Sums Of Variables Research Articles

Central limit theorems with a rate of convergence for time-dependent intermittent maps

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate of convergence. For maps chosen from a certain parameter range, but without additional assumptions on how the maps vary with time, we obtain a self-norming CLT provided that the variances of the partial sums grow sufficiently fast. When the maps are chosen randomly according to a shift-invariant probability measure, we identify conditions under which the quenched CLT holds, assuming fiberwise centering. Finally, we show a multivariate CLT for intermittent quasi-static systems. Our approach is based on Stein’s method of normal approximation.

Professional Stress among Junior Commissioned Officers and Non Commissioned Officers of Indian Military Intelligence

The present study focuses on the professional stress on work places among the Junior Commissioned Officers (JCOs) and Non-Commissioned Officers (NCOs) of Military Intelligence of Indian Army. 384 samples of Military Intelligence personnel will be taken for this study. Sources of data is Primary data include a structured questionnaire. Data was collected through structured questionnaire and measure through Likert’s scale, using Kaiser- Meyer-Olkin measure of sampling adequacy, Cronbach’s alpha for checking internal consistency, Bartlett sphericity test for testing the null hypothesis and various factor analysis including Eigenvalues, Extract square Sum loading, variance percent and Accumulation percent values relative comparison and Correlation matrix will be used as tools to arrive at desired results and statistical interpretations. The hypotheses put for test and the resultant values at 0.01 and 0.05 (for different factors) clearly indicated that there is an existence of association between different level of cadres and professional stress among personnel of Indian Military Intelligence. The authority who can formulate the rules and regulations and binding them on the lower cadres and professions to accept and adopt.

Clinical Outcomes after Re-irradiation in Recurrent Head and Neck Cancers treated with Intensity Modulated Proton and Photon Therapies

Loco-regional recurrence remains a challenge regardless of primary treatment modality in head and neck cancer (HNC). Re-irradiation (RR) is a potential option for local control in previously irradiated patients. We report our institutional experience comparing clinical outcomes in recurrent HNC treated curatively with intensity modulated proton (IMPT) and photon (IMRT) therapy. This is an IRB approved retrospective analysis of prospectively collected outcomes for loco-regionally recurrent or second primary HNC. All patients were treated with radiation to head and neck region at least once previously. Local recurrence (LR), overall survival (OS), disease-free survival (DFS) and acute toxicities occurring within 3 months of RR were analyzed. Statistical tools included Chi-square, Wilcoxon Rank Sum, Fischer Exact, and Unequal Variance T-Tests. We evaluated 44 patients with loco-regional recurrence treated with RR to the head and neck between April 2013 and December 2018. It included 26 patients (59%) treated with IMPT and 18 (41%) with IMRT. Median follow-up was 1.7 years in all patients with at least one year follow-up in both arms. All patients were treated with curative intent. Overall median RR dose was 63 Gy (IMPT=61.5 Gy, IMRT=69.6 Gy) whereas the overall median total dose was same in both arms, 130 Gy. IMPT used conventional fractionation in 17 (65%), SBRT in 8 (31%), and hyperfractionation in 1 (4%) patients. IMRT utilized hyperfractionation in 14 (78%), conventional in 3 (17%) and 1 (6%) SBRT. IMPT was found to have significantly lower rates of physician-reported overall grade 3 (G3) acute toxicities 31% vs 73% in IMRT (p=0.01). This included dysphagia (4% vs 39%, p=0.01), mucositis (8% vs 39%, p=0.001), and dermatitis (12% vs 33%, p=0.03). Commonly treated sites were 52% mucosal (n=23), 14% neck/nodal sites (n=6), and 32% both mucosal and neck sites (n=14), and 2% (n=1) cutaneous only treatment. IMPT patients with mucosal site RR had lower chances of G3 dysphagia (5% vs 40%, p=0.01) and lower G3 mucositis (9% vs 47%, p=0.02); and those with neck nodal/neck RR had lower chances of G3 dermatitis (18% vs 56%, p=0.16). OS at 2-year was 69% with IMPT compared to 58% with IMRT cohort (p=0.26). 2-year LR was 9.5% with IMPT vs 6.5% with IMRT (p=0.66). 2-year DFS was 54% with IMRT compared to 46% with IMPT, respectively (p=0.94). RR is a safe and effective treatment option in the management of recurrent HNC. IMPT RR was found to carry reduced rates of grade 3 toxicity compared to IMRT. IMPT appears to confer a similar rate of OS, DFS and LR compared to IMRT, although these results warrant further exploration in the form of larger prospective studies with longer follow up.

