A simulation study of sample size for multilevel logistic regression models

<p>Abstract</p> <p>Background</p> <p>Many studies conducted in health and social sciences collect individual level data as outcome measures. Usually, such data have a hierarchical structure, with patients clustered within physicians, and physicians clustered within practices. Large survey data, including national surveys, have a hierarchical or clustered structure; respondents are naturally clustered in geographical units (e.g., health regions) and may be grouped into smaller units. Outcomes of interest in many fields not only reflect continuous measures, but also binary outcomes such as depression, presence or absence of a disease, and self-reported general health. In the framework of multilevel studies an important problem is calculating an adequate sample size that generates unbiased and accurate estimates.</p> <p>Methods</p> <p>In this paper simulation studies are used to assess the effect of varying sample size at both the individual and group level on the accuracy of the estimates of the parameters and variance components of multilevel logistic regression models. In addition, the influence of prevalence of the outcome and the intra-class correlation coefficient (ICC) is examined.</p> <p>Results</p> <p>The results show that the estimates of the fixed effect parameters are unbiased for 100 groups with group size of 50 or higher. The estimates of the variance covariance components are slightly biased even with 100 groups and group size of 50. The biases for both fixed and random effects are severe for group size of 5. The standard errors for fixed effect parameters are unbiased while for variance covariance components are underestimated. Results suggest that low prevalent events require larger sample sizes with at least a minimum of 100 groups and 50 individuals per group.</p> <p>Conclusion</p> <p>We recommend using a minimum group size of 50 with at least 50 groups to produce valid estimates for multi-level logistic regression models. Group size should be adjusted under conditions where the prevalence of events is low such that the expected number of events in each group should be greater than one.</p

A Black Hole in the X-Ray Nova Velorum 1993

We have obtained 17 moderate-resolution (~2.5 A) optical spectra of the Galactic X-ray Nova Velorum 1993 in quiescence with the Keck-II telescope. The orbital period (P) is 0.285206 +/- 0.0000014 d, and the semiamplitude (K_2) is 475.4 +/- 5.9 km/s. Our derived mass function, f(M_1) = PK_2^3 /2 pi G = 3.17 +/- 0.12 M_sun, is close to the conventional absolute limiting mass for a neutron star (~ 3.0-3.2 M_sun) -- but if the orbital inclination i is less than 80 degrees (given the absences of eclipses), then M_1 is greater than 4.2-4.4 M_sun for nominal secondary-star masses of 0.5 M_sun (M0) to 0.65 M_sun (K6). The primary star is therefore almost certainly a black hole rather than a neutron star. The velocity curve of the primary from H-alpha emission has a semiamplitude (K_1) of 65.3 +/- 7.0 km/s, but with a phase offset by 237 degrees (rather than 180 degrees) from that of the secondary star. The nominal mass ratio q = M_2/M_1 = K_1/K_2 = 0.137 +/- 0.015, and hence for M_2 = 0.5-0.65 M_sun we derive M_1 = 3.64-4.74 M_sun. An adopted mass M_1 ~ 4.4 M_sun is significantly below the typical value of ~ 7 M_sun found for black holes in other low-mass X-ray binaries. Keck observations of MXB 1659-29 (V2134 Oph) in quiescence reveal a probable optical counterpart at R = 23.6 +/- 0.4 mag.Comment: 16 pages, 9 figures, added references, revised per. referee's comments Accepted for publication in August 1999 issue of PAS

Photometric Evolution of SNe Ib/c 2004ao, 2004gk and 2006gi

Photometric observations of three core collapse supernovae (SNe 2004ao, 2004gk and 2006gi), covering about 200 days of evolution are presented and analyzed. The photometric behaviour of the three objects is consistent with their membership of the envelope-stripped type Ib/c class. Pseudo-bolometric light curves are constructed. The corresponding measured $e$-folding times are found to be faster compared to the $^{56}$Co decay (i.e. 111.3 d), suggesting that a proportion of $\gamma$-rays increasing with time have escaped without thermalization, owing to the low mass nature of the ejecta. SN 2006gi has almost identical post maximum decline phase luminosities as SN 1999ex, and found to be similar to both SNe 1999dn and 1999ex in terms of the quasi-bolometric shape, placing it among the fast decliner Ib objects. SN 2004ao appears to fit within the slow decliner Ib SNe. SNe 2004ao and 2004gk display almost identical luminosities in the [50-100] days time interval, similar to SN 1993J. A preliminary simplified $\gamma -$ray deposition model is described and applied to the computed pseudo-bolometric light curves, allowing one to find a range in the ejecta and $^{56}$Ni masses. The optical and quasi-bolometric light curves, and the $B-V$ colour evolution of SN 2004gk are found to show a sudden drop after day 150. Correlating this fact to dust formation is premature and requires further observational evidence.Comment: Accepted for publication in The Astrophysical Journal; (11 two-columns Pages, 11 figures, 6 Tables; Scheduled for publication in April 2011

