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PubMed2004

Efficient regression analysis with ranked-set sampling.

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.

Biometry↗
PubMed1999

Necessary sample size for method comparison studies based on regression analysis.

BACKGROUND: In method comparison studies, it is of importance to assure that the presence of a difference of medical importance is detected. For a given difference, the necessary number of samples depends on the range of values and the analytical standard deviations of the methods involved. For typical examples, the present study evaluates the statistical power of least-squares and Deming regression analyses applied to the method comparison data. METHODS: Theoretical calculations and simulations were used to consider the statistical power for detection of slope deviations from unity and intercept deviations from zero. For situations with proportional analytical standard deviations, weighted forms of regression analysis were evaluated. RESULTS: In general, sample sizes of 40-100 samples conventionally used in method comparison studies often must be reconsidered. A main factor is the range of values, which should be as wide as possible for the given analyte. For a range ratio (maximum value divided by minimum value) of 2, 544 samples are required to detect one standardized slope deviation; the number of required samples decreases to 64 at a range ratio of 10 (proportional analytical error). For electrolytes having very narrow ranges of values, very large sample sizes usually are necessary. In case of proportional analytical error, application of a weighted approach is important to assure an efficient analysis; e.g., for a range ratio of 10, the weighted approach reduces the requirement of samples by >50%. CONCLUSIONS: Estimation of the necessary sample size for a method comparison study assures a valid result; either no difference is found or the existence of a relevant difference is confirmed.

Clinical Laboratory Techniques↗
PubMed1997

Regression analysis of interval-censored failure time data.

Interval-censored failure time data often occur, for example, in clinical trials or longitudinal studies. For the regression analysis of such data, there have been a number of methods proposed based on continuous regression models such as Cox's proportional hazards model. In practice, however, observed interval-censored data that arise from clinical trials are often given in a discrete scale due to the nature of clinical trials although the underlying variable may be continuous. It is apparent that in this case, one can better handle analysis of the data with the methods based on discrete models. In this paper, I propose a method based on a discrete logistic model for the regression analysis of interval-censored failure time data with focus on the comparison of failure time distributions among different treatments. I discuss the relationship between the proposed method and existing methods.

Clinical Trials as Topic↗
PubMed2000

Semiparametric regression analysis of interval-censored data.

We propose a semiparametric approach to the proportional hazards regression analysis of interval-censored data. An EM algorithm based on an approximate likelihood leads to an M-step that involves maximizing a standard Cox partial likelihood to estimate regression coefficients and then using the Breslow estimator for the unknown baseline hazards. The E-step takes a particularly simple form because all incomplete data appear as linear terms in the complete-data log likelihood. The algorithm of Turnbull (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) is used to determine times at which the hazard can take positive mass. We found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets. In the right-censored survival setting, the approach reduces to the standard Cox proportional hazards analysis, while the algorithm reduces to the one suggested by Clayton and Cuzick (1985, Applied Statistics 34, 148-156). The method is illustrated on data from the breast cancer cosmetics trial, previously analyzed by Finkelstein (1986, Biometrics 42, 845-854) and several subsequent authors.

Algorithms↗
PubMed2004

Understanding data in clinical research: a simple graphical display for plotting data (up to four independent variables) after binary logistic regression analysis.

In clinical research, suitable visualization techniques of data after statistical analysis are crucial for the researches' and physicians' understanding. Common statistical techniques to analyze data in clinical research are logistic regression models. Among these, the application of binary logistic regression analysis (LRA) has greatly increased during past years, due to its diagnostic accuracy and because scientists often want to analyze in a dichotomous way whether some event will occur or not. Such an analysis lacks a suitable, understandable, and widely used graphical display, instead providing an understandable logit function based on a linear model for the natural logarithm of the odds in favor of the occurrence of the dependent variable, Y. By simple exponential transformation, such a logit equation can be transformed into a logistic function, resulting in predicted probabilities for the presence of the dependent variable, P(Y-1/X). This model can be used to generate a simple graphical display for binary LRA. For the case of a single predictor or explanatory (independent) variable, X, a plot can be generated with X represented by the abscissa (i.e., horizontal axis) and P(Y-1/X) represented by the ordinate (i.e., vertical axis). For the case of multiple predictor models, I propose here a relief 3D surface graphic in order to plot up to four independent variables (two continuous and two discrete). By using this technique, any researcher or physician would be able to transform a lesser understandable logit function into a figure easier to grasp, thus leading to a better knowledge and interpretation of data in clinical research. For this, a sophisticated statistical package is not necessary, because the graphical display may be generated by using any 2D or 3D surface plotter.

