32 pp            81.5 (74.3--88.8)   83.1 (72.1--94.2)
  1050    NJ, MP         OHDeC                                                 Should you have a steroid injection for tennis elbow?                                                    Tennis elbow treatment                                 Text (paper, PDF)                                        7 pp                   77.4 (70.2--84.6)   72.5 (61.5--83.4)
  1197    MS, ED         OHDeC                                    Should you take steroids and immunosuppressive agents for lupus kidney disease?                                   Lupus kidney disease treatment                             Text (paper, PDF)                                        7 pp                   71.9 (64.7--79.1)   72.4 (61.4--83.4)
  1174    SS, SK         OHDeC                                                  Long Term Feeding Tube Placement in Elderly Patients                                                    End of life treatment                            Web site or Text (paper, PDF)                      37 Web pp with audio 23 pages      69.2 (62.1--76.4)   67.4 (56.5--78.2)
  35      MAD, AS         MCC                                             Making the Choice: What to do about early stage prostate cancer                                             Prostate cancer treatment                          Web site or Text (paper, PDF)                                49 Web pp                65.5 (58.3--72.7)   80.9 (69.9--91.9)
                                                                                28 pp
  48      MS, SK     Wakefield, MU        Genetic testing for hereditary non-polyposis colorectal cancer (HNPCC): A decision aid for people with a family history of HNPCC        Colorectal cancer: genetic testing                             Text (paper)                                           40 pp                  65.1 (57.8--72.3)      67 (56--78)
  3       MAD, AS     Shorten, ACM                                                                 Birth Choices                                                                    Vaginal birth after caesarean                                Text (paper)                                           14 pp                  64.0 (56.8--71.2)   73.6 (62.6--84.6)
  17      MS, MP       Elwyn, CU                                                                      Prosdex                                                                         Prostate cancer screening                                    Web site                              84 Web pp with audio&12 video clips   62.5 (55.2--69.8)   68.2 (57.1--79.4)
  37      MAD, SK      Col, CORE                                               Women\'s Interactive System for Decisions on Menopause                                                    Menopause treatment             Web site (portions of Web site unavailable at time of review)               441 Web pp                62.0 (54.9--69.2)   59.2 (48.4--70.1)
  13      MAD, ED     Leighl, UoT                             Decision Aid for Patients with Metastatic Colorectal Cancer Facing a Treatment Decision                                Colorectal cancer treatment                                 Text (paper)                                           32 pp                  62.0 (54.9--69.2)   74.7 (63.8--85.6)
  1046    MAD, SK     Mayo Clinic                                                               Birth Control Guide                                                                        Family planning                                         Web site                                             63 pp                  61.1 (54.0--68.3)   59.2 (48.4--70.1)
  1023    SS, MP         FIMDM                                                     Treatment Choices for Coronary Artery Disease                                                  Coronary artery disease treatment                                  Video                                             51 min                  56.1 (48.9--63.3)   61.6 (50.6--72.6)
  54      SS, MP          APCC                                             Localized Prostate Cancer: A guide for men and their families                                              Prostate cancer treatment                                  Text (paper)                                          103 pp                  54.8 (47.6--62.0)   53.2 (42.2--64.2)
  53      SS, AS    Lawrence, STVHCS                                                          Mammography Decision Aid                                                                 Breast cancer screening                               Decision board&script                                      4 pp                   52.6 (45.3--59.8)   63.2 (52.2--74.2)
                                                                                7 pp
  1012    MS, MP       Healthwise                                                 Should I take medicine for high blood pressure?                                                   High blood pressure treatment                                  Web site                                             18 pp                  51.8 (44.4--59.1)   35.5 (24.4--46.6)
  1121    NJ, SK         FIMDM                                          Hormone Therapy: When the PSA rises after prostate cancer treatment                                           Prostate cancer treatment                               Video&Text (paper)                                       37 min                  51.7 (44.5--59.0)   57.4 (46.4--68.4)
                                                                                29 pp
  1090    MS, AS         FIMDM                                                 Colon Cancer Screening: Deciding What\'s Right For You                                                   Colon cancer screening                                Video&Text (paper)                                       32 min                  50.5 (43.3--57.7)    56.9 (46--67.9)
                                                                                21 pp
  1011    MAD, ED      Healthwise                                                 Should I take antibiotics for acute bronchitis?                                                     Acute bronchitis treatment                                   Web site                                             33 pp                  49.0 (41.8--56.1)   41.4 (30.5--52.2)
  15      SS, SK      Barratt, UoS                                         Should I Start Having Mammograms to Screen for Breast Cancer?                                               Breast cancer Screening                                     Web site                                           15 Web pp                48.4 (41.3--55.6)   55.8 (44.9--66.7)
  64      MAD, MP      Taylor, GU                                        The Right Decision is Yours: A Guide to Prostate Cancer Check-Ups                                            Prostate cancer screening                                  Text (paper)                                           19 pp                  46.1 (38.9--53.4)   44.7 (33.7--55.7)
  1059    MAD, MP        MIDIRS                                            If your baby is in the breech position, what are your choices?                                                    Breech birth                                        Text (paper)                                  13 pp of 122 pp booklet         45.1 (37.8--52.3)   39.9 (28.9--50.9)
  1150    SS, AS      Mayo Clinic                                                          Enlarged prostate (BPH) guide                                                        Benign prostatic hypertrophy treatment                             Web site                                 69 Web pp with 11 video clips      44.7 (37.5--52.0)   46.3 (35.3--57.3)
  1067    NJ, AS       Healthwise                                                Should I have tests for irritable bowel syndrome?                                                Irritable bowel syndrome screening                               Web site                                             31 pp                  44.1 (36.8--51.4)   34.5 (23.3--45.6)
  49      MS, ED     Crouch, Baylor                                                        Statin Therapy Informed Choice                                                             High cholesterol treatment                                 Text (paper)                                           9 pp                   43.9 (36.7--51.1)   53.6 (42.6--64.6)
  1155    NJ, ED         MIDIRS                                                       Ultrasound scans: what you need to know                                                             Prenatal screening                                     Text (paper)                                  13 pp of 122 pp booklet         43.5 (36.2--50.7)   39.3 (28.3--50.3)
  6       SS, ED          NERI                                                       Urinary Incontinence: Finding the Solution                                                          Urinary incontinence                                     Video: Male                                          27 min                  43.3 (36.1--50.4)   48.5 (37.6--59.3)
                                                                                Female                                             21 min
  12      NJ, SK          NERI                                               Making the Right Choice: Decision aid for prostate cancer                                                Prostate cancer treatment                                      Video                                             39 min                  43.2 (35.9--50.4)   53.3 (42.3--64.3)
  1061    SS, ED      Mayo Clinic                                                           Carpal tunnel syndrome guide                                                               Carpal tunnel treatment                                     Web site                                 50 Web pp with 14 video clips      39.3 (32.2--46.5)    40.1 (29.2--51)
  1056    MS, SK         MIDIRS                                                                    Place of birth                                                                      Location of child birth                                   Text (paper)                                  11 pp of 122 pp booklet         37.3 (30.0--44.5)   36.1 (25.1--47.1)
  1       NJ, AS         US CDC                                          Prostate Cancer Screening. A decision guide for African Americans                                            Prostate cancer screening                          Web site or Text (paper, PDF)                                   1 p                   32.9 (25.6--40.3)    44.1 (33--55.2)
                                                                                20 pp

Adjusted scores: scores from the two raters were adjusted to take account of their personal propensity to give higher or lower scores. Components of variation were modelled by Bayesian modelling (Markov chain Monte Carlo) using WinBugs software, leading to estimated confidence intervals.

