To the Editor:—

We read with great interest the article by Kazama et al.  1They clarified the relationship between initial blood distribution volume and propofol induction dose using continuous infusion during the induction of anesthesia. The results are consistent with those of our study, 2and the study protocols differed in only two parameters: the infusion rate, and its basis. Kazama et al.  administered propofol at 40 mg · kg−1· h−1as a function of lean body mass (LBM), whereas we administered it at 15 mg · kg−1· h−1as a function of total body weight. Using multiple linear regression analysis, Kazama et al.  report that the induction dose can be determined from four variables, age, LBM, central blood volume (CBV), and hepatic blood flow (HBF), whereas we selected age, body weight, cardiac output (CO), and the plasma disappearance rate of indocyanine green (k) as our variables.

Multiple linear regression analysis in the study of physiologic systems provides a powerful statistical tool for sorting out the relationships among several variables in such experiments. However, there are many potential pitfalls when using regression analysis, including multicollinearity, which can lead to numerical problems in estimating the parameters in regression equations. 3Ideally, all selected predictive variables must be uncorrelated. When multiple regression analysis was applied to our results using the variables of Kazama et al. , 1age, LBM, CO, BV, and HBF were identified as significant factors for predicting the induction dose of propofol (P < 0.01, table 1). However, our statistical analysis (NCSS2000, Kaysville, UT) detected possible multicollinearity among the selected predictive variables.

Table 1. Coefficients Entered in Multiple Linear Regression Model for Patient Baseline Variables and Propofol Induction Dose at the Rate of 15 mg · kg−1· h−1

* Not selected as a predictor variable in the multiple linear regression model using the variables of Kazama et al.  1

+P < 0.0001.

LBM = lean body mass; SE = standard error; M = male; F = female. In our results, age did not demonstrate any correlation with BV or CBV, consistent with Kazama et al. , whereas age showed marked correlation with HBF, and CBV was significantly correlated with LBM and BV. Age has been reported as a predictive variable for HBF. 4Normalization of accurate BV measurement using LBM has been recommended in a clinical setting, 5because LBM is an absolute predictive factor for CBV. These relationships might become sources of multicollinearity, and ordinary least squares multiple linear regression can give nonsensical results for the estimated parameter magnitude, sign, or standard error. Hepatic blood flow is a cross-product of BV and clearance slope (K−1); thus, it might become another source of artificial multicollinearity.

The results of Kazama et al.  clearly demonstrate the predictive variables for propofol induction dose. Age and other circulatory variables play an important role in determining the dose, which is consistent with our results. The interpretation of the results using multiple regression analysis (including our study), however, might leave room for attention and discretion. Although multicollinearity can be avoided with good experimental design, not all interesting questions can be studied without encountering multicollinearity.

## References

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Kazama T, Ikeda K, Morita K, Ikeda T, Kikura M, Sato S: Relation between initial blood distribution volume and propofol induction dose requirement. A nesthesiology 2001; 94: 205–10
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Adachi YU, Watanabe K, Higuchi H, Satoh T: The determinants of propofol induction of anesthesia dose. Anesth Analg 2001; 92: 656–61
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Slinker BK, Glantz SA: Multiple regression for physiological data analysis: The problem of multicollinearity. Am J Physiol 1985; 249: R1–12
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Zoli M, Magalotti D, Bianchi G, Gueli C, Orlandini C, Grimaldi M, Marchesini G: Total and functional hepatic blood flow decrease in parallel with ageing. Age Ageing 1999; 28: 29–33
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Wright RR, Tono M, Pollycove M: Blood volume. Semin Nucl Med 1975; 5: 63–78