HEMIGEN: Human Embryo Image Generator Based on Generative Adversarial Networks.

We propose a method for generating the synthetic images of human embryo cells that could later be used for classification, analysis, and training, thus resulting in the creation of new synthetic image datasets for research areas lacking real-world data. Our focus was not only to generate the generic image of a cell such, but to make sure that it has all necessary attributes of a real cell image to provide a fully realistic synthetic version. We use human embryo images obtained during cell development processes for training a deep neural network (DNN). The proposed algorithm used generative adversarial network (GAN) to generate one-, two-, and four-cell stage images. We achieved a misclassification rate of 12.3% for the generated images, while the expert evaluation showed the true recognition rate (TRR) of 80.00% (for four-cell images), 86.8% (for two-cell images), and 96.2% (for one-cell images). Texture-based comparison using the Haralick features showed that there is no statistically (using the Student’s t-test) significant (p < 0.01) differences between the real and synthetic embryo images except for the sum of variance (for one-cell and four-cell images), and variance and sum of average (for two-cell images) features. The obtained synthetic images can be later adapted to facilitate the development, training, and evaluation of new algorithms for embryo image processing tasks.

Integration of Radiomic and Multi-omic Analyses Predicts Survival of Newly Diagnosed IDH1 Wild-Type Glioblastoma.

Predictors of patient outcome derived from gene methylation, mutation, or expression are severely limited in IDH1 wild-type glioblastoma (GBM). Radiomics offers an alternative insight into tumor characteristics which can provide complementary information for predictive models. The study aimed to evaluate whether predictive models which integrate radiomic, gene, and clinical (multi-omic) features together offer an increased capacity to predict patient outcome. A dataset comprising 200 IDH1 wild-type GBM patients, derived from The Cancer Imaging Archive (TCIA) (n = 71) and the McGill University Health Centre (n = 129), was used in this study. Radiomic features (n = 45) were extracted from tumor volumes then correlated to biological variables and clinical outcomes. By performing 10-fold cross-validation (n = 200) and utilizing independent training/testing datasets (n = 100/100), an integrative model was derived from multi-omic features and evaluated for predictive strength. Integrative models using a limited panel of radiomic (sum of squares variance, large zone/low gray emphasis, autocorrelation), clinical (therapy type, age), genetic (CIC, PIK3R1, FUBP1) and protein expression (p53, vimentin) yielded a maximal AUC of 78.24% (p = 2.9 × 10−5). We posit that multi-omic models using the limited set of ‘omic’ features outlined above can improve capacity to predict the outcome for IDH1 wild-type GBM patients.

Benign and Malignant Breast Cancer Features Based on Region Characteristics

Breast cancer is one of the most common malignant diseases among women. Mammography is at present one of the available method for early detection of abnormalities, which is related to breast cancer; there are different lesions that are breast cancer characteristic such as masses, which can be detected through this technique. In this work, we explore the application of density slicing and region growing techniques to the problem of finding the boundary of different breast tissue regions in mammograms and extracting these regions. The goal of the segmentation algorithm is to see if density slices images and region growing algorithm could separate different densities for the different breast patterns and calculating there features. Segmentation of the mammogram into different mammographic densities is useful for risk assessment and quantitative evaluation of density changes and for extracting the cancer regions. Our proposed methodology for the segmentation of mammograms has been tested on Mini-MIAS database images. The final result is the segmentation of Region of I interest (ROI) with edge map and different features extraction for analysis where the extracted regions are saved as images and the texture features were calculated using Gray Level Co-Occurrence Matrix (GLCM) along 0^°such as contrast, correlation, homogeneity, sum variance, entropy, energy, mean values and others to differentiate between the Benign and Malignant images. It was found that the features such as contrast, correlation, smoothness, and difference variance are the optimal features to differentiate between benign and malignant regions where the other features are approximately the same. Also region growing method is very fast for extracting cancer regions. Our results are important to design artificial intelligence system to diagnostic breast cancer into benign and malignant cancer.

Trophic Ecology of the Tropical Pacific Sponge Mycale grandis Inferred from Amino Acid Compound-Specific Isotopic Analyses.