**Abbreviations**: (APCC: Australian Prostate Cancer Collaboration; Barratt, UoS: University of Sydney; Crouch, Baylor: Baylor College of Medicine; Col, CORE: Center for Outcomes Research and Evaluation; Elwyn, CU: Cardiff University; FIMDM: Foundation for Informed Medical Decision Making; Lawrence, STVHCS: South Texas Veterans Health Care System; Leighl, UoT: University of Toronto; MCC: Michigan Cancer Consortium Prostate Cancer Action Committee; MIDIRS: Midwife Information and Resource Service; NERI: New England Research Institutes; OHDeC: Ottawa Health Decision Centre; Shorten, ACM: Australian College of Midwives; Taylor, GU: Georgetown University; US CDC: Centers for Disease Control and Prevention; Wakefield MU, Macquarie University).

Eight raters with diverse backgrounds and training were trained to undertake independent ratings: four in the UK (MA-D, MS, NJ, SS in Cardiff) and four in North America (SK, ED, AS in Ottawa; MP in Providence). Each DST was scored by two raters, one chosen randomly from each location, such that one rating was done in UK and the other in North America. New raters were asked to pilot the instrument on a 'test' DST and new raters also had access to raters who had completed the Stage 2 assessment if they required advice on item interpretation.

As in Stage 2, each item was scored on a 4-point scale, rescaled from 0 to 100, and dimension means were calculated. Two overall scores were calculated, scaled 0 to 100: the unweighted mean of all items (38 or 47, depending on whether the DST addressed a treatment or a test/screening decision) and the weighted mean score, a mean of the 9 or 10 dimension-specific means. The latter score upweights items belonging to dimensions comprising few items and downweights items from dimensions with many, but each dimension contributes an equal weight into the final score.

Summary statistics were calculated for dimension scores and unweighted and weighted overall means. Weighted means were modelled by rater and tool in a two-way balanced incomplete ANOVA model. Intraclass correlations and Cronbach\'s alpha, by each rater and by dimension means, were also calculated. The quality of each DST was then characterised by the average of the weighted mean scores from the two raters, adjusted by the model to take account of their personal propensity to give higher or lower scores. We wanted to predict the degree of accuracy if others used IPDASi in the future, considering one or two raters, known to us (i.e. one of the existing eight raters) or unknown to us. To achieve this, components of variation were determined by Bayesian modelling (Markov chain Monte Carlo) using WinBugs software [@pone.0004705-Lunn1], to arrive at estimated confidence interval half-widths for differing future rating situations. The raters\' qualitative comments were summarised.

Stage 4 Agreement on IPDASi-SF (short form) {#s2d}
-------------------------------------------

A core set of items was also chosen to develop a 'short form' (IPDASi-SF) aiming to test whether a 'minimum' quality threshold could be established. By agreement in the development group, these criteria were chosen based on having an *equimedian* score of 9 (i.e. maximum agreement) in the IPDAS consensus process [@pone.0004705-Elwyn2]. The equimedian is designed to represent the cumulative distribution function for a population with equal numbers in each of the four stakeholder groups [@pone.0004705-Elwyn2]. In addition, core-set items represented key concepts for each dimension. The 19 items selected for the IPDASi-SF consisted of 3 items for tests/screening and 16 others for all DSTs including: Information (4 items: options available, positive features, negative features, and fair comparison); Probabilities (3 items: reference class, event rates, compare probabilities); Values (1 item: personal importance); Development (3 items: patients\' needs, impartial review, tested with patients) ; Disclosure (1 item: information about funding); Evaluation (2 items: knowledge, improved decision quality); Evidence (2 items: citations to studies, production date). The three items selected for the test/screening dimension included: next steps, chances of detection, non-symptomatic. These SF items were not highlighted for special attention during the rating process. Unweighted mean scores were calculated (i.e. all SF items and not the means related to their respective dimensions), and correlations (Pearson) with the IPDASi overall mean adjusted weighted score ([Table 2](#pone-0004705-t002){ref-type="table"}).

10.1371/journal.pone.0004705.t002

###### Development of IPDASi versions and IPDASi-SF: item retention and dimension merging.

![](pone.0004705.t002){#pone-0004705-t002-2}

  Stage                                             1                                                                         2                                                                                3                                                          4
  ------------------------------ ---------------------------------------- ---------------------------------------------------------------------------------------------------------- ---------------------------------------------------------- ----------------------------------------------------------
  **IPDASi version**                            IPDASi v1                                                                 IPDASi v2                                                                          IPDASi v3                                                  IPDASi SF
  **Number of items**              62[\*](#nt103){ref-type="table-fn"}                                                        48                                                                                47                                                         19
  **Assessors/Raters**            Expert group (GE, DS, RT, CB, SB, TW).                           Cardiff: MA-D, MS, NJ, SS; North America: SK, ED, AS MP.                           Cardiff: MA-D, MS, NJ, SS; North America: SK, ED, AS MP.   Cardiff: MA-D, MS, NJ, SS; North America: SK, ED, AS MP.
  **Number of DSTs evaluated**                      3                                                                         3                                                                                30                                                         30
  **Dimensions**
  Information                                       8                                                                         8                                                                                8                                                          4
  Probabilities                                     10                                                                        8                                                                                8                                                          3
  Values                                            3                                                                         5                                                                                4                                                          1
  Decision Guidance                                 3                                                                         2                                                                                2                                                          --
  Development                                       7                                                                         6                                                                                6                                                          3
  Evidence                                          6                                                                         5                                                                                5                                                          2
  Disclosure                                        2                                                                         2                                                                                2                                                          1
  Plain Language                                    3                                                                         1                                                                                1                                                          --
  Evaluation                                        7                                                                         2                                                                                2                                                          2
  Test                                              5                                                                         9                                                                                9                                                          3
  Web-based                                         6                      Items did not meet inclusion assumption of being applicable to all DSTs and were therefore not included.
  Balance                                           2                                                   This dimension was merged with probabilities.