Cyclotron effective mass of 2D electron layer at GaAs/AlGaAs heterojunction subject to in-plane magnetic fields

We have found that Fermi contours of a two-dimensional electron gas at \rmGaAs/Al_xGa_{1-x}As interface deviate from a standard circular shape under the combined influence of an approximately triangular confining potential and the strong in-plane magnetic field. The distortion of a Fermi contour manifests itself through an increase of the electron effective cyclotron mass which has been measured by the cyclotron resonance in the far-infrared transmission spectra and by the thermal damping of Shubnikov-de Haas oscillations in tilted magnetic fields with an in-plane component up to 5 T. The observed increase of the cyclotron effective mass reaches almost 5 \% of its zero field value which is in good agreement with results of a self-consistent calculation.Comment: 4 pages, Revtex, figures can be obtained on request from [email protected]; to appear in Phys. Rev. B (in press). No changes, the corrupted submission replace

An Exploration of the Role of Substance Misuse Nurses in Scotland

Executive Summary Background With the increase of drug misuse over the past two decades, the role of the Substance Misuse Nurse has increased dramatically. Research on the role of nurses working in this field is minimal and there is little known about what they do, what they think about their clients and their role, and how they approach treatment. A pilot study on substance misuse nurses in Grampian indicated that nurses may be key gatekeepers to specialist services and some nurses appeared to have an important role in clinical decision making. However, clinical decision making and other key aspects of nurse practice may vary across services in different geographical areas. This research was designed to gain a better understanding of the role of the substance misuse nurse in Scotland. Aims and Objectives The aim of this research was to describe and analyse the role of substance misuse nurses working with drug misusers in Scotland. The objectives were: • to identify the population of specialist nurses working directly in the management of illicit drug users in Scotland and gain baseline data on their demography, caseload, services provided and level of interaction with other health professionals; • to compare their attitudes to drug misusers with those of other health professionals; • to explore their beliefs about the effectiveness of different treatment options; • to examine their role in the initial client assessment and subsequent management; • to describe their interaction with the client; • to explore their relationship with other professionals. Methods Mixed quantitative and qualitative methods were used. The population of Substance Misuse Nurses and midwives working specifically with drug misusers across Scotland were identified and posted a comprehensive questionnaire. The questionnaire covered issues including qualifications, training, attitudes and beliefs about treatment and aspects of practice such as caseloads, services provided and relationships with other health and social professionals. Face-to-face interviews were conducted with a sub-sample of nurses including a range of gender, experience, and NHS areas. Interviews covered nurses’ assessment and decision making regarding treatment and relationships with other professionals. Observations of specialist nurse and client consultations allowed for some insight into the general structure of the consultation, the setting where the consultation took place and the roles of nurse and client in assessment and treatment planning. Characteristics of SMS nurses and services • A scoping exercise indentified 272 nurses. Of these 244 were sent a questionnaire (the remainder having left or being on sick leave). Of these, 79% responded. • Seventy percent (70%) were Grade G or above indicating a senior level workforce. • Most nurses were employed in substance misuse services (48%) or, similarly, drug and alcohol services (30%). • Formal training (university certificate/diploma) in substance misuse had been undertaken by 40% of nurses, induction training (i.e. at the start of employment) by 62% of nurses. • The median caseload was 38 clients. • The majority of consultations took place in clinical consultation rooms but this was not observed to influence the consultation. • Nurses reported that the average length of a consultation was 38 minutes. All of the observed consultations were scheduled for 30 minutes but half over-ran. Motivation, attitudes and beliefs • The challenging nature of working with drug misusers was a positive motivating factor for nurses working in this field. • Seventy-seven percent (77%) of nurses considered working with drug misusers to be rewarding, although 79% also considered that this population were not easy to deal with. Opinion was split about whether drug misusers could be manipulative in consultations. Initial assessment of clients • Waiting times for assessment were generally an issue of concern to nurses. • A detailed assessment was almost always conducted at the first consultation. • An SMR24 was almost always completed at the first consultation. • Interviews and observation of nurse-client consultations found that the approach to assessment seemed consistent across geographical areas. • Assessment included: brief physical examination, urine sampling, detailed exploration of drug use, exploration of physical