Many sponges host abundant and active microbial communities that may play a role in the uptake of dissolved organic matter (DOM) by the sponge holobiont, although the mechanism of DOM uptake and metabolism is uncertain. Bulk and compound-specific isotopic analysis of whole sponge, isolated sponge cells, and isolated symbiotic microbial cells of the shallow water tropical Pacific sponge Mycale grandis were used to elucidate the trophic relationships between the host sponge and its associated microbial community. δ15N and δ13C values of amino acids in M. grandis isolated sponge cells are not different from those of its bacterial symbionts. Consequently, there is no difference in trophic position of the sponge and its symbiotic microbes indicating that M. grandis sponge cell isolates do not display amino acid isotopic characteristics typical of metazoan feeding. Furthermore, both the isolated microbial and sponge cell fractions were characterized by a similarly high ΣV value-a measure of bacterial-re-synthesis of organic matter calculated from the sum of variance among individual δ15N values of trophic amino acids. These high ΣV values observed in the sponge suggest that M. grandis is not reliant on translocated photosynthate from photosymbionts or feeding on water column picoplankton, but obtains nutrition through the uptake of amino acids of bacterial origin. Our results suggest that direct assimilation of bacterially synthesized amino acids from its symbionts, either in a manner similar to translocation observed in the coral holobiont or through phagotrophic feeding, is an important if not primary pathway of amino acid acquisition for M. grandis.

Application of Gray Level co-Occurrence Matrix Algorithm for Detection of Discrete Structural Changes in Cell Nuclei After Exposure to Iron Oxide Nanoparticles and 6-Hydroxydopamine.

The gray level co-occurrence matrix (GLCM) algorithm is a contemporary computational biology method which, today, is frequently used to detect small changes in texture that are not visible using conventional techniques. We demonstrate that the toxic compound 6-hydroxydopamine (6-OHDA) and iron oxide nanoparticles (IONPS) have opposite effects on GLCM features of cell nuclei. Saccharomyces cerevisiae yeast cells were treated with 6-OHDA and IONPs, and imaging with GLCM analysis was performed at three different time points: 30 min, 60 min, and 120 min after the treatment. A total of 200 cell nuclei were analyzed, and for each nucleus, 5 GLCM parameters were calculated: Angular second moment (ASM), Inverse difference moment (IDM), Contrast (CON), Correlation (COR) and Sum Variance (SVAR). Exposure to IONPs was associated with the increase of ASM and IDM while the values of SVAR and COR were reduced. Treatment with 6-OHDA was associated with the increase of SVAR and CON, while the values of nuclear ASM and IDM were reduced. This is the first study to indicate that IONPs and 6-OHDA have opposite effects on nuclear texture. Also, to the best of our knowledge, this is the first study to apply the GLCM algorithm in Saccharomyces cerevisiae yeast cells in this experimental setting.

Correlations between P53 Mutation Status and Texture Features of CT Images for Hepatocellular Carcinoma.

To investigate the performance of texture analysis in characterizing P53 mutations of hepatocellular carcinomas (HCCs) based on computed tomography (CT). A total of 63 HCC patients underwent CT scans and were tested for P53 mutations. Patients were divided into two groups of P53(-) and P53(+) according to the P53 scores. First- and second-order texture features were computed from the CT images and compared between groups using independent Student's t-test. A Spearman's correlation coefficient was used for correlations to assess the relationship between the different P53 sores and CT data. The performance of texture features in differentiating the P53 mutations of HCC was assessed using receiver operating characteristic analysis. The mean values of angular second moment (ASM; mean = 0.001) and contrast (mean = 194.727) for P53(-) were higher than those of P53(+). Meanwhile the mean values of correlation (mean = 0.735), sum variance (mean = 1,111.052), inverse difference moment (IDM; mean = 0.090), and entropy (mean = 3.016) for P53(-) were lower than those of P53(+). Significant correlations were found between P53 scores and ASM (r = - 0.439), contrast (r = - 0.263), correlation (r = 0.551), sum of squares (r = 0.282), sum variance (r = 0.417), IDM (r = 0.308), and entropy (r = 0.569). Five texture parameters (ASM, contrast, correlation, IDM, and entropy) were predictive of P53 mutation status, with areas under the curve ranging from 0.621 to 0.792. There was a direct relationship between P53 mutations and gray-level co-occurrence matrix, but not with histograms for HCC patients. Correlation and entropy seemed to be the most promising in differentiating P53 (-) from P53(+).