IPDASi v1 is equivalent to the IPDAS Checklist.

Test dimension items applicable to relevant DSTs.

Results {#s3}
=======

[Table 2](#pone-0004705-t002){ref-type="table"} provides a synopsis of the different versions, detailed in the four stages.

Stage 1 Refinement and preparation of instrument (IPDAS v1) {#s3a}
-----------------------------------------------------------

Results of the seven raters were compared. The number of comments made at the interpretation level and the wide variation in scoring indicated a need for further item development. In addition some items had double criteria. In October 2006, five researchers met (AC, AOC, DS, CB&GE) and, using the results of this Stage, judged each item against two criteria, clarity and feasibility of measurement. All item phrasings were modified and it was decided to base the development of IPDASi on the following assumptions.

1.  All items should be *applicable* to the assessment of all DSTs. This enables the computation of a standard quality score per DST with no adjustment for specific content. An exception was made for DSTs designed to guide deliberations about undertaking diagnostic or screening tests. This type of DST would be subject to an additional dimension of items relating specifically to information on test characteristics.

2.  All items should meet the criterion of measurement feasibility. At this Stage, we decided to have 10 dimensions in IPDASi, mirroring the dimensions agreed in the IPDAS consensus process. Further information on dimension and items is presented in Stage 3.

Stage 2 Refinement and preparation of instrument (IPDAS v2) {#s3b}
-----------------------------------------------------------

Mean scores on a 0--100 scale for the three DSTs were as follows, with SDs reflecting inter-rater variation: HRT 68.7 (6.9); BCS 46.0 (6.5); PSA 38.5 (6.4). The intraclass correlation coefficient was 0.89. These results provided sufficient confidence to refine the instrument for a larger reliability study (Stage 3). Qualitative comments revealed where more specific item anchors descriptors were required, achieved collaboratively using a shared online spreadsheet. Discussions regarding dimension weighting led to agreement that the mean of each dimension should contribute equally to the total score.

Stage 3 Dual rater assessments of 30 DSTs (IPDAS v3) {#s3c}
----------------------------------------------------

[Table 1](#pone-0004705-t001){ref-type="table"} describes the sample of DSTs and provides the results. [Table 3](#pone-0004705-t003){ref-type="table"} lists the items used in IPDAS v3. Three DSTs were assessed from each of the five selected major producers. The other 15 were obtained by approaching 36 developers (representing 47 DSTs). Eighteen developers did not respond and we found that five of the DSTs were no longer in use. After repeated contacts, 13 developers (representing 15 DSTs) agreed to participate in the study, resulting in an overall sample of 30 DSTs.

10.1371/journal.pone.0004705.t003

###### IPDASi v3 Dimensions and Items.

![](pone.0004705.t003){#pone-0004705-t003-3}

  Dimension                                                                                Item
  ----------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  **Information**                                                                                1. The decision support technology describes the health condition or problem (intervention, procedure or investigation) for which the index decision is required
  Providing information about options in sufficient detail for making a specific decision                                                     2. The decision support technology describes the decision that needs to be considered (the index decision)
                                                                                3. The decision support technology describes the options available for the index decision
                                                                                4. The decision support technology describes the natural course of the health condition or problem, if no action is taken.
                                                                                5. The decision support technology describes the positive features (benefits or advantages) of each option
                                                                                6. The decision aid describes negative features (harms, side effects or disadvantages) of each option.
                                                                                7. The decision support technology makes it possible to compare the positive and negative features of the available options.
                                                                                8. The decision support technology shows the negative and positive features of options with equal detail (for example using similar fonts, order, and display of statistical information).
  **Probabilities**                                                                                1. The decision support technology provides information about outcome probabilities associated with the options (i.e. the likely consequences of decisions)
  Presenting outcome probabilities                                                                                2. The decision support technology specifies the defined group (reference class) of patients for which the outcome probabilities apply.
                                                                                3. The decision support technology specifies the event rates for the outcome probabilities (in natural frequencies).
                                                                                4. The decision support technology specifies the time period over which the outcome probabilities apply.
                                                                                5. The decision support technology allows the user to compare outcome probabilities across options using the same denominator and time period.
                                                                                6. The decision support technology provides information about the levels of uncertainty around event or outcome probabilities (e.g. by giving a range or by using phrases such as "our best estimate is...")
                                                                                7. The decision support technology provides more than one way of viewing the probabilities (e.g. words, numbers, and diagrams).
                                                                                8. The decision support technology provides balanced information about event or outcome probabilities to limit framing biases.
  **Values**                                                                                1. The decision support technology describes the features of options to help patients imagine what it is like to experience the physical effects.
  Clarifying and expressing values                                                                                2. The decision support technology describes the features of options to help patients imagine what it is like to experience the psychological effects.
                                                                                3. The decision support technology describes the features of options to help patients imagine what it is like to experience the social effects.
                                                                                4. The decision support technology asks patients to think about which positive and negative features of the options matter most to them.
  **Decision Guidance**                                                                                1. The decision support technology provides a step-by-step way to make a decision.
  Structured guidance in deliberation and communication                                                                      2. The decision support technology includes tools like worksheets or lists of questions to use when discussing options with a practitioner.
  **Development**                                                                                1. The development process included finding out what clients or patients need to prepare them to discuss a specific decision
  Using a systematic development process                                                                                2. The development process included finding out what health professionals need to prepare them to discuss a specific decision with patients
                                                                                3. The development process included expert review by clients/patients not involved in producing the decision support technology
                                                                                4. The development process included expert review by health professionals not involved in producing the decision aid.
                                                                                5. The decision support technology was field tested with patients who were facing the decision.
                                                                                6. The decision support technology was field tested with practitioners who counsel patients who face the decision.
  **Evidence**                                                                                1. The decision support technology (or associated documentation) provides citations to the studies selected.
  Using evidence                                                                                2. The decision support technology (or associated documentation) describes how research evidence was selected or synthesized.
                                                                                3. The decision support technology (or associated documentation) provides a production or publication date.
                                                                                4. The decision support technology (or associated documentation) provides information about the proposed update policy.
                                                                                5. The decision support technology (or associated documentation) describes the quality of the research evidence used.
  **Disclosure**                                                                                1. The decision support technology (or associated technical documentation) provides information about the funding used for development.
  Disclosure and transparency                                                                                2. The decision support technology includes author/developer credentials or qualifications.
  **Plain Language**                                                                                1. The decision support technology (or associated documentation) reports readability levels (using one or more of the available scales).
  Using plain language
  **DST Evaluation**                                                                                1. There is evidence that the decision support technology improves the match between the features that matter most to the informed patient and the option that is chosen
                                                                                2. There is evidence that the patient decision support technology helps patients improve their knowledge about options\' features
  **Test** (for DSTs that are directed at investigations or screening tests)                                                                              1. The decision support technology describes what the test is designed to measure.
                                                                                2. The decision support technology includes information about the chances of having a true positive test result.
                                                                                3. The decision support technology includes information about the chances of having a true negative test result.
                                                                                4. The decision support technology includes information about the chances of having a false positive test result.
                                                                                5. The decision support technology includes information about the chances of having a false negative test result.
                                                                                6. If the test detects the condition or problem, the decision support technology describes the next steps typically taken.
                                                                                7. The decision support technology describes the next steps if the condition or problem is not detected.
                                                                                8. The decision support technology describes the chances that the disease is detected with and without the use of the test.
                                                                                9. The decision support technology has information about the consequences of detecting the condition or disease that would never have caused problems if screening had not been done (lead time bias).