problems, discussion of social and family support, housing and employment status and history of involvement in the criminal justice system. • Consultations were often brought to a close by discussing treatment expectations. • Initial assessment could take place over more than one appointment and several appointments could be required before a treatment plan was implemented. Making treatment decisions • Clients were actively encouraged to participate in treatment decisions. • Although 84% of nurses reported they were expected to follow a treatment protocol only 44% said they always did (for any treatment). • Eighty-six percent (86%) of nurses had seen the National Clinical Guidelines (DoH, 1999), and those who were interviewed felt that these provided a good framework for treatment, although they were perhaps lacking in detail. • Nurses reported that they often consulted widely with other health professionals but, most frequently, with the client, before making a treatment decision. • A third of nurses reported writing prescriptions for a doctor to sign. • Seventy percent (70%) of respondents felt nurses should be able write prescriptions but only if they were experienced nurses with appropriate training. Comparing beliefs of nurses with those of GPs and pharmacists Nurses were asked some questions which had been asked of GPs and pharmacists in previous national surveys conducted in 2000. This allowed for comparisons to be made: • When making treatment decisions nurses were less influenced than GPs by the attitude and behaviour of drug misusers. • When making treatment decisions nurses were more influenced than GPs by societal factors such as reducing the transmission of infectious disease. • Nurses were less likely than GPs to favour detoxification as a treatment approach, although 83% of nurses agreed that a community based detoxification programme was an effective tool for the treatment of drug misuse. • Nurses were more confident than GPs about their ability to successfully manage polydrug users. • Nurses and GPs were split in their beliefs about the effectiveness of dihydrocodeine. • Nurses believed more strongly than pharmacists that maintenance prescribing could stop the use of illicit drugs. • Fewer nurses than pharmacists believed that controlled drug dispensing should take place in central clinics rather than community pharmacies. Multidisciplinary working • Over half of nurses considered their relationship with pharmacists, GPs, health visitors/community nurses, hospital doctors and social workers to be good. • Opportunities to discuss services with local policy makers were considered insufficient. • Relationships with GPs seemed positive because nurses felt GPs valued their specialist knowledge. • Nurses had frequent contact with pharmacists and respected the difficulties of a pharmacist’s work. • Relationships with social services were variable. Some nurses felt undervalued by their social work colleagues, or felt there was a lack of joint planning for individual client care. • Nurses were clear about what circumstances should lead to a break in confidentiality between services and of how to go about this. • Integrated drug services were seen as potentially beneficial but there were specific concerns about the implications for clients of sharing information with other agencies and practical concerns about the size of joint assessment tools. Health and Safety at work • Sixty-four percent (64%) of nurses reported that they had been physically or verbally abused by clients, and half of those who had been subject to abuse felt current safety provision in their service was insufficient. Nurses in most areas said that the safety of staff was considered to be a high service priority, but there was evidence from interviews this was still lacking in some areas. • Greater use of personal alarms and alarms in consultation rooms, use of mobile phones, and specialised training were suggested as ways of improving safety. • Nurses said that the majority of their consultations take place in clinics/consultation rooms rather than clients’ homes. • The feeling was commonly expressed among interviewees that their work could be stressful, and this was seen as due to paperwork, excessive caseloads and working in isolation. Discussion of Findings This study provides baseline information which can be used to inform individual nurses, services, policy makers and researchers. Some individual nurses reading this report might find an element that is simply describing what they already know. This is inevitable but it is hoped individual nurses will still find interest in the views and practice of others within their profession. The value of this report is that it has quantified these findings on a national basis, providing robust data for workforce planning and needs assessment. It has not been possible to compare findings, and thus the practice of substance misuse nurses in Scotland, with other areas or countries because there is no comparable published work. It is also not possible to give guidelines or examples of ‘good practice’ as this would have involved data collection from clients and other professionals which was outwith this study’s remit. This study has found a reassuring consistence of practice across Scotland. Although many substance misuse nurses work in some degree of isolation there is an apparently high level of discussion and consultation with other service colleagues which provides support. The