1592-P: Prediction Method for Infection Risk in Perioperative Patients with Diabetes

Background/Purpose: Perioperative blood glucose management is important for complication prevention and early hospital discharge. The relation between blood glucose fluctuations and infection is few reported. This study aimed to find predictive risk factors to identify high-risk patients with diabetes requiring more extensive management. Methods: A retrospective study was performed on the perioperative blood glucose management of 105 patients. The presence of infection within one month after surgery was the primary outcome, and the predictive factors were identified. For statistical analysis, analysis of variance or Wilcoxon rank sum test was used. Based on univariate analysis, principle component analysis and logistic analysis were performed to prepare a prediction model of infection onset within one month after surgery using predictive risk factors. The area under the receiver operating characteristic curve (AUC) was evaluated. Results: Patients with infection within one month after surgery had higher mean blood glucose levels (185.1±28.7 vs. 168.3±33.6 mg/dL, P=0.013), larger preoperative blood glucose fluctuations (54.9±24.1 vs. 37.7±23.1 mg/dL, P=0.006), lower albumin level (3.6±0.6 vs. 3.9±0.6 g/dL, P=0.046), longer operation time (432.5±179.6 vs. 282.5±178.3 minute, P&amp;lt;0.001), more bleeding (972.3±920.1 vs. 436.4±795.8 mg/dL, P=0.003), and longer postoperative hospitalization periods (51.9±56.1 vs. 22.4±24.3 days, P&amp;lt;0.001) than patients without infection. They also had greater frequency of adverse events (hazard ratio (HR)=3.19, P=0.013) and mortality within 1 year (HR=4.03, P=0.026). Preoperative blood glucose fluctuation and operation time were considered as more reliable factors of the prediction model. The model had high prediction accuracy with AUC 0.801. Discussion: Preoperative blood glucose fluctuations and long operation time were risk factors for infection in perioperative patients with diabetes. This prediction model can detect these high-risk patients. Disclosure M. Koshizaka: Research Support; Self; Astellas Pharma Inc., Pfizer Health Research Foundation, Taisho Pharmaceutical Co., Ltd. R. Ishibashi: None. Y. Maeda: None. T. Ishikawa: None. Y. Maezawa: None. M. Takemoto: None. K. Yokote: None. Funding Pfizer Health Research Foundation

State-independent uncertainty relations from eigenvalue minimization

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper, we present procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the many known techniques developed to this aim. To demonstrate the simplicity of the method, we analyze multiple instances, that involve two or more observables, both bounded and unbounded.

Optimizing method of mechanism angle of upper limb rehabilitation robot at glenohumeral joint

At present, there are seventy million stroke patients in China and annual death toll of stroke is 1 million 650 thousand people. The survivors about 75% become disabled persons and lose the ability to move. To address this issue, a kind of rehabilitation exoskeleton robot called YANARM is proposed which for training of shoulder complex. This paper, a kind of method for optimizing the angle parameters of series dynamic axes under given workspace conditions is presented. The forward and inverse kinematics solutions of glenohumeral mechanism are solved based on the exponential product formula (POE) and the Paden-Kahan sub-problem. The range of joint rotation angle can be inversely solved according to the end of the arm position at the borderline of the workspace. A curve between the angle and the CP which equal mean variance of joint rotation range plus sum of all joint rotation ranges is solved. The mechanism angle of glenohumeral joint is optimized by this method.

Variance of gametic diversity and its application in selection programs

The variance of gametic diversity ( σgamete2) can be used to find individuals that more likely produce progeny with extreme breeding values. The aim of this study was to obtain this variance for individuals from routine genomic evaluations, and to apply gametic variance in a selection criterion in conjunction with breeding values to improve genetic progress. An analytical approach was developed to estimate σgamete2 by the sum of binomial variances of all individual quantitative trait loci across the genome. Simulation was used to verify the predictability of this variance in a range of scenarios. The accuracy of prediction ranged from 0.49 to 0.85, depending on the scenario and model used. Compared with sequence data, SNP data are sufficient for estimating σgamete2 Results also suggested that markers with low minor allele frequency and the covariance between markers should be included in the estimation. To incorporate σgamete2 into selective breeding programs, we proposed a new index, relative predicted transmitting ability, which better utilizes the genetic potential of individuals than traditional predicted transmitting ability. Simulation with a small genome showed an additional genetic gain of up to 16% in 10 generations, depending on the number of quantitative trait loci and selection intensity. Finally, we applied σgamete2 to the US genomic evaluations for Holstein and Jersey cattle. As expected, the DGAT1 gene had a strong effect on the estimation of σgamete2 for several production traits. However, inbreeding had a small impact on gametic variability, with greater effect for more polygenic traits. In conclusion, gametic variance, a potentially important parameter for selection programs, can be easily computed and is useful for improving genetic progress and controlling genetic diversity.