The time taken to assess a DST varies considerably, dependent on its complexity. A simple DST comprising a leaflet could be completed in two hours but assessing multimedia web-based DST required at least 8 hours. A weighted overall score (scaled from 0 to 100) for each DST is shown, averaged over two raters, and then adjusted for the pair of raters. Adjusted IPDASi scores ranged widely from 33 to 82 ([Table 2](#pone-0004705-t002){ref-type="table"}). The intraclass correlation for the weighted overall score was 0.80. Correlations of dimension scores with the weighted overall score were all positive (0.31 to 0.68). Cronbach\'s alpha values for the 8 raters ranged from 0.72 to 0.93. Cronbach\'s alphas based on the means in the 9 dimensions ranged from 0.50 to 0.81, indicating that the dimensions, although relatively well correlated, measure different aspects of DST quality. Calculations of the standard deviation (SD) presenting imprecision using a Bayesian model based on the existing eight raters, and projected for different number of known (one of the existing eight raters used) and unknown raters, for whom we have no information about their scoring tendencies, resulted in the following estimates: two known raters, 6.6; one known rater, 9.4; two unknown raters, 9.3; one unknown rater, 13.1. Qualitative comments were received on some items, requesting clarifications. This was achieved by adding examples and more descriptive elements to the anchor statements.

Stage 4 Agreement on IPDASi short form {#s3d}
--------------------------------------

The mean unweighted score for the short-form 16 item IPDASi was 56.1, similar to 56.3 for all items. The correlation of the unweighted IPDASi-SF to the overall mean weighted score (IPDASi score in [Table 2](#pone-0004705-t002){ref-type="table"}) is 0.87 (CI 0.79--0.92). The ranking of the DSTs according to the SF version are very similar, with adjusted scores ranging from 34.5 to 83.1. DST number 32 still ranks highest, but the order shifts at the lower end of the scale. However, the aim of the IPDASi-SF was not to rank DSTs in order of quality but to determine whether or not a limited set of IPDASi items may be useful in determining minimal levels of quality.

Discussion {#s4}
==========

Principal Findings {#s4a}
------------------

This work demonstrates that IPDASi has the potential to assess the quality of DSTs. The four stage process revealed the need to make significant changes in the IPDAS checklist and modifications to the set of assumptions so that a measurement tool could be applied across the range of all possible DSTs. Having undertaken this work, we also suggest that IPDASi could provide formative feedback about dimensions in which DST developers could make improvements to subsequent versions. A short-form may also support the development of rapidly applicable quality standards. In addition, the study demonstrated the high correlation between IPDASi and IPDASi-SF, demonstrating support for the instrument\'s ability to provide correspondence between scores that indicate high quality at detailed dimension assessment and a version with focus on fewer items.

The study also displayed the levels of measurement imprecision when two raters assess each tool, and points to the need to ensure rater calibration and training in the use of IPDASi prior to assessment. We propose that IPDASi ratings should therefore be undertaken by raters who are familiar with DST development and use and who have undergone calibration training.

Strengths and weaknesses {#s4b}
------------------------

The instrument design is based on prior international consensus which provided a framework in which to assess DST quality, and in addition, a set of criterion-based 'items' for a new instrument. Secondly, the work was planned by researchers who followed a detailed protocol and met regularly. Thirdly, a staged approach was used, adopting the principles of instrument development [@pone.0004705-Streiner1]. Limitations of the study included the limited size of the sample and our focus on only DSTs developed in English, a constraint imposed by resource availability. There are also further opportunities to examine the validity of IPDASi, for example by examining whether low IPDASi scores for the 'probability information' dimension are associated with low patient knowledge about probabilities, when measured in controlled trials. Additionally, the raters used in the second and third stages were all researchers in the DST field and had some content expertise, so it is likely that raters with more diverse backgrounds may not perform as well. There was no opportunity in this study to provide intensive group training to all raters to ensure tight calibration and standardisation of item interpretation. To mitigate against this weakness, a detailed online manual that provided details about scale anchor definitions was available. Nonetheless, the results indicate that there is room to improve inter-rater reliability.

Results in context {#s4c}
------------------

Two other studies have used the IPDAS checklist. Coulter et al undertook a detailed assessment of 40 information materials to support people in making decisions about their health and health care [@pone.0004705-Coulter2]. They found that the overall quality of information was poor and no systematic processes were adopted to give attention to presentational issues, such as readability or to ensure the validity of evidence. O\'Connor et al used the checklist to assess the registered trials and found that several IPDAS process measures had not been used [@pone.0004705-OConnor5]. Williams used IPDASi v2 to assess DSTs for genetic testing for breast cancer [@pone.0004705-Williams1]. We are not aware of any other work that has developed a quantitative measure of DST quality.

Implications {#s4d}
------------

IPDASi, and IPDASi-SF, will be available as a quality assessment method to developers, researchers and purchasers, and given a recognised need to set standards and achieve benchmarks, will be subject to further development. The existing IPDASi provides an assessment of the quality of a DST\'s components, and in the absence of any other method, will be used as a tool to provide formative advice to DSTs developers and as a summative assessment for those who want to compare their tools against existing benchmarks (<http://www.ipdasi.org>). In due course, data from these assessments might form a platform for potential certification but questions remain. There is for instance only one dimension on evaluation outcomes. The items in this dimension cannot be scored unless the developers have actually conducted an evaluation. It is likely that developers may assert that not all DSTs require evaluation, provided they meet other requirements. However, we contend that research in this field is at an early stage. There is no agreement as yet on the essential 'active' components of DSTs [@pone.0004705-Charles1]; moreover the theoretical underpinning for both their mode of action, measurement models and implementation strategies needs strengthening [@pone.0004705-Durand1], [@pone.0004705-Gravel1]. Further work is needed to assess which DSTs designs are superior to one another. Prospective studies that compare theoretically derived DSTs components and deliberation tools are required to help explore these areas.