role of the nurse in the initial assessment and treatment plan is critical. Nevertheless, decisions regarding treatment plans were made largely between nurses and clients, with nurses making use of service protocols/guidelines. Some might question whether a nurse is the most appropriate person to undertake these tasks. Ability to conduct physical examination, some knowledge of pharmacology, mental health and psychology as well as an ability to explore the wider social context is required. On reflection a nurse, with mental health qualifications seems to have the most appropriate skills for this. There is a willingness by nurses to take on the role of prescribing albeit in a limited capacity, and only by very experienced nurses with appropriate training. Currently, a minority of nurses reported writing prescriptions to be signed by doctors, which is possible for doctors with handwriting exemptions. This raises issues about clinical governance. In signing the prescription a GP is still taking responsibility even though s/he may know little about the patient’s current condition. An important strand of a substance misuse nurse’s practice is ongoing support or counselling for clients. This raises issues about models of counselling followed and nurses’ competencies in doing this. The nature or model of counselling used by nurses was not explicitly covered in this research and further exploration of counselling would be an area for future research. Relationships with other professionals, were generally reported to be good. Nurses generally believed GPs valued their role. Comparison of attitudes of substance misuse nurses with earlier surveys of pharmacists and GPs indicates they are more positive in general and about treatment outcomes in particular. Nurses viewed the challenging aspect of working with drug misusers more positively than pharmacists and GPs. Nurses were less positive about their ability to influence policy. Currently substance misuse nurses have little input at policy level. At a local level, through Drug and Alcohol Action Teams (DAATs) this could improve the feeling of ownership towards service developments related to the Joint Future agenda. Service managers are currently the key link between nurses and DAATs. Perhaps a service nurse with more client contact should also attend to provide client feedback. At a national level greater nursing input into policy could give this specialist group a greater feeling of professional cohesion as well as keeping policy makers informed. Concerns about health and safety at work need to be considered at a national professional level as well as locally. Whether these issues should be addressed through the involvement of an organisation such as the Association of Nurses in Substance Abuse (ANSA) or an appointed individual is for discussion. Recommendations • All substance misuse nurses should receive induction training prior to commencing their post. Greater time should be protected to allow participation in training. • There should be further exploration of what models of counselling, if any, are followed to assess whether current training is adequate. • Appointment scheduling may need review as there was evidence that consultation time was routinely underestimated. Frequency of missed appointments needs to be considered at the same time. • Staffing of substance misuse nurses should be expanded in order to reduce: excessive caseloads; lengthy waiting lists; insufficient cover for holidays, training and absences; and occupational stress. • Nurses could be involved in GP training to share their experience of managing difficult cases such as poly-drug users and widen GPs perspective of the social benefits of drug misuse treatment. • Nurses should be kept aware of developments on integrated care for drug misusers. This would allow them to understand the principles behind integrated care and be aware of how their service fits into the overall plan. • Extending the role of senior substance misuse nurses to include the prescribing of controlled drugs should be considered. • A clearer job title should be given to nurses working in substance misuse so that they may be easily identified and representable at both DAAT and Scottish Executive level, e.g. Specialist Nurse in Substance Misuse. • Efforts should be made to improve substance misuse nurses’ opportunities to influence policy. • All substance misuse nurses should be provided with appropriate on going training, procedures and practices to allow them to carry out their work safely

Optical Spectroscopy of Type Ia Supernovae

We present 432 low-dispersion optical spectra of 32 Type Ia supernovae (SNe Ia) that also have well-calibrated light curves. The coverage ranges from 6 epochs to 36 epochs of spectroscopy. Most of the data were obtained with the 1.5m Tillinghast telescope at the F. L. Whipple Observatory with typical wavelength coverage of 3700-7400A and a resolution of ~7A. The earliest spectra are thirteen days before B-band maximum; two-thirds of the SNe were observed before maximum brightness. Coverage for some SNe continues almost to the nebular phase. The consistency of the method of observation and the technique of reduction makes this an ideal data set for studying the spectroscopic diversity of SNe Ia.Comment: Accepted for publication in the Astronomical Journal, 109 pages (including data table), 44 figures, full resolution figures at http://www.noao.edu/noao/staff/matheson/Iaspec.ps.g