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PubMed1995

Effects of correlated and uncorrelated measurement error on linear regression and correlation in medical method comparison studies.

It is well known that when uncorrelated measurement error affects both variables in linear regression, there is attenuation of the correlation coefficient and regression slope. The effect of correlated measurement error, however, has received little attention. In medical method comparison studies, such error correlation results from the presence of other, unknown explanatory variables that affect the results of the new test method and the reference test method to which it is being compared. The contribution of correlated measurement error to the observed correlation coefficient can be accounted for by the expression rho t1t2 = rho1 rho2 + rho E1E2 (1-rho2(1))1/2(1-rho 2(2))1/2 where rho t1t2 is the observed correlation between tests 1 and 2, rho 1 and rho 2 are the correlation with true values for tests 1 and 2, respectively, and rho E1E2 is the correlation between the test errors. The first term describes the attenuation due to uncorrelated error, the second term describes the effect of correlated error. A positive correlation between the measurement errors reduces the attenuation of observed correlation and slope, but, when the reference method is excellent, the effect is very small. For poorer reference tests whose correlations with true values are less than 0.9, however, error correlation may result in a slope and correlation coefficient that differ importantly from the values obtained with either uncorrelated error or with no reference test error. Negatively correlated measurement errors magnify the attenuation of slope and correlation. One might suspect the presence of correlated error when the observed regression slope is close to or exceeds 1 and the reference test is known to have suboptimal reliability. This paper provides several clinical examples of potentially correlated diagnostic methods.

Cardiac Output↗
PubMed1989

Analysis of reciprocal creatinine plots by two-phase linear regression.

The progression of renal diseases is often monitored by the serial measurement of plasma creatinine. The slope of the linear relation that is frequently found between the reciprocal of creatinine concentration and time delineates the rate of change in renal function. Minor changes in slope, perhaps indicating response to therapeutic intervention, can be difficult to identify and yet be of clinical importance. We describe the application of two-phase linear regression to identify and characterise changes in slope using a microcomputer. The method fits two intersecting lines to the data by computing a least-squares estimate of the position of the slope change and its 95% confidence limits. This avoids the potential bias of fixing the change at a preconceived time corresponding with an alteration in treatment. The program then evaluates the statistical and clinical significance of the slope change and produces a graphical output to aid interpretation.

Adult↗
PubMed2000

Using linear regression functions to abstract high-frequency data in medicine.

This paper investigates the problem of representing medical time series in linear piece-wise functions and proposes a novel algorithm to transform time-stamped numeric data into simple linear regression functions. We apply methods that involve the hat matrix leverage value and the studentized deleted residual to identify outliers, and a heuristic approach to remove them from the data sets. By distinguishing the breaking points from true outliers, we can efficiently break the data set with respect to the underlying patterns. Using a rough segmentation step, our approach avoids using the whole data set as input, and reduces space requirement. The experimental results indicate our method can achieve more accurate representation of the underlying patterns in data sets collected in the intensive care units efficiently.

Algorithms↗
PubMed2003

Comparison of neural network and multiple linear regression as dissolution predictors.

The predictive performance of an artificial neural network (NN) was compared with the first-order multiple linear regression (MLR) using mean dissolution data of 28 diltiazem immediate release tablet formulations. The performance was evaluated using "Weibull" function parameters alpha and beta. Weibull parameters were used as dissolution markers of the eight principal, mainly compositional, variables. The parameters were obtained by fitting the Weibull function to the mean (n = 12) dissolution profiles of 28 diltiazem hydrochloride tablet formulations. The generated set of 28 pairs of Weibull function parameters was evaluated for internal and external predictability using both the MLR and the artificial NN. A three-layered 8-5-2 feedforward NN was found to be an adequate descriptor of the dissolution data. Internal predictions were based on the data of 24 products. External predictions used the 24 product data to test four products not used in the training phase. The predictive performances of the two techniques were evaluated using bias (mean prediction error; MPE) and precision (mean absolute error; MAE). The study results suggested that, for the studied data set, NN is a superior internal and external predictor to MLR. The artificial NN predicted order of the formulation composition variables, influencing the dissolution parameters as follows: hydrogenated oil > microcrystallinecellulose > ethyl cellulose > eudragit > hydroxypropylcellulose > coat > hydroxypropylmethylcellulose > Speed.

Chemistry, Pharmaceutical↗
PubMed2002

Examination of different pointwise linear regression methods for determining visual field progression.

