Simple Linear Regression Line Research Articles

Predicting the Outcomes of Oropharyngeal Surgery in Patients With Obstructive Sleep Apnea Using Tongue-Retaining Devices.

To determine the efficacy of a tongue-retaining device (TRD) in predicting the outcomes of oropharyngeal surgery in patients with obstructive sleep apnea (OSA) before surgery. A prospective case-control study. A single tertiary medical center. Patients with moderate-severe OSA who underwent both uvulopalatopharyngoplasty and tongue base suspension between January 2022 and July 2022 were included. Each patient underwent a series of 3 overnight polysomnography. Objective outcomes include apnea-hypopnea index (AHI), minimal oxygen saturation, and reduction rate of AHI. The correlation between the reduction rate of AHI with TRD and surgery was analyzed with linear regression. The reduction rates of AHI were significantly different between the group using TRD (44 ± 24%) and the postoperative group (55 ± 21%). The cross-tabulation revealed a strong association between a positive response to TRD treatment and a positive response to surgery. The use of TRD to evaluate surgical response demonstrated a positive predictive value of 90% and a negative predictive value of 70%. A strong correlation between the decrease in AHI was observed in both TRD and surgery groups, which was demonstrated by a steep slope in the scatter plot and a significant simple linear regression line. Preoperative TRD response is an accurate tool for predicting the success of oropharyngeal surgery in managing OSA patients before surgical treatment. Furthermore, a quantifiable positive linear correlation exists between the efficacy of preoperative TRD treatment and surgery.

Simultaneous confidence tubes for comparing several multivariate linear regression models.

Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu etal. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated withexamples.

Effects of Extreme Flooding on Output of Selected Crops in Anambra State, Nigeria from 1990 to 2019

The study has analyzed effects of extreme flooding on output of selected root and tuber crops in Anambra State, Nigeria for the period of 1990-2019using secondary data collected on cassava, yam and sweet potato output from the agricultural production survey of Anambra State Agricultural Development Programme and annual averages of rainfall from the Nigeria Meteorological Agency inAwka station. Data collected were analysed by using multivariate simple linear regression and trend analysisin linear trend analysis and line graph. Results respectively showed an increasing trend in output of cassava, yam and sweet potato within the researched period with a depression in output of cassava and yam in 2014 and 2015. The regression results showed that coefficients of determination (R2) values of yam output were (0.620), cassava output (0.560) and sweet potato (0.580), which implied that 63%, 56% and 58% changed in output of roots and tuber crops accounted for rainfall within the research period. Specifically, rainfall (0.002) was positively related to yam output at (p<0.05). This implied excessive amount of rainfall resulting flooding, which influenced the output of production of yam. Rainfall (-0.015) and (-0.003) were negatively related to output of cassava and sweet potato at 5% probability level, which indicated extreme rainfall translating into flooding, which adversely affected the output of cassava and sweet potato in this area. The result of the tested hypothesis showed that extreme flooding had significant negative effects on output of roots and tuber crops in the researched area. Based on results, it was concluded that extreme flooding deleteriously affected output of root and tuber crops in Anambra state, Nigeria. Therefore, farmers were advised to change their crop production technologies including time of planting to suit changes in rainfall pattern in order to avert their adverse effects.

Longitudinal Analysis of CAD/CAM Restoration Incorporation Rates into Navy Dentistry.