The IPDAS collaboration and the resulting instruments (IPDASi and IPDASi-SF) need to meet the following challenges: How can new dimensions and items be considered? How are valid 'option menus' in DSTs derived and agreed when there are complex debates about equity, economics and evidence? Should there be items that assess the use of theory in the development of these methods, given that these are examples of 'complex interventions' and deserve attention to frameworks of design and mode of action [@pone.0004705-Campbell1]. These challenges provide an agenda for future research.

What this paper adds {#s4e}
--------------------

### What is already known on this subject {#s4e1}

Interest in decision support technologies is rapidly increasing and they are being accessed by ever larger number of patients, especially in the United States.

A quality *checklist* for decision support technologies has been published by the International Patient Decision Aid Standards Collaboration.

The checklist was not designed to provide precise, quantitative assessments about the quality these interventions.

### What this study adds {#s4e2}

Describes the development of an instrument which can assess the quality of decision support technologies, thereby enabling formative and summative feedback to developers and purchasers.

**Competing Interests:**The authors have declared that no competing interests exist.

**Funding:**Canadian Institutes of Health Research Group grant; Cardiff University internal funding. No other external funding.

[^1]: Conceived and designed the experiments: GE AO AE. Performed the experiments: GE AO CB MAD ED NJ SK AS SS MS. Analyzed the data: GE CB RGN MP MAD ED NJ SK AS SS MS. Contributed reagents/materials/analysis tools: GE. Wrote the paper: GE AO CB RGN MP MAD ED NJ SK AS SS MS SJB NC AC KE MH MHR NM DS RT TW TvdW AE.


---
abstract: 'Monochromatic gamma-ray lines are thought to be the smoking gun signal of the annihilation or decay of dark matter since they do not suffer from deflection or absorption on galactic scales. A recent claim on strong evidence for two gamma-ray lines from the inner galaxy suggests that two-body final states might be one photon plus a Z boson or one photon plus a Higgs boson. In this study, we investigate which final state is more possible by analyzing the energy resolution of the Fermi-LAT. It is concluded that the former case, i.e. one photon plus a Z boson is more plausible than the latter one, i.e. one photon and a Higgs boson since in the latter case the mass of dark matter particle shows tension with a constraint coming from the energy resolution of the Fermi-LAT.'
---

=cmr5 \#1[\#1\^[\^]{}]{}

\#1

DPUR/TH/31\
July, 2012\

[**Remarks on Two Gamma Ray Lines from the Inner Galaxy** ]{}

Ichiro Oda [^1]

Department of Physics, Faculty of Science, University of the Ryukyus,\
Nishihara, Okinawa 903-0213, Japan.\

There is overwhelming evidence that dark matter pervades our universe undoubtedly, but the identity and nature of dark matter have remained elusive thus far [@Bertone]. The possible connection with proposed extensions beyond the Standard Model (SM) of elementary particles, currently being seeked for at Large Hadron Collider (LHC), makes the identification of dark matter one of the highest priority purposes in particle physics and cosmology. Among a lot of candidates of dark matter particles (denoted as $\chi$ in what follows), the fact that the annihilation cross-section at the electro-weak scale yields the appropriate relic abundance without any artificial fine-tuning has made weakly interacting massive particles (WIMPs) natural dark matter particles [@Jungman].

There are basically three kinds of methods for detecting dark matter particles, which are collider searches, direct and indirect detections. In particular, in the indirect method, one searches for the dark matter annihilation or decay products in cosmic rays which include gamma-rays, electrons, positrons and neutrinos etc. Most of interests in the indirect detection have been recently focused on gamma-rays generated by dark matter annihilation from regions in the surrounding universe with a high density of dark matter such as the galactic center, dwarf spheroidal galaxies and galaxy clusters. Here the lore is that only the dark matter annihilation can produce monochromatic photon lines whereas all standard cosmic phenomena we are aware of have continuous spectra which can be well approximated by a power law. To put differently, an observation of gamma-ray lines from the galactic center etc. can be regarded as a smoking gun signal of dark matter.

However, the world is not so simple and there is a catch. Dark matter is by definition ’dark’, so it does not couple to photons directly at the tree-level. Thus, the dark matter annihilation into photons is induced by loop effects whose rate is in general orders of magnitudes smaller (typically, by the factor $\alpha^2$ with $\alpha$ being the fine-structure constant) than the annihilation into other SM particles. For this reason, most of models treating with dark matter do not account for gamma-ray lines at an observable level although there exist a handful of models where the dark matter annihilation into photons is enhanced by some mechanism and consequently the resulting lines could be observed. Another reason why it is difficult to observe the photon lines is that current detectors have an energy resolution not better than $10\%$, thereby implying that the signal might be smeared or drowned in the continuous background spectra.

In a recent paper by Weniger [@Weniger], it is claimed that a monochromatic gamma-ray line is present at $E_\gamma \approx 130 GeV$ in the data collected during about last 4 years by the Fermi satellite [@Fermi] with a local (global, i.e. after taking account of the look-elsewhere effect) significance of $4.6 \sigma \ (3.3 \sigma)$.[^2] When interpreted as dark matter particles annihilating into a pair of photons [@Bergstrom], the dark matter mass becomes $M_\chi \approx 130 GeV$ and a partial annihilation cross-section takes the value $\langle \sigma v \rangle_{\chi \chi \rightarrow \gamma \gamma} \approx 10^{-27} cm^3/s$, which is a typical cross-section value for weak interaction, and about $1/10$ of the total annihilation cross-section expected if dark matter is a thermal relic from the big bang. However, we should mention that there is some tension between this finding of the gamma-ray line and the result of a line-research analysis by the Fermi-LAT collaboration [@Fermi] even if this tension might stem from a different method of data-analysis.

More recently, using the Fermi-LAT data again, Su and Finkbeiner examine the diffuse $80-200 GeV$ emission in the inner galaxy, and claim that a pair of gamma-ray lines, near $110 GeV$ and $130 GeV$, could provide us with a marginally better fit than a single line [@Su]. An appealing point of their study is that they analyzed photons within $5^\circ$ of galaxy center while the Fermi-LAT collaboration puts constraints on line emission coming from regions outside $5^\circ$ of galaxy center, so there is no conflict between results obtained by both the groups.