PURPOSE: To compare the specificity and sensitivity of several different methods for using pointwise linear regression (PLR) to detect progression (deterioration) in visual fields. METHODS: First, theoretical results were derived to predict which of the considered PLR methods would be the most specific and hence the least sensitive. Then, a "Virtual Eye" simulation model was developed that simulates series of sensitivity readings for a point over time. The model adds normally distributed noise (estimated from published results) to the sensitivity at each point to produce a series of fields to be analyzed using each method. Stable and deteriorating eyes were simulated, with the latter defined to have a noise-free loss of 2 dB/y at a significant cluster of points over the series. RESULTS: The most sensitive method tested was to flag a visual field as progressing if it had a point that exhibited a statistically significant slope (at the 1% level) of at least -1 dB/y in the sensitivity. The most specific was a new "Three-Omitting" method that is being proposed, using two confirmation fields in a novel way. Current methods of using confirmation fields to verify a significant slope incorrectly flagged up to twice as many stable eyes as having progressing fields as did our new method. CONCLUSIONS: Using the new proposed PLR method is recommended in preference to current PLR methods in any applications when a high degree of specificity is the main priority.

Computer Simulation↗
PubMed2006

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Algorithms↗
PubMedDate not supplied

INAKT--an interactive non-linear regression program for enzyme inactivation and affinity labelling studies.

An interactive program for analysing enzyme activity-time data using non-linear regression analysis is described. Protection studies can also be dealt with. The program computes inactivation rates, dissociation constants and promotion or inhibition parameters with their standard errors. It can also be used to distinguish different inactivation models. The program is written in SIMULA and is menu-oriented for refining or correcting data at the different levels of computing.

Affinity Labels↗
PubMed1986

A BASIC program for deriving linear regression formulas for intraocular lens power prediction.

We present an original BASIC program written specifically for the ophthalmologist that allows calculation of linear regression formulas for prediction of emmetropic lens power from the surgeon's own data. The program features ongoing data storage, options for analyzing specific ranges (such as longer axial lengths), and calculation of residuals. The program is user-friendly and may be used with minimal computer knowledge. The authors will copy the program at no charge on a user's initialized diskette.

Computers↗
PubMed2003

Rank estimation of log-linear regression with interval-censored data.

Interval-censored data arise in a wide variety of research and application fields such as cancer and AIDS studies. In this paper, we study a log-linear regression model when data are subject to interval censoring. We use a U-statistic based on ranks to estimate regression coefficients and establish large sample properties of the estimator. We illustrate the performance of the proposed estimate with simulations and a numerical example.

Acquired Immunodeficiency Syndrome↗
PubMed2001

A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

Computational Biology↗
PubMed2000

[Determination of chlorzoxazone and paracetamol in co-chlorzoxazone tablet by multi-wavelength linear regression method].

This paper reports that the contents of chlorzoxazone and paracetamol in the co-chlorzoxazone tablet may be determined by the multi-wavelength linear regression method. The program was edited by BASIC. The average recovery and RSD of chlorzoxazone and paracetamol were 98.67%, 0.34% and 100.05%, 0.31% (n = 5), respectively. This method is simple and rapid with satisfactory results.

Acetaminophen↗
PubMed1989

[Synchronous fluorescent determination of phenol and resorcinol using linear regression of multiwavelength data].

A method for simultaneous determination of phenol and resorcinol in mixtures using fluorimetry is developed by combining synchronous fluorescence technique with linear regression of multiwavelength data. The effect of solution pH and other mental variables was examined and the optimal condition for determination of phenol and resorcinol was established. The proposed method was applied to fluorescent assay of resorcinol based on preparation with recoveries of 97.18 ( +/- 2.42)% and 98.15 (+/- 2.70)% for phenol and resorcinol, respectively.

Phenols↗
PubMed2004

TSS concentration in sewers estimated from turbidity measurements by means of linear regression accounting for uncertainties in both variables.

In order to replace traditional sampling and analysis techniques, turbidimeters can be used to estimate TSS concentration in sewers, by means of sensor and site specific empirical equations established by linear regression of on-site turbidity Tvalues with TSS concentrations C measured in corresponding samples. As the ordinary least-squares method is not able to account for measurement uncertainties in both T and C variables, an appropriate regression method is used to solve this difficulty and to evaluate correctly the uncertainty in TSS concentrations estimated from measured turbidity. The regression method is described, including detailed calculations of variances and covariance in the regression parameters. An example of application is given for a calibrated turbidimeter used in a combined sewer system, with data collected during three dry weather days. In order to show how the established regression could be used, an independent 24 hours long dry weather turbidity data series recorded at 2 min time interval is used, transformed into estimated TSS concentrations, and compared to TSS concentrations measured in samples. The comparison appears as satisfactory and suggests that turbidity measurements could replace traditional samples. Further developments, including wet weather periods and other types of sensors, are suggested.

