Nonparametric Estimation of Data Dimensionality Prior to Data Compression: the case of the Human Development Index

In many applications in applied statistics researchers reduce the complexity of a data set by combining a group of variables into a single measure using factor analysis or an index number. We argue that such compression loses information if the data actually has high dimensionality. We advocate the use of a non-parametric estimator, commonly used in physics (the Takens estimator), to estimate the correlation dimension of the data prior to compression. The advantage of this approach over traditional linear data compression approaches is that the data does not have to be linearized. Applying our ideas to the United Nations Human Development Index we find that the four variables that are used in its construction have dimension three and the index loses information.

Body Mass Index Is More Predictive of Progenitor Number in Bone Marrow Stromal Cell Population Than Age in Men: Expanding the Predictors of the Progenitor Compartment

Research has focused on in vitro expansion of bone marrow stromal cells with the aim of developing cell-based therapies or tissue-engineered constructs. There is debate over whether there is a reduction in stem cells/osteoprogenitors in the bone marrow compartment with increasing age. The aim of this study was to investigate patient factors that affect the progenitor pool in bone marrow samples. Six milliliters of marrow aspirate was obtained from the femoral canal of 38 primary hip replacement patients (aged 28-91). Outcome measures were total nucleated cell count, colony-forming efficiency, alkaline phosphatase expression, and expression of stem cell markers. There was a nonsignificant negative correlation between age and both colony-forming efficiency and stem cell marker expression. However, body mass index showed a positive, significant correlation with colony area and number in men-accounting for up to 75% of the variation. In conclusion, body mass index, not age, was highly predictive of the number of progenitors found in bone marrow, and this relationship was sex specific. These results may inform the clinician's treatment choice when considering bone marrow-based therapies. Further, it highlights the need to widen research into patient factors that affect the adult stem cell population beyond age and reinforces the need to consider sexes separately.

Index of sources of stress in nursing students: a confirmatory factor analysis.

Aim. This paper is a report of a study to test the proposed factor structure of the Index of Sources of Stress in Nursing Students. Background. Research across many countries has identified a number of sources of distress in nursing students but little attempt has been made to understand and measure sources of eustress or those stressors likely to enhance performance and well-being. The Index of Sources of Stress in Nursing Students was developed to do this. Exploratory factor analysis suggested a three-factor structure, the factors being labelled: learning and teaching; placement-related and course organization. It is important, however, to subject the instrument to confirmatory factor analysis as a further test of construct validity. Method. A convenience sample of final year nursing students (n = 176) was surveyed in one university in Northern Ireland in 2007. The Index of Sources of Stress in Nursing Students, which measures sources of stress likely to contribute to distress and eustress, was completed electronically. The LISREL programme was used to carry out the confirmatory factor analysis and test the factor structure suggested in the exploratory analysis. Findings. The proposed factor structure for the items measuring ‘Uplifts’ proved to be a good fit to the data and the proposed factor structure for the items measuring ‘Hassles’ showed adequate fit. Conclusion. In nursing programmes adopting the academic model and combining university-based learning with placement experience, this instrument can be used to help identify the sources of stress or course demands that students rate as distressing and those that help them to achieve. The validity of the ISSN could be further evaluated in other education settings.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

On generating set index functions for randomized caches

Caches hide the growing latency of accesses to the main memory from the processor by storing the most recently used data on-chip. To limit the search time through the caches, they are organized in a direct mapped or set-associative way. Such an organization introduces many conflict misses that hamper performance. This paper studies randomizing set index functions, a technique to place the data in the cache in such a way that conflict misses are avoided. The performance of such a randomized cache strongly depends on the randomization function. This paper discusses a methodology to generate randomization functions that perform well over a broad range of benchmarks. The methodology uses profiling information to predict the conflict miss rate of randomization functions. Then, using this information, a search algorithm finds the best randomization function. Due to implementation issues, it is preferable to use a randomization function that is extremely simple and can be evaluated in little time. For these reasons, we use randomization functions where each randomized address bit is computed as the XOR of a subset of the original address bits. These functions are chosen such that they operate on as few address bits as possible and have few inputs to each XOR. This paper shows that to index a 2(m)-set cache, it suffices to randomize m+2 or m+3 address bits and to limit the number of inputs to each XOR to 2 bits to obtain the full potential of randomization. Furthermore, it is shown that the randomization function that we generate for one set of benchmarks also works well for an entirely different set of benchmarks. Using the described methodology, it is possible to reduce the implementation cost of randomization functions with only an insignificant loss in conflict reduction.

Highly accurate and efficient evaluation of randomising set index functions

Randomising set index functions can reduce the number of conflict misses in data caches by spreading the cache blocks uniformly over all sets. Typically, the randomisation functions compute the exclusive ors of several address bits. Not all randomising set index functions perform equally well, which calls for the evaluation of many set index functions. This paper discusses and improves a technique that tackles this problem by predicting the miss rate incurred by a randomisation function, based on profiling information. A new way of looking at randomisation functions is used, namely the null space of the randomisation function. The members of the null space describe pairs of cache blocks that are mapped to the same set. This paper presents an analytical model of the error made by the technique and uses this to propose several optimisations to the technique. The technique is then applied to generate a conflict-free randomisation function for the SPEC benchmarks. (C) 2003 Elsevier Science B.V. All rights reserved.

Perimetric progression in open angle glaucoma and the Visual Field Index (VFI)

PURPOSE: To evaluate the changes in the Visual Field Index (VFI) in eyes with perimetric glaucomatous progression, and to compare these against stable glaucoma patients.