Computer-aided design/computer-aided manufacturing (CAD/CAM) has gained increasing popularity since the first commercially viable dental system was introduced in the mid-1980s. Digitally milled dental restorations can be fabricated chairside in the course of one dental appointment, reducing time, cost, and manpower when compared with traditional laboratory-fabricated analog restorations. Clinical performance, physical properties, and esthetics of digital restorations have been shown to be comparable to traditional analog restorations. The Navy has incorporated CAD/CAM systems into dental clinics on multiple platforms to include ships. The efficiency of this technology has the potential to positively impact dental health and mission readiness. The objective of the present study was to evaluate placement rates of CAD/CAM restorations by Navy dental providers. Placement rates of CAD/CAM restorations from October 2011 to June 2017 (Department of Defense created codes specific to CAD/CAM restorations in 2011) and of laboratory-fabricated analog restorations from January 2008 to June 2017 were queried from the Dental Common Access System (DENCAS) and Corporate Dental Access system (CDA) and evaluated. Scatterplots for each dental restoration category were generated using monthly production data and overlaid with simple linear regression lines and 95% confidence intervals. Regression analysis was performed to determine whether changes in the monthly percentages of placements before and after CAD/CAM were increasing or decreasing and to determine whether the monthly percent change from before CAD/CAM implementation and after CAD/CAM implementation was significantly different from one another. A total of 20,512 CAD/CAM restorations were placed by Navy providers over the 68-month period. A year-over-year increase in digitally fabricated restorations was observed. As a percentage of total indirect restorations, CAD/CAM units surged from 13.8% in 2012 to 38.1% in 2017. All ceramic restorations fabricated by the classical analog method also increased significantly through the period. Traditional analog porcelain fused to metal (PFM) restorations and large amalgam restorations, which frequently serve a similar clinical purpose as indirect or direct full or partial tooth coverage restorations, both decreased significantly after CAD/CAM productivity tracking was initiated. Implementation of CAD/CAM digital restorations has led to a significant decline in specific traditional analog procedures since productivity tracking of CAD/CAM was initiated in 2011. Navy dentistry has embraced CAD/CAM as an efficient means to prepare sailors and marines for deployments, improve operational dental readiness, and potentially decrease dental emergencies by reducing the need for provisional restorations. The trend toward increased utilization of digital dentistry is expected to continue for the following reasons: (1) incorporation of CAD/CAM technology into dental school curricula, (2) advancement of CAD/CAM systems equipped with fast-evolving user interfaces, (3) increased accessibility to CAD/CAM technology in Navy clinics, and (4) training of a greater proportion of dentists in digital CAD/CAM technology. Future studies should investigate the survival rate of CAD/CAM restorations placed within military settings, cost, and manpower of maintaining CAD/CAM units, and impact on military dental laboratories associated with increased CAD/CAM usage.

Optimization of the reconstruction parameters in [123I]FP-CIT SPECT

The aim of this work was to obtain a set of parameters to be applied in [123I]FP-CIT SPECT reconstruction in order to minimize the error between standardized and true values of the specific uptake ratio (SUR) in dopaminergic neurotransmission SPECT studies. To this end, Monte Carlo simulation was used to generate a database of 1380 projection data-sets from 23 subjects, including normal cases and a variety of pathologies. Studies were reconstructed using filtered back projection (FBP) with attenuation correction and ordered subset expectation maximization (OSEM) with correction for different degradations (attenuation, scatter and PSF). Reconstruction parameters to be optimized were the cut-off frequency of a 2D Butterworth pre-filter in FBP, and the number of iterations and the full width at Half maximum of a 3D Gaussian post-filter in OSEM. Reconstructed images were quantified using regions of interest (ROIs) derived from Magnetic Resonance scans and from the Automated Anatomical Labeling map. Results were standardized by applying a simple linear regression line obtained from the entire patient dataset. Our findings show that we can obtain a set of optimal parameters for each reconstruction strategy. The accuracy of the standardized SUR increases when the reconstruction method includes more corrections. The use of generic ROIs instead of subject-specific ROIs adds significant inaccuracies. Thus, after reconstruction with OSEM and correction for all degradations, subject-specific ROIs led to errors between standardized and true SUR values in the range [−0.5, +0.5] in 87% and 92% of the cases for caudate and putamen, respectively. These percentages dropped to 75% and 88% when the generic ROIs were used.

Location and Scale Estimation with Correlation Coefficients

This article shows how to use any correlation coefficient to produce an estimate of location and scale. It is part of a broader system, called a correlation estimation system (CES), that uses correlation coefficients as the starting point for estimations. The method is illustrated using the well-known normal distribution. This article shows that any correlation coefficient can be used to fit a simple linear regression line to bivariate data and then the slope and intercept are estimates of standard deviation and location. Because a robust correlation will produce robust estimates, this CES can be recommended as a tool for everyday data analysis. Simulations indicate that the median with this method using a robust correlation coefficient appears to be nearly as efficient as the mean with good data and much better if there are a few errant data points. Hypothesis testing and confidence intervals are discussed for the scale parameter; both normal and Cauchy distributions are covered.

Easy-to-construct confidence bands for comparing two simple linear regression lines

This paper shows how to construct confidence bands for the difference between two simple linear regression lines. These confidence bands provide directly the information on the magnitude of the difference between the regression lines over an interval of interest and, as a by-product, can be used as a formal test of the difference between the two regression lines. Various different shapes of confidence bands are illustrated, and particular attention is paid towards confidence bands whose construction only involves critical points from standard distributions so that they are consequently easy to construct.

Exact Confidence Bounds for Comparing Two Regression Lines with a Control Regression Line on a Fixed Interval

AbstractThe problem of finding exact simultaneous confidence bounds for comparing simple linear regression lines for two treatments with a simple linear regression line for the control over a fixed interval is considered. The assumption that errors are iid normal random is considered. It is assumed that the design matrices for the two treatments are equal and the design matrix for the control has the same number of copies of each distinct row of the design matrix for the treatments. The method is based on a pivotal quantity that can be expressed as a function of four t variables. The probability point depends on the size of an angle associated with the interval. We present probability points for various sample sizes and angles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiple Comparison of Several Linear Regression Models

Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many–one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples.