Biomedical Research↗
PubMed2005

Regression analysis utilizing subjective evaluation of emotional experience in PET studies on emotions.

A methodological study on subject-specific regression analysis (SSRA) exploring the correlation between the neural response and the subjective evaluation of emotional experience in eleven healthy females is presented. The target emotions, i.e., amusement and sadness, were induced using validated film clips, regional cerebral blood flow (rCBF) was measured using positron emission tomography (PET), and the subjective intensity of the emotional experience during the PET scanning was measured using a category ratio (CR-10) scale. Reliability analysis of the rating data indicated that the subjects rated the intensity of their emotional experience fairly consistently on the CR-10 scale (Cronbach alphas 0.70-0.97). A two-phase random-effects analysis was performed to ensure the generalizability and inter-study comparability of the SSRA results. Random-effects SSRAs using Statistical non-Parametric Mapping 99 (SnPM99) showed that rCBF correlated with the self-rated intensity of the emotional experience mainly in the brain regions that were identified in the random-effects subtraction analyses using the same imaging data. Our results give preliminary evidence of a linear association between the neural responses related to amusement and sadness and the self-evaluated intensity of the emotional experience in several regions involved in the emotional response. SSRA utilizing subjective evaluation of emotional experience turned out a feasible and promising method of analysis. It allows versatile exploration of the neurobiology of emotions and the neural correlates of actual and individual emotional experience. Thus, SSRA might be able to catch the idiosyncratic aspects of the emotional response better than traditional subtraction analysis.

Adolescent↗
PubMed1980

The possibilities of regression analysis application for prognosis in surgical oncology.

Regressive computer analysis was used for prognostic evaluation of immediate and long-term results of radical treatment of gastrointestinal cancer of different localization. The data were derived from 1,630 patients with gastric, colonic, and rectal cancer who were radically operated upon at N.N. Petrov Oncological Research Institute, the USSR Ministry of Health. A prognostic formula was suggested and verified for determination of the period of greatest risk of gastric cancer recurrences and metastases. Formulae were also devised for foreseeing the degrees of postoperative risk in patients with gastric, colonic, and rectal cancer.

Colonic Neoplasms↗
PubMed2005

Regression analysis of gait parameters with speed in normal children walking at self-selected speeds.

Dimensionless analysis ensures that differences in sizes (e.g. height and weight) of children have a minimal influence on gait parameters. The results of changes in speed on gait parameters were examined using dimensionless analysis on data from a prospective 5-year study of 16 children. Linear regression analysis of peak and trough values of temporal distance parameters, ground reaction forces, joint angles, moments and powers provide a quantitative description of gait development with normalised speed. These linear relationships can be used to estimate gait parameters from speed measurements for normal subjects. However, caution is advised in using the data to attempt to predict an individual's gait parameters due to the wide spread of data about the regression lines and we do not recommend that the data be used to extrapolate the regression data to wider speed ranges.

Biomechanical Phenomena↗
PubMed1991

[Conditional logistic regression analysis of coronary heart disease].

A case-control study on 215 pairs was carried out in Jinan. Conditional Logistic regression analysis showed that the following five factors were associated with coronary heart disease, i.e., hypertension, hypercholesterolemia and heavy smoking, serum copper and HDL-C/TC. The former three were risk factors, and the latter two were protective factors. There is remarkable dose-response relation between heavy smoking and coronary heart disease. The data analysis show that these five factors are contributory to coronary heart disease with synergism.

Case-Control Studies↗
PubMed2004

Variability of breast cancer risk in observational studies of hormone replacement therapy: a meta-regression analysis.