PATIENTS AND METHODS: Consecutive patients with open angle glaucoma with a minimum of 6 reliable visual fields and 2 years of follow-up were identified. Perimetric progression was assessed by 4 masked glaucoma experts from different units, and classified into 3 categories: "definite progression," "suspected progression," or "no progression." This was compared with the Glaucoma Progression Analysis (GPA) II and VFI linear regression analysis, where progression was defined as a negative slope with significance of <5%.

RESULTS: Three hundred ninety-seven visual fields from 51 eyes of 39 patients were assessed. The mean number of visual fields was 7.8 (SD 1.1) per eye, and the mean follow-up duration was 63.7 (SD 13.4) months. The mean VFI linear regression slope showed an overall statistically significant difference (P<0.001, analysis of variance) for each category of progression. Using expert consensus opinion as the reference standard, both VFI analysis and GPA II had high specificity (0.93 and 0.90, respectively), but relatively low sensitivity (0.45 and 0.41, respectively).

CONCLUSIONS: The mean VFI regression slope in our cohort of eyes without perimetric progression showed a statistically significant difference compared with those with suspected and definite progression. VFI analysis and GPA II both had similarly high specificity but low sensitivity when compared with expert consensus opinion.

A Tight Upper Bound on Bit Error Rate of Joint OFDM and Multi-Carrier Index Keying

This letter investigates performance enhancement by the concept of multi-carrier index keying in orthogonal frequency division multiplexing (OFDM) systems. For the performance evaluation, a tight closed-form approximation of the bit error rate (BER) is derived introducing the expression for the number of bit errors occurring in both the index domain and the complex domain, in the presence of both imperfect and perfect detection of active multi-carrier indices. The accuracy of the derived BER results for various cases are validated using simulations, which can provide accuracy within 1 dB at favorable channels.

The statistical significance of randomized controlled trial results is frequently fragile: A case for a Fragility Index

Objectives

A P-value <0.05 is one metric used to evaluate the results of a randomized controlled trial (RCT). We wondered how often statistically significant results in RCTs may be lost with small changes in the numbers of outcomes.

Study Design and Setting

A review of RCTs in high-impact medical journals that reported a statistically significant result for at least one dichotomous or time-to-event outcome in the abstract. In the group with the smallest number of events, we changed the status of patients without an event to an event until the P-value exceeded 0.05. We labeled this number the Fragility Index; smaller numbers indicated a more fragile result.

Results

The 399 eligible trials had a median sample size of 682 patients (range: 15-112,604) and a median of 112 events (range: 8-5,142); 53% reported a P-value <0.01. The median Fragility Index was 8 (range: 0-109); 25% had a Fragility Index of 3 or less. In 53% of trials, the Fragility Index was less than the number of patients lost to follow-up.

Conclusion

The statistically significant results of many RCTs hinge on small numbers of events. The Fragility Index complements the P-value and helps identify less robust results. 

Assessment of clinical response to ivacaftor with lung clearance index in cystic fibrosis patients with a G551D-CFTR mutation and preserved spirometry:A randomised controlled trial

Background: Ivacaftor has shown a clinical benefit in patients with cystic fibrosis who have the G551D-CFTR mutation and reduced lung function. Lung clearance index (LCI) using multiple-breath washout might be an alternative to and more sensitive method than forced expiratory volume in 1 s (FEV₁) to assess treatment response in the growing number of children and young adults with cystic fibrosis who have normal spirometry. The aim of the study was to assess the treatment effects of ivacaftor on LCI in patients with cystic fibrosis, a G551D-CFTR mutation, and an FEV₁ >90% predicted. Methods: This phase 2, multicentre, placebo-controlled, double-blind 2×2 crossover study of ivacaftor treatment was conducted in patients with cystic fibrosis, at least one G551D-CFTR allele, and an FEV₁ >90% predicted. Patients also had to have an LCI higher than 7·4 at screening, age of 6 years or older, and a weight higher than or equal to 15 kg. Eligible patients were randomly allocated to receive one of two treatment sequences (placebo first followed by ivacaftor 150 mg twice daily [sequence 1] or ivacaftor 150 mg twice daily first followed by placebo [sequence 2]) of 28 days' treatment in each period, with a 28-day washout between the two treatment periods. Randomisation (ratio 1:1) was done with block sizes of 4, and all site personnel including the investigator, the study monitor, and the Vertex study team were masked to treatment assignment. The primary outcome measure was change from baseline in LCI. The study is registered at ClinicalTrials.gov, NCT01262352. Findings: Between February and November, 2011, 21 patients were enrolled, of which 11 were assigned to the sequence 1 group, and 10 to the sequence 2 group. 20 of these patients received treatment and 17 completed the trial (eight in sequence 1 group and 9 in sequence 2 group). Treatment with ivacaftor led to significant improvements compared with placebo in LCI (difference between groups in the average of mean changes from baseline at days 15 and 29 was -2·16 [95% CI -2·88 to -1·44]; p<0·0001). Adverse events experienced by study participants were similar between treatment groups; at least one adverse event was reported by 15 (79%) of 19 patients who received placebo and 13 (72%) of 18 patients who received ivacaftor. No deaths occurred during study period. Interpretation: In patients with cystic fibrosis aged 6 years or older who have at least one G551D-CFTR allele, ivacaftor led to improvements in LCI. LCI might be a more sensitive alternative to FEV₁ in detecting response to intervention in these patients with mild lung disease. Funding: Vertex Pharmaceuticals Incorporated. © 2013 Elsevier Ltd.