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Regression is an analysis tool used in much of the research we read, and the terminology can be daunting. In reality, bivariate regression analysis is simply an extension of correlational analysis. This article was written to help the reader understand bivariate regression analysis.
Regression techniques that appropriately use all available eyes have infrequently been applied in the ophthalmologic literature, despite advances both in the development of statistical models and in the availability of computer software to fit these models. We considered the general linear model and polychotomous logistic regression approaches of Rosner and the estimating equation approach of Liang and Zeger, applied to both linear and logistic regression. Methods were illustrated with the use of two real data sets: (1) impairment of visual acuity in patients with retinitis pigmentosa and (2) overall visual field impairment in elderly patients evaluated for glaucoma. We discuss the interpretation of coefficients from these models and the advantages of these approaches compared with alternative approaches, such as treating individuals rather than eyes as the unit of analysis, separate regression analyses of right and left eyes, or utilization of ordinary regression techniques without accounting for the correlation between fellow eyes. Specific advantages include enhanced statistical power, more interpretable regression coefficients, greater precision of estimation, and less sensitivity to missing data for some eyes. We concluded that these models should be used more frequently in ophthalmologic research, and we provide guidelines for choosing between alternative models.
Three algorithms for assessment of respiratory sinus arrhythmia (RSA) have been evaluated: cross-correlation function, histogram analysis and regression plot. The algorithms were tested experimentally in a group of 11 subjects. A cross-correlation function with a high time resolution (1 ms) was used for investigation of the time lag between instantaneous heart rate and respiration (CTL). This time lag was not affected by the breathing rate in a range of 8 to 29 breaths per minute. A mathematical model of CTL compared with experimental results indicates that respiratory sinus arrhythmia is probably modulated directly by the respiratory network in the brainstem rather than by a baroreflex in the range of breathing rate investigated. Histogram analysis reflects the impact of inspiration and expiration on respiratory sinus arrhythmia. For this purpose heart rate changes were separated into two distributions (inspiration-expiration). The result value (U-VAL) of the Mann-Whitney U-test reflects the impact of respiration on heart rate variability. Regression analysis of heart rate versus respiration shows that the heart rate increase is more closely coupled to inspiration than the heart rate decrease to expiration. Both, CTL and U-VAL are thought to be useful parameters for clinical investigation of RSA.
PURPOSE: To clarify the pathologic stages of adenocarcinoma of the gastric cardia in which the prognosis is worse than in adenocarcinoma of the middle or distal part of the stomach, and to determine prognostic factors in these stages by multivariate analysis. PATIENTS AND METHODS: We analyzed 2,536 cases of surgically resected gastric adenocarcinoma of all pathologic stages. Four hundred seventy-two cases of gastric carcinoma, in which cumulative survival of gastric cardia was poor, were subjected to Cox regression analysis for prognostic factors, and to logistic regression analysis for factors influencing venous or lymphatic invasion. RESULTS: The prognosis of adenocarcinoma of the gastric cardia was inferior when compared with similarly staged carcinomas of the middle or lower part of the stomach when there was invasion of proper muscle layer or subserosal layer, with no lymph node metastasis or with only adjacent (group 1) lymph nodes metastases (T2N0 or T2N1, according to the Japanese classification). In these stages, the prognostic factors were age, histologic type, venous invasion, and location of the tumor in the upper part of the stomach. Tumor location in the upper stomach was also a predictor for the presence of venous invasion. CONCLUSION: The prognosis of adenocarcinoma of the gastric cardia is poor in patients with T2 tumors with no or few lymph node metastases. Additional treatment after surgery may be necessary to improve the survival of this population.
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BACKGROUND: Regression calibration as a method for handling measurement error is becoming increasingly well-known and used in epidemiologic research. However, the standard version of the method is not appropriate for exposure analyzed on a categorical (e.g. quintile) scale, an approach commonly used in epidemiologic studies. A tempting solution could then be to use the predicted continuous exposure obtained through the regression calibration method and treat it as an approximation to the true exposure, that is, include the categorized calibrated exposure in the main regression analysis. METHODS: We use semi-analytical calculations and simulations to evaluate the performance of the proposed approach compared to the naive approach of not correcting for measurement error, in situations where analyses are performed on quintile scale and when incorporating the original scale into the categorical variables, respectively. We also present analyses of real data, containing measures of folate intake and depression, from the Norwegian Women and Cancer study (NOWAC). RESULTS: In cases where extra information is available through replicated measurements and not validation data, regression calibration does not maintain important qualities of the true exposure distribution, thus estimates of variance and percentiles can be severely biased. We show that the outlined approach maintains much, in some cases all, of the misclassification found in the observed exposure. For that reason, regression analysis with the corrected variable included on a categorical scale is still biased. In some cases the corrected estimates are analytically equal to those obtained by the naive approach. Regression calibration is however vastly superior to the naive method when applying the medians of each category in the analysis. CONCLUSION: Regression calibration in its most well-known form is not appropriate for measurement error correction when the exposure is analyzed on a percentile scale. Relating back to the original scale of the exposure solves the problem. The conclusion regards all regression models.
Logistic regression analysis was used to investigate the dose-response relationship for environmental cadmium exposure and to consider the effect age had on this association. The target population comprised 3178 inhabitants of Japan who were more than 50 y of age and who lived in a cadmium-polluted area and 1134 inhabitants who lived in nonpolluted areas of Japan. Logistic regression analysis was completed on the dose-response relationship between urinary cadmium concentration (i.e., an indicator of cadmium body burden) and beta2-microglobulinuria (i.e., an index of renal tubular dysfunction caused by exposure to cadmium). Both age and urinary cadmium concentration were associated significantly with beta2-microglobulinuria. Based on the relationship that was determined, we calculated, by age and sex, the values of urinary cadmium concentration that corresponded to the prevalence rates of beta2-microglobulinuria in the nonpolluted population. The resulting values were 1.6-3.0 micrograms/g creatinine for men and 2.3-4.6 micrograms/g creatinine for women.