Body composition modeling. Application to exploration of the resting energy expenditure fat-free mass relationship.

There are now many published methods for predicting resting energy expenditure (REE) from measured body mass and composition. Although these published reports extend back almost a century, new related studies appear on a regular basis. It remains unclear what the similarities and differences are between these many methods and what, if any, advantages the newly introduced REE prediction models offer. These issues led us to develop an organizational system for REE prediction methods with the ultimate aim of clarifying prevailing ambiguities in the field. Our classification scheme is founded on the mathematical function type (descriptive and mechanistic) and body composition level (whole body-->molecular) used in REE prediction model development. The model is applied in an exploration of the well-established empirical relationship between REE and fat-free body mass (FFM). The developed relationships indicate that REE vs. FFM is a curvilinear relationship in mammals as a whole, that the relationship can be described as a linear function in humans, and that the simple linear regression line coefficients can be reconstructed from established tissue-system level component relationships. Our classification system, the first founded on a conceptual basis, highlights similarities and differences between the many diverse REE body composition prediction methods, provides a framework for teaching REE-body composition relationships to students, and suggests important future research opportunities.

Monte Carlo estimation of extrapolation of quality-adjusted survival for follow-up studies.

The expected quality-adjusted survival (QAS) for an index population with a specific disease can be estimated by summing the product of the survival function and the mean quality of life function of the population. In many follow-up studies with heavy censoring, the expected QAS may not be well estimated due to the lack of data beyond the close of follow-up. In this paper, we first created a reference population from the life tables of the general population according to the Monte Carlo method. Secondly, we fitted a simple linear regression line to the logit of the ratio of quality-adjusted survival functions for the index and reference populations up to the end of follow-up. Finally, combining information on the reference population with the fitted line, we predicted the expected quality-adjusted survival curve beyond the follow-up period for the index population. Simulation studies have shown that the simple Monte Carlo estimation procedure is a potential approach for estimating expected QAS and the survival function beyond the follow-up with a certain degree of accuracy.

Validation of limulus tests for endotoxin evaluation in dialysate

Summary: To measure endotoxin (ET) levels in dialysate accurately, three commercial limulus tests (Endospecy, Seikagaku, Tokyo, Japan; Kinetic QCL, BioWhittacker, MD, USA; ET single test‐ES, Wako, Osaka, Japan) were validated in order to determine whether or not they are enhanced or inhibited by bicarbonate dialysate. Two reference standard ET, one from US Pharmacopoeia (Escherichia coli reference standard endotoxin; RSE) and the other from European Pharmacopoeia (Salmonella RSE), were adjusted with dialysate at concentrations of 0.05, 0.10 and 0.15 EU/mL for measurement by each kit. A simple linear regression line forced to the origin was generated for each kit. the validation criteria, based upon accuracy and precision analysis, includes the fact that the range of slope of the regression line of 95% confidence must fall between 0.75 and 1.25, and the correlation coefficient must be no less than 0.99 with significance (P < 0.05). No enhancement/inhibition was observed with Endospecy. Kinetic QCL showed enhancement with Salmonella RSE and no enhancement/inhibition with E. coli RSE. the ET single test‐ES kit was inhibited with both RSE. Clinical dialysate samples were also measured for ET activity by each limulus kit which revealed that Endospecy and Kinetic QCL gave almost identical values; however, the ET single test‐ES kit gave significantly lower values (41%) than the others (P < 0.05). These results suggest that either the validation test using RSE or comparative analysis with an already validated kit (Endospecy) is necessary for measuring ET levels in dialysate.

Respirometry of the lecithotrophic larvae of the parasitic barnacle, Sacculina carcini

Abstract The respiration of the larval stages of the parasitic barnacle, Sacculina carcini , was measured with an oxygen electrode. Stage I nauplii were difficult to collect, but two measurements were made on male larvae to give the highest rate per larva figure of 1.17 × 10 −3 μl O 2 h −1 larva −1 . There was good agreement in the respiration rates of the other, later stages, with the smaller female larvae giving the slightly higher weight-specific rates. It was concluded that the cyprids showed two distinct respiration rates depending on their level of activity. Overall Q 10 values from respiration rates at 10°C and 18°C were 2.01 for male larvae and 2.33 for female larvae. In an experiment measuring respiration of a single nauplius stage at different temperatures, the weight-specific rates with increasing temperature (6–24°C range) occurred close to a simple linear regression line. However, when the data points were joined up, the expected rate/temperature curve became obvious. The respiration rates found for S. carcini larvae were compared with those for other invertebrate lecithotrophic larvae, and good agreement was found with one exception, the larva of Bugula neritina (Bryozoa).