Moreover, Su and Finkbeiner also mention that the pair of gamma-ray lines shows a WIMP of mass $127 GeV$ annihilating to $\gamma \gamma$ and $\gamma Z$ [@Bergstrom2]. Even more interestingly, they say that the pair of lines could be compatible with the “Higgs in Space” scenario [@Jackson] where a WIMP of mass $141 GeV$ annhilates into a photon $\gamma$ and a Higgs particle $h$. It is worthwhile to emphasize that if the latter scenario were really true, the indirect detection method of dark matter could have confirmed the existence of the Higgs particle of $125 GeV$ before LHC with the local significance $5 \sigma$!

In this short article, assuming that a correct picture obtained from the Fermi-LAT data is not a single photon line like Weniger but two lines like Su and Finkbeiner, we wish to ask ourselves the following interesting question: Is the “Higgs in Space” scenario able to be confirmed through the analysis of the Fermi-LAT data? In order to answer it, the key idea lies in an observation that the energy resolution of the Fermi-LAT is $10 \%$, i.e. $\frac{\Delta E_\gamma}{E_\gamma} = 0.1$ and this uncertainty leads to a condition on value of the dark matter mass. Then, it turns out that the value of the dark matter particle mass in the “Higgs in Space” scenario is in tension with this condition, so we cannot definitively state that the pair of gamma-ray lines is compatible with the “Higgs in Space” scenario.

Let us start with the following physical situation: Two dark matter particles which annihilate into $\gamma + Y$ (where $Y$ describes a photon $\gamma$, a Z boson $Z$ or a Higgs particle $h$) move with non-relativistic velocities $v \approx 10^{-3} c$. Then, it is easy to see that the energy and momentum conservation laws provide the photon with energy $$\begin{aligned}
E_\gamma = M_\chi ( 1 - \frac{M_Y^2}{4 M_\chi^2} ).
\label{Energy}\end{aligned}$$ In particular, for the annihilation process $\chi + \chi \rightarrow \gamma + \gamma$, we have two photons with energy equal to the dark matter mass $E_\gamma = M_\chi$, which shows a monochromatic $\gamma \gamma$ line with a small energy spread owing to the Doppler effect. A similar gamma-ray peak is expected to be observed for the $\gamma Z$ final state as well as the $\gamma h$ one, but in these cases the intrinsic width of the $Z$ boson and the Higgs particle has to be considered.

One advantage of the satellite experiments like the Fermi-LAT compared to the terrestrial ones is the excellent energy resolution possible, by which one can distinguish a line of $\gamma Z$ final state from that of $\gamma \gamma$ (or $\gamma h$). If not a single but two lines were observed, a comparison between the two lines would give us useful information on a underlying theory behind dark matter physics. For instance, a comparison of line strenghts would provide information on the cross-sections.

Furthermore, it is worthwhile to point out that the energy resolution $\varepsilon \equiv \frac{\Delta E_\gamma}{E_\gamma}$ gives us the condition that the two lines are separable. In the case of $Y = \{\gamma, Z\}$, the two lines take the photon energy $$\begin{aligned}
E_{1\gamma} = M_\chi, \hspace{2.0em}  E_{2\gamma} = M_\chi ( 1 - \frac{M_Z^2}{4 M_\chi^2} ).
\label{Lines1}\end{aligned}$$ The difference of energy between the two lines $\delta E_\gamma$ and its relative ratio $\delta$ are respectively defined as $$\begin{aligned}
\delta E_\gamma &\equiv& E_{1\gamma} - E_{2\gamma} = \frac{M_Z^2}{4 M_\chi},  \nonumber\\
\delta &\equiv& \frac{\delta E_\gamma}{E_\gamma}.
\label{Difference1}\end{aligned}$$ Now let us note that the condition for distinguishing the two photon lines is given by $$\begin{aligned}
\varepsilon  \ll \delta \Longleftrightarrow   \varepsilon \ll \frac{M_Z^2}{4 M_\chi E_\gamma}.
\label{Condition1}\end{aligned}$$ In other words, to discriminate the two photon lines with precision, the energy resolution of a detector must be sufficiently less than the ratio of the energy difference of two peaks to the photon energy observed in the detection.

Since it is now natural to choose $E_\gamma = E_{1\gamma} = M_\chi$, the condition (\[Condition1\]) leads to the constraint on the dark matter mass $$\begin{aligned}
M_\chi \ll \frac{M_Z}{\sqrt{4 \varepsilon}}.
\label{DM mass1}\end{aligned}$$ The Fermi-LAT has the energy resolution $\varepsilon = 0.1$ and the Z boson has mass $M_Z = 91 GeV$, so this constraint reads[^3] $$\begin{aligned}
M_\chi \ll 144 GeV.
\label{Limit1}\end{aligned}$$ In the paper by Su et al. [@Su], the dark matter mass is calculated to be $M_\chi = 127 GeV$ whose value is consistent with this constraint (\[Limit1\]).

Next, let us move on to a case of different gamma-ray lines $Y = \{Z, h \}$ where the two lines take the photon energy $$\begin{aligned}
E_{1\gamma} = M_\chi ( 1 - \frac{M_Z^2}{4 M_\chi^2} ), \hspace{2.0em}
E_{2\gamma} = M_\chi ( 1 - \frac{M_h^2}{4 M_\chi^2} ).
\label{Lines2}\end{aligned}$$ Then, the difference between the two lines and its relative ratio are respectively given by $$\begin{aligned}
\delta E_\gamma &\equiv& E_{1\gamma} - E_{2\gamma} = \frac{M_h^2 - M_Z^2}{4 M_\chi},  \nonumber\\
\delta &\equiv& \frac{\delta E_\gamma}{E_\gamma} = \frac{M_h^2 - M_Z^2}{4 M_\chi E_\gamma}.
\label{Difference2}\end{aligned}$$ In this case as well, taking $E_\gamma = E_{1\gamma}$, the condition $\varepsilon  \ll \delta$ leads to the constraint on the dark matter mass $$\begin{aligned}
M_\chi \ll \sqrt{\frac{M_h^2 + ( \varepsilon - 1 ) M_Z^2}{4 \varepsilon}}.
\label{DM mass2}\end{aligned}$$ Using the fact that $\varepsilon = 0.1$ and the Higgs boson has mass $M_h = 125 GeV$, one arrives at $$\begin{aligned}
M_\chi \ll 143 GeV.
\label{Limit2}\end{aligned}$$ In this case, the dark matter mass is calculated to be $M_\chi = 141 GeV$ [@Su] which is almost the same size as the upper bound $143 GeV$ in (\[Limit2\]). In this sense, the calculated value $M_\chi = 141 GeV$ is in tension with the constraint (\[Limit2\]), so an interpretation of the two photon lines as dark matter annihilating into $\gamma Z$ and $\gamma h$ is dubious. Incidentally, in the extreme situation $E_\gamma = M_\chi$, Eq. (\[Limit2\]) reads $M_\chi \ll 135 GeV$ which is obviously inconsistent with $M_\chi = 141 GeV$. The only way to have a consistent result is to improve the energy resolution of the detector. For instance, if we can have the more excellent energy resolution $\varepsilon = 0.05 \ (\varepsilon = 0. 01)$, the constraint (\[DM mass2\]) on the dark mass is reduced to the form $M_\chi \ll 197 GeV \ (M_\chi \ll 430 GeV)$ which is compatible with $M_\chi = 141 GeV$.