Diffusive behavior of ergodic sums over rotations

For a rotation by an irrational [Formula: see text] on the circle and a BV function [Formula: see text], we study the variance of the ergodic sums [Formula: see text]. When [Formula: see text] is not of constant type, we construct sequences [Formula: see text] such that, at some scale, the ergodic sums [Formula: see text] satisfy an ASIP. Explicit non-degenerate examples are given with an application to the rectangular periodic billiard in the plane.

Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures

In recent years different inerter-based vibration absorbers (IVAs) emerged for the earthquake protection of building structures coupling viscous and tuned-mass dampers with an inerter device. In the three most popular IVAs the inerter is functioning either as a motion amplifier [tuned-viscous-mass-damper (TVMD) configuration], mass amplifier [tuned-mass-damper-inerter (TMDI) configuration], or mass substitute [tuned-inerter-damper (TID) configuration]. Previous work has shown that through proper tuning, IVAs achieve enhanced earthquake-induced vibration suppression and/or weight reduction compared to conventional dampers/absorbers, but at the expense of increased control forces exerted from the IVA to the host building structure. These potentially large forces are typically not accounted for by current IVA tuning approaches. In this regard, a multi-objective IVA design approach is herein developed to identify the compromise between the competing objectives of (i) suppressing earthquake-induced vibrations in buildings, and (ii) avoiding development of excessive IVA (control) forces, while, simultaneously, assessing the appropriateness of different modeling assumptions for practical design of IVAs for earthquake engineering applications. The potential of the approach to pinpoint Pareto optimal IVA designs against the above objectives is illustrated for different IVA placements along the height of a benchmark 9-storey steel frame structure. Objective (i) is quantified according to current performance-based seismic design trends using first-passage reliability criteria associated with the probability of exceeding pre-specified thresholds of storey drifts and/or floor accelerations being the engineering demand parameters (EDPs) of interest. A variant, simpler, formulation is also considered using as performance quantification the sum of EDP variances in accordance to traditional tuning methods for dynamic vibration absorbers. Objective (ii) is quantified through the variance of the IVA force. It is found that reduction of IVA control force of up to 3 times can be achieved with insignificant deterioration of building performance compared to the extreme Pareto optimal IVA design targeting maximum vibration suppression, while TID and TMDI achieve practically the same building performance and significantly outperform the TVMD. Moreover, it is shown that the simpler variant formulation may provide significantly suboptimal reliability performance. Lastly, it is verified that the efficacy of optimal IVA designs for stationary conditions is maintained for non-stationary stochastic excitation model capturing typical evolutionary features of earthquake excitations.

Variance of arithmetic sums and L-functions in 𝔽q[t

We compute the variances of sums in arithmetic progressions of generalised k-divisor functions related to certain L-functions in $\mathbb{F}_q(t)$, in the limit as $q\to\infty$. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when $q\to\infty$, in terms of matrix integrals, which may be evaluated. Our results extend those obtained previously in the special case corresponding to the usual $k$-divisor function, when the L-function in question has degree one. They illustrate the role played by the degree of the L-functions; in particular, we find qualitatively new behaviour when the degree exceeds one. Our calculations apply, for example, to elliptic curves defined over $\mathbb{F}_q(t)$, and we illustrate them by examining in some detail the generalised $k$-divisor functions associated with the Legendre curve.

Elucidation of microstructural changes in leaves during senescence using spectral domain optical coherence tomography

Leaf senescence provides a unique window to explore the age-dependent programmed degradation at organ label in plants. Here, spectral domain optical coherence tomography (SD-OCT) has been used to study in vivo senescing leaf microstructural changes in the deciduous plant Acer serrulatum Hayata. Hayata leaves show autumn phenology and change color from green to yellow and finally red. SD-OCT image analysis shows distinctive features among different layers of the leaves; merging of upper epidermis and palisade layers form thicker layers in red leaves compared to green leaves. Moreover, A-scan analysis showed a significant (p < 0.001) decrease in the attenuation coefficient (for wavelength range: 1100–1550 nm) from green to red leaves. In addition, the B-scan analysis also showed significant changes in 14 texture parameters extracted from second-order spatial gray level dependence matrix (SGLDM). Among these parameters, a set of three features (energy, skewness, and sum variance), capable of quantitatively distinguishing difference in the microstructures of three different colored leaves, has been identified. Furthermore, classification based on k-nearest neighbors algorithm (k-NN) was found to yield 98% sensitivity, 99% specificity, and 95.5% accuracy. Following the proposed technique, a portable noninvasive tool for quality control in crop management can be anticipated.