Bayesian inferences on nonlinear functions of the parameters in linear regression

A variety of statistical problems (e.g. the x-intercept in linear regression, the abscissa of the point of intersection of two simple linear regression lines or the point of extremum in quadratic regression) can be viewed as questions of inference on nonlinear functions of the parameters in the general linear regression model. In this paper inferences on the threshold temperatures and summation constants in crop development will be made. A Bayesian approach for the general formulation of this problem will be developed. By using numerical integration, credibility intervals for individual functions as well as for linear combinations of the functions of the parameters can be obtained. The implementation of an odds ratio procedure is facilitated by placing a proper prior on the ratio of the relevant parameters.

Net subsidence and number of cycles; their interrelationship in different Permian Gondwana basins of peninsular India

Seven data sets were structured from subsurface lithologs of Permian Gondwana coal measures comprising the Karharbari, Barakar and Raniganj formations of the Koel-Damodar and Mahanadi basins of peninsular India. All three formations are fluvial in nature and composed largely of fining-upward cycles of clastic sediments capped by coal/carbonaceous shale. Simple linear regression lines and correlation coefficients were computed for total thickness of strata (net subsidence) and number of cycles in each data set. The strong positive relationships between total thickness of strata and number of cycles in Permian coal measures suggest that the fluvial cycles of Karharbari, Barakar and Raniganj are formed by intrabasinal mechanisms of channel migration, sedimentation and subsidence rather than tectonic events in the source area. The slopes of linear regression lines fitted to the data sets vary more than has hitherto been supposed and are classified into two categories. Three out of seven regression lines exhibit steeper slopes and they are closely similar in this respect to other Permian and Upper Carboniferous coal measures of Australia, Great Britain and Germany; the other four have gentler slopes. These dissimilarities in the slopes of regression lines are attributed to the differential rate of increase in the number of cycles with respect to the total thickness of the strata (net subsidence) as well as the differential subsidence of the Permian Gondwana Supergroup through space and time.

Clinical relevance of phase of steady-state VEPs to P100 latency of transient VEPs

Pattern visual evoked potentials (VEPs) to transient and steady-state stimulation were recorded in 10 normal subjects at 4 levels of luminance (180, 57, 22 and 11 cd/m 2). VEPs were also recorded in 5 patients with optic neuropathy at a fixed luminance (180 cd/m 2). The relationship between P100 latency of transient VEPs (T-VEPs) and the phase of steady-state VEPs (S-VEPs) was analyzed. As luminance decreased in normal subjects, P100 latency was prolonged and the phase lag increased. A significant linear relationship between the P100 latency and phase was found. Patients showed both the prolonged P100 latency and the delayed phase. The simple linear regression line of the phase-P100 latency function of normal subjects closely matched the patients' values. These results suggest that changes in the phase may be equivalent to changes in the P100 latency. S-VEPs, therefore, may be clinically useful in assessing visual function.

BARDEN INLET, N.C. A CASE STUDY OF INLET MIGRATION

The migratory pattern of a small coastal inlet was examined in terms of the factors generally acknowledged to control inlet behavior. That is, the tidal discharge which acts to flush the inlet and, on the other hand, the intrusive littoral materials depositing in the inlet environment. Specifically, a "flow conveyance index" was computed and compared to shoreline movements. The "flow conveyance index" was defined as the ratio of the mean distribution of the overall planform area of the throat of the inlet to the mean distribution of the planform areas of shoals within the throat of the inlet. High and low "flow conveyance index" values would correspond, respectively, to periods of relatively high and low inlet flushing conditions. A consistent pattern obtained from this analysis, wherein high and low index values corresponded with high and low shoreline movements. Additionally, the plot of rates of shore movements against rates of change of "flow conveyance index" was fitted with a simple linear regression line having a positive correlation coefficient of 0.85. Further analyses of the mean distribution of the shoals within the throat of the inlet demonstrated the cause of timevarying rates of movement of points along the spiriferous east shoreline of the inlet. Shoreline movement rates were plotted on a time-space plane and isolines of shore movement rates contoured. The result was a three-dimensional image of shore movement rates over time and distance. The position of the centroid of the inlet shoal distribution at different times was superimposed upon the three-dimensional image. This revealed that variations of shoreline movement rates along the shore at any point in time are dependent on the mean position of the inlet shoal distribution. Also, the direction of movement of the mean position of the inlet shoal distribution appeared to indicate the predominant direction of flushing action, that is, flood or ebb tides.