In this study, the surface properties of and work required to remove 12 commercially available and developmental catheters from a model biological medium (agar), a measure of catheter lubricity, were characterised and the relationships between these properties were examined using multiple regression and correlation analysis. The work required for removal of catheter sections (7 cm) from a model biological medium (1% w/w agar) were examined using tensile analysis. The water wettability of the catheters were characterised using dynamic contact angle analysis, whereas surface roughness was determined using atomic force microscopy. Significant differences in the ease of removal were observed between the various catheters, with the silicone-based materials generally exhibiting the greatest ease of removal. Similarly, the catheters exhibited a range of advancing and receding contact angles that were dependent on the chemical nature of each catheter. Finally, whilst the microrugosities of the various catheters differed, no specific relationship to the chemical nature of the biomaterial was apparent. Using multiple regression analysis, the relationship between ease of removal, receding contact angle and surface roughness was defined as: Work done (N mm)=17.18+0.055 Rugosity (nm)-0.52 Receding contact angle ( degrees ) (r=0.49). Interestingly, whilst the relationship between ease of removal and surface roughness was significant (r=0.48, p=0.0005), in which catheter lubricity increased as the surface roughness decreased, this was not the case with the relationship between ease of removal and receding contact angle (r=-0.18, p>0.05). This study has therefore uniquely defined the contributions of each of these surface properties to catheter lubricity. Accordingly, in the design of urethral catheters, it is recommended that due consideration should be directed towards biomaterial surface roughness to ensure maximal ease of catheter removal. Furthermore, using the method described in this study, differences in the lubricity of the various catheters were observed that may be apparent in their clinical use.
Multiple regression is widely employed to study the contribution of components to the toxicologic effect of a mixture. Here, use is made of the fact that data obtained from standard curves of substances and from their mixtures are separable in regression analysis. Thus, under an assumption of additivity of responses, regression coefficients obtained for components in mixtures alone should be the same as for the individual substances. A t-test is developed such that nonsignificant t values support additivity, negative significant values support antagonism, and positive significant values support synergism. The results are applied to data on the mutagenicity of binary mixtures of azaserine, 4-nitroquinoline N-oxide, and 9-aminoacridine in TA 100 in the Ames assay.
Multiple regression is an analysis tool used much more frequently than bivariate regression analysis in the research we are reading. This article is designed to help the reader understand multiple regression analysis and confidence intervals.
PURPOSE: A growing body of literature suggests that statins may have chemopreventive potential against cancer. Our aim was to examine the strength of this association through a detailed meta-analysis and meta-regression analysis of randomized controlled trials (RCTs). METHODS: A comprehensive search for trials published up to 2005 was performed, reviews of each study were conducted, and data were abstracted. Before meta-analysis, the studies were evaluated for publication bias and heterogeneity. Pooled relative risk (RR) estimates and 95% CIs were calculated using the random- and fixed-effects models. Subgroup, sensitivity, and meta-regression analyses were also conducted. RESULTS: Thirty-five RCTs of statins for cardiovascular outcomes contributed to the analysis (n = 109,143). The degree of variability between trials was consistent with what would be expected to occur by chance alone. Statin use was not associated with a substantially increased or decreased overall risk of cancer (RR = 0.99; 95% CI, 0.94 to 1.04). Similarly, statin use did not significantly affect respiratory cancer risk (RR = 0.95; 95% CI, 0.83 to 1.09). However, the meta-regression analysis indicated that age of study participants modified the association between statin use and cancer risk (P = .003). CONCLUSION: Our findings do not support a protective effect of statins against cancer. However, this conclusion is limited by the relatively short follow-up periods (4.5 years on average) of the studies analyzed. Thus, it is important to continue monitoring the long-term safety profiles of statins. Until then, physicians need to be vigilant in ensuring that statin use remains restricted to the approved indications.
Multiple regression analysis in 1493 cases (1256 male cases, 237 female cases) who were examined in the short-term human dry dock managed by the Fukuoka University Hospital, was done with gamma-GTP as the dependent variable and other parameters as the independent variables. As the result, 16 variables including LAP, alcohol, GPT, triglyceride, HDL and obesity rate were selected as the variables explaining gamma-GTP by stepwise methods in men. The standard regression coefficient of alcohol is shown to be greater than that of obesity on gamma-GTP. On the contrary, neither alcohol nor the obesity rate was included in this regression formula in women.
A multiple regression analysis, which allows a simultaneous introduction of smoothing, was adopted for a numerical deconvolution process to obtain the transport function from a pair of indicator dilution curves. This process solves concurrently restricting linear quadratic or cubic equations that are fitted to small sections of the transport function curve, an equation that forces the tail part to zero, and uses conditions that restrict the area under the transport function to unity. Each restricting linear equation can be manually stressed by adjusting its corresponding weight iteratively so that unreasonable oscillations emerging on any particular portion of the transport function curve can be suppressed. Stability of the method was tested with various pairs of dilution curves in terms of mathematical models and with those experimentally obtained from the dog portal circulation. The deconvolution by means of the regression analysis with simultaneous smoothing was shown to be far less sensitive to observational errors in the dilution curves or sampling rates than that by means of the direct method without the regression analysis. Multiple regression analysis with simultaneous smoothing was also applied to the deconvolution process using the multiple fitting functions developed by Knopp et al. (Ann. Biomed. Eng. 4: 44-59, 1976). This process was shown to perform a stable deconvolution as well.
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We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.
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