Now let us comment on species of the dark matter particles. It is natural to suppose that the dark matter annihilation occurs in the s-wave state. Then, if final states of the two photon lines are found to be $Y = \{\gamma, Z\}$, the dark matter particle must be a scalar boson, Majorana fermion or Dirac fermion from the relation between statistics and spin. On the other hand, if final states turn out to be $Y = \{Z, h \}$, the dark matter particle should be a Dirac fermion or a vector boson. In particular, note that the Landau-Yang theorem [@Landau] requires us that a vector particle cannot annihilate into two photons since the spatial part of wave function must be symmetric.[^4] Furthermore, note that in this context the Dirac fermion has an interesting feature in that if the dark matter particle were a Dirac fermion, three photon lines could be observed as long as some (unknown) symmetry does not forbid the three annihilation processes and the processes are allowed kinematically.

In this article, it has been shown that an interpretation of two gamma-ray lines found in Ref. [@Su], as the dark matter annihilation into $Z$ and $h$ in the “Higgs in Space” scenario shows tension with the energy resolution of the Fermi-LAT. On the other hand, another interpretation of them as the annihilation into $\gamma$ and $Z$ is consistent with it. Moreover, we have proposed that in order to advocate the “Higgs in Space” scenario, the energy resolution needs to be improved in future. As a future work, we wish to take into consideration a issue of the velocity of dark matter in the framework developed recently by the author [@Oda].

[**Acknowledgements**]{}

This work is supported in part by the Grant-in-Aid for Scientific Research (C) No. 22540287 from the Japan Ministry of Education, Culture, Sports, Science and Technology.

[99]{}

G. Bertone (ed.), [“Particle Dark Matter: Observations, Models and Searches”, Cambridge University Press, 2010.]{}

For review and references, see for instance, G. Jungman, M. Kamionkowski and K. Griest, [Phys. Rept. [**267**]{} (1996) 195]{}; G. Bertone, D. Hooper and J. Silk, [Phys. Rept. [**405**]{} (2005) 279.]{}

C. Weniger, [arXiv:1204.2797 \[hep-ph\].]{}

M. Ackermann et al. \[Fermi-LAT Collaboration\], [arXiv:1205.2739 \[astro-ph.HE\].]{}

S. Profumo and T. Linden, [arXiv:1204.6047 \[astro-ph.HE\]]{}; A. Ibarra, S. Lopez Gehler and M. Pato, [arXiv:1205.0007 \[hep-ph\]]{}; E. Tempel, A. Hektor and M. Raidal, [arXiv:1205.1045 \[hep-ph\]]{}; E. Dudas, Y. Mambrini, S. Pokorski and A. Romagnoni, [arXiv:1205.1520 \[hep-ph\]]{}; J. M. Cline, [arXiv:1205.2688 \[hep-ph\]]{}; A. Boyarsky, D. Malyshev and O. Ruchayskiy, [arXiv:1205.4700 \[astro-ph.HE\]]{}; L. Bergstrom, [arXiv:1205.4882 \[astro-ph.HE\]]{}; A. Rajaraman, T. M. P. Tait and D. Whiteson, [arXiv:1205.4723 \[hep-ph\]]{}; K. -Y. Choi and O. Seto, [arXiv:1205.3276 \[hep-ph\]]{}; B. Kyae and J. -C. Park, [arXiv:1205.4151 \[hep-ph\]]{}; H. M. Lee, M. Park and W. -I. Park, [arXiv:1205.4675 \[hep-ph\]]{}; B. S. Acharya, G. Kane, P. Kumar, R. Lu and B. Zheng, [arXiv:1205.5789 \[hep-ph\]]{}; M. R. Buckley and D. Hooper, [arXiv:1205.6811 \[hep-ph\]]{}; X. Chu, T. Hambye, T. Scarna and M. H. G. Tytgat, [arXiv:1206.2279 \[hep-ph\]]{}; D. Das, U. Ellwanger and P. Mitropoulos, [arXiv:1206.2639 \[hep-ph\]]{}; Z. Kang, T. Li, J. Li and Y. Liu, [arXiv:1206.2863 \[hep-ph\]]{}; N. Weiner and I. Yavin, [arXiv:1206.2910 \[hep-ph\]]{}; L. Feng, Q. Yuan and Y. -Z. Fan, [arXiv:1206.4758 \[astro-ph.HE\]]{}; W. Buchmuller and M. Garny, [arXiv:1206.7056 \[hep-ph\]]{}; T. Cohen, M. Lisanti, T. R. and J. G. Wacker, [arXiv:1207.0800 \[hep-ph\].]{}

L. Bergstrom and H. Snellman, [Phys. Rev. [**D 37**]{} (1988) 3737.]{}

M. Su and D. P. Finkbeiner, [arXiv:1206.1616 \[astro-ph.HE\].]{}

L. Bergstrom and P. Ullio, [Nucl. Phys. Rev. [**B 504**]{} (1997) 27]{}; P. Ullio and L. Bergstrom, [Phys. Rev. [**D 57**]{} (1998) 1962.]{}

C. B. Jackson, G. Servant, G. Shaughnessy, T. M. P. Tait and M. Taoso, [JCAP [**1004**]{} (2010) 004, arXiv:0912.0004 \[hep-ph\].]{}

L. D. Landau, [Dokl. Akad. Nawk., USSR [**60**]{} (1948) 207]{}; C. N. Yang, [Phys. Rev. [**77**]{} (1950) 242.]{}

I. Oda, [Mod. Phys. Lett. [**A 27**]{} (2012) 1250116, arXiv:1204.1547 \[hep-ph\].]{}

[^1]: E-mail address: ioda@phys.u-ryukyu.ac.jp

[^2]: The paper by Weniger has subsequently given rise to much activity on this subject [@Profumo].

[^3]: We nelect a contribution from the velocity of dark matter since it only gives rise to a slight modification of the dark matter mass.

[^4]: The multiplet with the total $1$ spin is always anti-symmetric when composed from two photons.