Calibration↗
PubMed2002

Evaluation of the end-expiratory pressure by multiple linear regression and Fourier analysis in humans.

This study was designed to compare the end-expiratory pressure (EEP) during mechanical ventilation (MV) measured dynamically (EEPdyn), by multiple linear regression (MLR) of the airway pressure (Pao) vs volume (V) and flow (V') and after Fourier analysis (FA) of the Pao and V'. Pao and V' were recorded from 32 ICU patients (II without respiratory disease, 10 COPD, II ARDS) under MV, at three levels of PEEPe (0, 5 and 10 hPa). Volume was calculated by numerical integration of V'. Data were analysed by MLR and FA, while the actual value of EEPdyn was recognised on the Pao signal at zero V' and V. EEPdyn, EEPMLR and EEPFA were compared for all patients, for each group of patients and for every level of applied PEEPe. Despite the different evaluation of respiratory mechanics between MLR and FA, the EEP values were always not significantly different between the three applied methods (P > 0.05). A high degree of correlation was found between them, taken two at a time (r > 0.99, P < 0.001). Two non-invasive analytical methods for the evaluation of respiratory mechanics during MV, MLR and FA offer a reliable and clinically useful estimation of EEP during MV.

Adult↗
PubMed1978

Factors predicing survival after portacaval shunt: a multiple linear regression analysis.

The predictive value of 15 pre- and peroperative parameters upon survival after portacaval shunt was analyzed in a retrospective investigation of 134 elective operations. A multiple linear regression model was used. Survival was measured at three different points of time: one month, one year and five years after the operation. Survival at one month was influenced by the parameters bilirubin/s and ascites only. Survival at one year was influenced by albumin/s, sex, bilirubin/s, BSP, heart disease history and ascites Survival at five years was influenced by albumin/s, alkaline phosphatase/s, history of alcohol abuse, and globulin/s. These findings indicate that prediction of survival after portacaval shunt is an intricate process and that considerable improvement of the child criteria is possible.

Female↗
PubMed1996

patial pattern analysis of beta-amyloid (A beta) deposits in Alzheimer disease by linear regression.

The spatial patterns of discrete beta-amyloid (Abeta) deposits in brain tissue from patients with Alzheimer disease (AD) were studied using a statistical method based on linear regression, the results being compared with the more conventional variance/mean (V/M) method. Both methods suggested that Abeta deposits occurred in clusters (400 to <12,800 mu m in diameter) in all but 1 of the 42 tissues examined. In many tissues, a regular periodicity of the Abeta deposit clusters parallel to the tissue boundary was observed. In 23 of 42 (55%) tissues, the two methods revealed essentially the same spatial patterns of Abeta deposits; in 15 of 42 (36%), the regression method indicated the presence of clusters at a scale not revealed by the V/M method; and in 4 of 42 (9%), there was no agreement between the two methods. Perceived advantages of the regression method are that there is a greater probability of detecting clustering at multiple scales, the dimension of larger Abeta clusters can be estimated more accurately, and the spacing between the clusters may be estimated. However, both methods may be useful, with the regression method providing greater resolution and the V/M method providing greater simplicity and ease of interpretation. Estimates of the distance between regularly spaced Abeta clusters were in the range 2,200-11,800 mu m, depending on tissue and cluster size. The regular periodicity of Abeta deposit clusters in many tissues would be consistent with their development in relation to clusters of neurons that give rise to specific neuronal projections.

Aged↗
PubMed1994

Multicomponent analysis for alkaline phosphatase isoenzyme determination by multiple linear regression.

Alkaline phosphatase (EC 3.1.3.1) isoenzymes in serum may be determined by multicomponent analysis of the enzyme activities in the presence of multiple inhibitors. To determine inhibition coefficients of the isoenzymes, we used multiple linear regression analysis to compare alkaline phosphatase activities in the presence of known inhibitors with electrophoretically determined isoenzyme activities in plasma and serum samples. All possible combinations of exactly determined and overdetermined linear systems of inhibitors were ranked according to their prediction error to select an optimum set. The best multicomponent system for prediction included the use of levamisole, phenylalanine, and heat inhibition at 56 degrees C and 65 degrees C to determine bone, hepatic, intestinal, and placental isoenzymes. Consideration of the hepatic isoenzyme as liver and macromolecular fractions resulted in significantly worse predictions. Error analysis involving repeat determinations and a simplex optimization of the inhibition coefficients indicated that the inaccuracy of the comparison electrophoretic method may have been a major factor affecting poor isoenzyme prediction in some samples.

Alkaline Phosphatase↗