Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Implementing a system of quality-of-life diagnosis and therapy for breast cancer patients: results of an exploratory trial as a prerequisite for a subsequent RCT

A system for quality-of-life diagnosis and therapy (QoL system) was implemented for breast cancer patients. The system fulfilled the criteria for complex interventions (Medical Research Council). Following theory and modeling, this study contains the exploratory trial as a next step before the randomised clinical trial (RCT) answering three questions: (1) Are there differences between implementation sample and general population? (2) Which amount and type of disagreement exist between patient and coordinating practitioners (CPs) in assessed global QoL? (3) Are there empirical reasons for a cutoff of 50 points discriminating between healthy and diseased QoL? Implementation was successful: 74% of CPs worked along the care pathway. However, CPs showed preferences for selecting patients with lower age and UICC prognostic staging. Patients and CPs disagreed considerably in values of global QoL, despite education in QoL assessment by outreach visits, opinion leaders and CME: Zero values of QoL were only expressed by patients. Finally, the cutoff of 50 points was supported by the relationship between QoL in single items and global QoL: no patients with values above 50 dropped global QoL below 50, but values below 50 and especially at 0 points in single items, induced a dramatic fall of global QoL down to below 50. The exploratory trial was important for defining the complex intervention in the definitive RCT: control for age and prognostic stage grading, support for a QoL unit combining patient's and CP's assessment of QoL and support for the 50-point cutoff criterion between healthy and diseased QoL

Does patient-physiotherapist agreement influence the outcome of low back pain? A prospective cohort study

BACKGROUND: Recent research suggests that agreement between patients' and health professionals' perceptions may influence the outcome of various painful conditions. This issue has received little attention in the context of low back pain and physiotherapy interventions. The current study aimed at exploring the relationship between patient-physiotherapist agreement on baseline low back pain intensity and related functional limitations, and changes in patient outcomes four weeks later. METHODS: Seventy-eight patient-physiotherapist dyads were included in the study. At baseline, patients and physiotherapists completed a Numerical Rating Scale and the Roland-Morris Disability Questionnaire. Patients' perceptions were reassessed over the phone at follow-up. RESULTS: Using multiple regression, baseline level of patient-physiotherapist agreement on pain intensity was associated with both outcome measures at follow-up. Agreement on functional limitations had no impact on outcomes. CONCLUSION: The results of this study indicate that patient-physiotherapist agreement has some impacts on the short-term outcomes of low back pain. Further research is needed to confirm these findings

Prognostic value of performance status assessed by patients themselves, nurses, and oncologists in advanced non-small cell lung cancer

Accuracy in the assessment of performance status by oncologists has not been well evaluated. We investigated possible discrepancies in the assessment of performance status among patients, nurses, and oncologists, and evaluated the prognostic importance of each assessment. Two hundred and six inpatients with inoperable, advanced non-small cell lung cancer were investigated prospectively. Weighted Kappa statistics for inter-observer agreement were 0.53 between oncologists and patients and 0.63 between oncologists and nurses. There was a significant difference among the assessments by the three groups (P < 0.001). Oncologists gave the healthiest performance status assessment, nurses an intermediate assessment, and patients the poorest. When included separately in the Cox model, the assessment by each group was significantly correlated with survival. However, the assessment by the patients themselves failed to distinguish survival of patients with performance status 1 and 2. Among the three models including patient-, nurse-, and oncologist-assessed PS, that including oncologist-assessed PS best fitted to the observed survival data. These results showed that the assessment by the patients themselves is different from those by the nurses and the oncologists and provided additional support for the use of the assessment by oncologists in clinical oncology. © 2001 Cancer Research Campaign http://www.bjcancer.co

Measurement of overall quality of life in nursing homes through self-report: the role of cognitive impairment

Measuring quality of life is a necessity for adequate interventions. This paper concerns the usefulness of six self-report measures for overall quality of life for nursing home residents with various levels of cognitive impairment. It was investigated which proportion of residents from four cognition groups could complete a scale, and internal consistency and construct validity of the scales were studied. Data collection took place in ten Dutch nursing homes (N = 227). The proportion of residents that could complete each scale varied. The Depression List could be administered most often to the cognitively most impaired group (43%; Mini Mental State Examination-scores 0–4). In the three cognition groups with MMSE-score >5, internal consistency of the Depression List, Geriatric Depression Scale and Negative Affect Scale was adequate in all three groups (alpha ≥.68). Intercorrelation was highest for the Philadelphia Geriatric Center Morale Scale, the Depression List, and the Geriatric Depression Scale (rho ≥.65). Nonetheless, self-report scales were not strongly correlated with two observational scales for depression, especially in cognitively severely impaired residents (rho ≤.30). In conclusion, it may not be possible to measure overall quality of life through self-report, and possibly also through observation, in many nursing home residents

Catch-up growth up to ten years of age in children born very preterm or with very low birth weight

BACKGROUND: Improved survival due to advances in neonatal care has brought issues such as postnatal growth and development more to the focus of our attention. Most studies report stunting in children born very preterm and/or small for gestational age. In this article we study the growth pattern of these children and aim to identify factors associated with postnatal catch-up growth. METHODS: 1338 children born with a gestational age <32 weeks and/or a birth weight of <1500 grams were followed during a Dutch nationwide prospective study (POPS). Subgroups were classified as appropriate for gestational age and <32 weeks (AGA) or small for gestational age (<32 wks SGA and ≥32 wks SGA). Data were collected at different intervals from birth until 10 years for the 962 survivors and compared to reference values. The correlation between several factors and growth was analysed. RESULTS: At 10 years the AGA children had attained normal height, whereas the SGA group demonstrated stunting, even after correction for target height (AGA: 0.0 SDS; SGA <32 wks: -0.29SDS and ≥32 wks: -0.13SDS). Catch-up growth was especially seen in the SGA children with a fast initial weight gain. BMI was approximately 1 SD below the population reference mean. CONCLUSION: At 10 years of age, children born very preterm AGA show no stunting. However, many children born SGA, especially the very preterm, show persistent stunting. Early weight gain seems an important prognostic factor in predicting childhood growth