# Derived from Marcus D. Hanwell's suggestion
# https://blog.kitware.com/cmake-and-the-default-build-type/

# Set a default build type if none was specified
set(default_build_type "Release")

# For builds from Git, default to Debug
if (EXISTS "${CMAKE_SOURCE_DIR}/.git")
    set(default_build_type "Debug")
endif()

# Multi-config generators (such as the VS one) will set the config types
if (NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
    message(STATUS "Setting build type to '${default_build_type}' as none was specified.")
    set(CMAKE_BUILD_TYPE "${default_build_type}" CACHE
        STRING "Choose the type of build." FORCE)
    # Set the possible values of build type for cmake-gui
    set_property(CACHE CMAKE_BUILD_TYPE PROPERTY STRINGS "Debug" "Release" "MinSizeRel" "RelWithDebInfo")
else()
    message(STATUS "CMake build type: ${CMAKE_BUILD_TYPE}")
endif()


/*
 * Copyright (c) 2010, 2013, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
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 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package javafx.event;

// PENDING_DOC_REVIEW

import java.io.InvalidObjectException;
import java.io.ObjectStreamException;
import java.io.Serializable;
import java.util.ArrayList;
import java.util.Deque;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Set;
import java.util.WeakHashMap;

/**
 * This class represents a specific event type associated with an {@code Event}.
 *

 * Event types form a hierarchy with the {@link EventType#ROOT} (equals to
 * {@link Event#ANY}) as its root. This is useful in event filter / handler
 * registration where a single event filter / handler can be registered to a
 * super event type and will be receiving its sub type events as well.
 * Note that you cannot construct two different EventType objects with the same
 * name and parent.
 *
 *

 * Note about deserialization: All EventTypes that are going to be deserialized
 * (e.g. as part of {@link Event} deserialization), need to exist at the time of
 * deserialization. Deserialization of EventType will not create new EventType
 * objects.
 *
 * @param <T> the event class to which this type applies
 * @since JavaFX 2.0
 */
public final class EventType<T extends Event> implements Serializable{

    /**
     * The root event type. All other event types are either direct or
     * indirect sub types of it. It is also the only event type which
     * has its super event type set to {@code null}.
     */
    public static final EventType<Event> ROOT =
            new EventType<Event>("EVENT", null);

    private WeakHashMap<EventType<? extends T>, Void> subTypes;

    private final EventType<? super T> superType;

    private final String name;

    /**
     * Constructs a new {@code EventType} with the {@code EventType.ROOT} as its
     * super type and the name set to {@code null}.
     * @deprecated Do not use this constructor, as only one such EventType can exist
     */
    @Deprecated
    public EventType() {
        this(ROOT, null);
    }

    /**
     * Constructs a new {@code EventType} with the specified name and the
     * {@code EventType.ROOT} as its super type.
     *
     * @param name the name
     * @throws IllegalArgumentException if an EventType with the same name and
     * {@link EventType#ROOT}/{@link Event#ANY} as parent
     */
    public EventType(final String name) {
        this(ROOT, name);
    }

    /**
     * Constructs a new {@code EventType} with the specified super type and
     * the name set to {@code null}.
     *
     * @param superType the event super type
     * @throws IllegalArgumentException if an EventType with "null" name and
     * under this supertype exists
     */
    public EventType(final EventType<? super T> superType) {
        this(superType, null);
    }

    /**
     * Constructs a new {@code EventType} with the specified super type and
     * name.
     *
     * @param superType the event super type
     * @param name the name
     * @throws IllegalArgumentException if an EventType with the same name and
     * superType exists
     */
    public EventType(final EventType<? super T> superType,
            final String name) {
        if (superType == null) {
            throw new NullPointerException(
                    "Event super type must not be null!");
        }

        this.superType = superType;
        this.name = name;
        superType.register(this);
    }

    /**
     * Internal constructor that skips various checks
     */
    EventType(final String name,
                      final EventType<? super T> superType) {
        this.superType = superType;
        this.name = name;
        if (superType != null) {
            if (superType.subTypes != null) {
                for (Iterator i = superType.subTypes.keySet().iterator(); i.hasNext();) {
                    EventType t  = (EventType) i.next();
                    if (name == null && t.name == null || (name != null && name.equals(t.name))) {
                        i.remove();
                    }
                }
            }
            superType.register(this);
        }
    }

    /**
     * Gets the super type of this event type. The returned value is
     * {@code null} only for the {@code EventType.ROOT}.
     *
     * @return the super type
     */
    public final EventType<? super T> getSuperType() {
        return superType;
    }

    /**
     * Gets the name of this event type.
     *
     * @return the name
     */
    public final String getName() {
        return name;
    }

    /**
     * Returns a string representation of this {@code EventType} object.
     * @return a string representation of this {@code EventType} object.
     */
    @Override
    public String toString() {
        return (name != null) ? name : super.toString();
    }

    private void register(javafx.event.EventType<? extends T> subType) {
        if (subTypes == null) {
            subTypes = new WeakHashMap<EventType<? extends T>, Void>();
        }
        for (EventType<? extends T> t : subTypes.keySet()) {
            if (((t.name == null && subType.name == null) || (t.name != null && t.name.equals(subType.name)))) {
                throw new IllegalArgumentException("EventType \"" + subType + "\""
                        + "with parent \"" + subType.getSuperType()+"\" already exists");
            }
        }
        subTypes.put(subType, null);
    }

    private Object writeReplace() throws ObjectStreamException {
        Deque<String> path = new LinkedList<String>();
        EventType<?> t = this;
        while (t != ROOT) {
            path.addFirst(t.name);
            t = t.superType;
        }
        return new EventTypeSerialization(new ArrayList<String>(path));
    }

    static class EventTypeSerialization implements Serializable {
        private List<String> path;

        public EventTypeSerialization(List<String> path) {
            this.path = path;
        }

        private Object readResolve() throws ObjectStreamException {
            EventType t = ROOT;
            for (int i = 0; i < path.size(); ++i) {
                String p = path.get(i);
                if (t.subTypes != null) {
                    EventType s = findSubType(t.subTypes.keySet(), p);
                    if (s == null) {
                        throw new InvalidObjectException("Cannot find event type \"" + p + "\" (of " + t + ")");
                    }
                    t = s;
                } else {
                    throw new InvalidObjectException("Cannot find event type \"" + p + "\" (of " + t + ")");
                }
            }
            return t;
        }

        private EventType findSubType(Set<EventType> subTypes, String name) {
            for (EventType t : subTypes) {
                if (((t.name == null && name == null) || (t.name != null && t.name.equals(name)))) {
                    return t;
                }
            }
            return null;
        }

    }
}