Optimum Placement of Phasor Measurement Units in Power Systems

In this paper, we proposed to evaluate the optimal phasor measurement unit (PMU) placement based on the sum of variance (SV) of the robust estimators. Variance is traditionally used as a measure of the quality of estimates. In this paper, after satisfying the requirements of the minimum number of PMUs, maximum measurement redundancy, and observability, the placements obtained are further distinguished on the basis of the variance of the estimated states. Both the weighted least squares (WLS) and robust estimators are considered. Examples on the IEEE 30-bus system using least absolute value (LAV) estimation are given. The covariance of the state estimates from the WLS can be calculated using the existing formulas. However, there is no equivalent formula for the robust LAV estimator. A formula is derived in this paper using influence function to approximately calculate the covariance matrix of the state estimates from the robust LAV estimator. The optimum placement, i.e., the placement with the smallest SV, can be selected.

Patient Transfer Decision Difficulty Scale: Development and psychometric testing of emergency department visits by long-term care residents.

Background and objectivesNurses serve as gatekeepers of the health of long-term care facility (LTCF) residents and are key members deciding whether residents should visit an emergency department (ED). Inappropriate decisions as to ED visits may result in ED overcrowding, excessive medical expenses, and nosocomial infections. Currently, there is a lack of effective tools for assessing the barriers and level of difficulty experienced by LTCF nurses. The purposes of this study were to develop a Patient Transfer Decision Difficulty Scale (PTDDS) and test its effectiveness.MethodsThis study randomly sampled LTCFs in Taiwan and surveyed two or three nurses in every institution selected. Registered return envelopes were provided for participants to return self-completed questionnaires. Three steps were used to develop the scale and items: in step I, the instrument was developed; in step II, psychometric testing was conducted, which entailed performing an exploratory factor analysis (EFA) to verify the construct validity and reliability of the developed items; and in step III, a confirmation study was conducted using a confirmatory factor analysis (CFA) and structural equation modeling to cross-validate the factors and items.ResultsThe cumulative sum of variance explained by the measurement models of the three factors in the PTDDS was 63.54%.When deciding whether to transfer LTCF residents to EDs, the most pronounced barrier experienced by nurses were for judging the severity of “clinical episodes”, which had an explanatory power of 37.49%. The second and third pronounced barriers and decision difficulty experienced by nurses were “communication and information” and “timing of the residents’ emergency visits,” which explained 16.81% and 9.24% of the variance, respectively.ConclusionsThe cross-validation results obtained using the EFA and CFA showed favorable reliability and validity of the PTDDS. For future studies, this study recommends performing large-scale investigations of the level of decision difficulty and related factors experienced by nurses in LTCFs of varying levels and types.

The correlation between baseline score and post-intervention score, and its implications for statistical analysis

BackgroundWhen using a continuous outcome measure in a randomised controlled trial (RCT), the baseline score should be measured in addition to the post-intervention score, and it should be analysed using the appropriate statistical analysis.MethodsWe derive the correlation between the change score and baseline score and show that there is always a correlation (usually negative) between the change score and baseline score. We discuss the following correlations and provide the mathematical derivations in the Appendix:Correlation between change score and baseline scoreCorrelation between change score and post scoreCorrelation between change score and average score.The setting here is a parallel, two-arm RCT, but the method discussed in this paper is applicable for any studies or trials that have a continuous outcome measure; it is not restricted to RCTs.ResultsWe show that using the change score as the outcome measure does not address the problem of regression to the mean, nor does it take account of the baseline imbalance. Whether the outcome is change score or post score, one should always adjust for baseline using analysis of covariance (ANCOVA); otherwise, the estimated treat effect may be biased. We show that these correlations also apply when comparing two measurement methods using Bland-Altman plots.ConclusionsThe correlation between baseline and post-intervention scores can be derived using the variance sum law. We can then use the derived correlation to calculate the required sample size in the design stage. Baseline imbalance may occur in RCTs, and ANCOVA should be used to adjust for baseline in the analysis stage.