OBJECTIVES: A re-analysis of data from 51 epidemiological studies reported a significant 14% increase in the risk of breast cancer associated with the use of hormone replacement therapy (HRT). Unlike randomized trials, these observational studies varied in design and methods. This study was conducted to explore the impact of study design factors on the rate ratio. METHODS: We performed a meta-regression analysis of 39 epidemiological studies of HRT and breast cancer. The rate ratio of breast cancer associated with ever use of HRT was evaluated in relation to study design, study period, country, primary study objective, method of exposure measurement, age control, adjustment factors related to reproduction and menopause, and the presence of breast cancer surveillance. We used stepwise multiple regression analysis, weighted by the inverse of the variance of the logarithm of the rate ratio, to estimate ratios of rate ratios for these factors. RESULTS: Exposure measured by personal interview and/or medical record review was associated with a 14% lower rate ratio estimate as compared with telephone interview or self-administered questionnaire (P = 0.018). Among studies that did not adjust for age at menopause, the rate ratio was 12% lower if the primary objective was HRT effect than not (P = 0.016), while it was 43% higher among studies that adjusted for age at menopause (P = 0.042). An index that included as six desirable design features, breast cancer surveillance, matching of controls, more reliable exposure information, adjustment for age at menopause and reproductive risk factors, and as primary objective the effect of HRT suggests that studies with none of these properties would lead to a rate ratio estimate of 1.14 (95% CI: 1.00-1.29) while studies with all six properties would produce a rate ratio of 0.98 (95% CI: 0.83-1.15). CONCLUSIONS: Design factors of epidemiological studies could be an alternative explanation for the reported 14% increase in the risk of breast cancer associated with the use of HRT.

Breast Neoplasms↗
PubMed1985

Residuals in multiple regression analysis.

An examination of residuals can be used as a technique to determine the best model for use in multiple-regression analysis. In addition to R2 and the Fisher F ratio, a complete analysis of residuals has been used by statisticians for many years to estimate bias and to choose the best equation to fit physicochemical as well as biological and psychosociological data. However, residual analysis has seldom appeared in studies in pharmaceutics, pharmacology, or medicinal chemistry. This report gives two examples to show the usefulness of residual analysis in the pharmaceutical sciences.

Aminopyridines↗
PubMed1975

Assessment of biological age by multiple regression analysis.

In order to generate a reference value of aging, estimation of chronological age of healthy subjects was made by multiple regression analysis. It was shown that the estimated ages of hypertensive subjects by the formula used were significantly higher than their chronological ages. It was further observed that parameters representing various ability of movements might yield an alternative regression formula and that the accuracy in age estimation was improved with application of a second-order regression formula.

Accommodation, Ocular↗
PubMed1994

Multiple stepwise regression analysis of physiologic tension and secondary messengers in chronic burn trauma.

In this report, we have used a multiple stepwise regression analysis to determine the best derived multivariate equation between a dependent and multiple independent parameters. All parameters were derived from harvested gastrocnemius muscle subjected to chronic burn trauma. Correlations between seven different parameters were tested. Physiologic tension, calcium, adenosine 3':5' cyclic monophosphate (cAMP), inositol 1,4,5-triphosphate (IP3) and its catabolites comprised one large data matrix. From it, the various parameters were substituted as the dependent variable. The remaining parameters all comprised a multiple independent group. From such a format, the stepwise regression was run. The simultaneous co-governing of independent parameters over one dependent parameter provides a means of mathematically proving multiple correlations. Such findings provide a new perspective in interpreting chemical signalling.

Animals↗
PubMed1989

Generalized likelihood ratio concept and logistic regression analysis for multiple diagnostic categories.

Albert (Clin Chem 1982;28:1113-9) has proposed estimation of likelihood ratios by logistic regression analysis. The usual likelihood-ratio approach for estimation of post-test probability of disease from sensitivity and specificity data of a diagnostic test has been extended by Birkett (J Clin Epidemiol 1988; 41:491-4) for situations with more than two diagnostic categories. We suggest here a combination of these ideas, demonstrating this by a re-evaluation of previously published data on the validity of neopterin as a tool for differential diagnosis between chronic non-A, non-B hepatitis and fatty liver. Analysis of neopterin data in combination with the ratio between serum concentrations of aspartate aminotransferase and of alanine aminotransferase yielded a good discrimination between three mutually exclusive diagnostic categories, namely, fatty liver and chronic persistent and chronic aggressive non-A, non-B hepatitis. The approach is flexibly applicable to situations with different pre-test probabilities. The sum of estimated post-test probabilities deviates slightly from the sum of pre-test probabilities. This deviation is a function of the coefficients obtained in logistic regression, and an analytical expression for the deviation is given. The generalized likelihood-ratio approach appears promising in complex diagnostic situations when multiple diagnostic tests are available.

Alanine Transaminase↗
PubMed1985

[Long-term prognosis of drug and surgery treated patients with acquired aortic valve diseases: survival statistics and multivariate Cox regression analysis].

Data of 417 patients with advanced chronic aortic valve disease were retrospectively analyzed using a life table and Cox regression analysis. Aortic valve replacement was recommended to all patients based on clinical and hemodynamic findings. While most patients underwent prosthetic aortic valve replacement (n = 349), a minority of patients was treated medically (n = 68). Prognosis was better (p less than 0.01 in the Cox model) in surgically treated as compared to medically treated patients with aortic stenosis (4-year survival rate 82 versus 44%). In patients with aortic insufficiency no significant difference of long-term prognosis was found between surgically and medically treated patients.

Anti-Bacterial Agents↗
PubMed2006

Numerical equivalence of imputing scores and weighted estimators in regression analysis with missing covariates.

Imputation, weighting, direct likelihood, and direct Bayesian inference (Rubin, 1976) are important approaches for missing data regression. Many useful semiparametric estimators have been developed for regression analysis of data with missing covariates or outcomes. It has been established that some semiparametric estimators are asymptotically equivalent, but it has not been shown that many are numerically the same. We applied some existing methods to a bladder cancer case-control study and noted that they were the same numerically when the observed covariates and outcomes are categorical. To understand the analytical background of this finding, we further show that when observed covariates and outcomes are categorical, some estimators are not only asymptotically equivalent but also actually numerically identical. That is, although their estimating equations are different, they lead numerically to exactly the same root. This includes a simple weighted estimator, an augmented weighted estimator, and a mean-score estimator. The numerical equivalence may elucidate the relationship between imputing scores and weighted estimation procedures.

Case-Control Studies↗
PubMed2005

Factors influencing outcome after hepatic portoenterostomy for biliary atresia: a logistic regression analysis.

BACKGROUND/OBJECTIVE: The association of many factors with the outcome in Biliary atresia (BA) after hepatic portoenterostomy has drawn the attention of many pediatric hepatologists and hepatobiliary surgeons. Understanding these factors will become an important subject in prediction of the postoperative status and in indicating further proper management. MATERIAL AND METHOD: During the last 9 years, 159 BA babies were treated by hepatic portoenterostomy. The authors reviewed the following factors and how they related to outcome: age at operation, total bilirubin (TB) level, type of BA, postoperative bile drainage, hepatic histological features at operation, preoperative and postoperative cholangitis. A multiple logistic regression analysis was used to indicate the factors which significantly influenced the outcome. RESULTS: Of the 159 BA babies, clearing of jaundice confirmed by the color of stool and postoperative serum bilirubin level less than 2 mg % was observed in 54 patients (Group A). Bile drainage with mild jaundice (TB 2-5 mg %) was detected in 65 patients (Group B). The operation failed to create bile flow clinically and biochemically in 40 patients (Group C). Some patients in the last group died during follow-up due to hepatic disease. The multiple logistic regression analysis revealed that the age at operation (> 8 weeks of age), and the presence of portal and parenchymal inflammation at operation significantly related to the failure of portoenterostomy which was followed by portal hypertension with or without esophageal varices. The presence of cholangitis was also significantly related to a poor outcome. CONCLUSION: The age at operation, portal and parenchymal inflammation and the presence of cholangitis are significant factors which relate to the poor prognosis of BA. Recognition of these will lead to proper long-term management.

Age Factors↗