Ebook A handbook of applied statistics in pharmacology: Part 1

(BQ) Part 1 book A handbook of applied statistics in pharmacology presents the following contents: Probability, distribution; mean, mode, median; variance, standard deviation, standard error, coefficient of variation; analysis of normality and homogeneity of variance; transformation of data and outliers; tests for significant differences,...

A Handbook of Applied Statistics in Pharmacology Median Lower Hinge Upper Hinge Whisker Whisker Hinge Spread A SCIENCE PUBL PUBLISHERS UBLIISHERS BOOK 130 135 140 145 150 155 160 165 170 A Handbook of Applied Statistics in Pharmacology A Handbook of Applied Statistics in Pharmacology Katsumi Kobayashi Safety Assessment Division, Chemical Management Center National Institute of Technology and Evaluation (NITE) Tokyo, Japan K Sadasivan Pillai Frontier Life Science Services (A Unit of Frontier Lifeline Hospitals) Thiruvallur District Chennai, India p, A SCIENCE PUBLISHERS BOOK CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 2012919 International Standard Book Number-13: 978-1-4665-1540-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Foreword Life expectancy has signi¿cantly increased in the last century, thanks to the discovery and development of new drugs by pharmaceutical industries Search for new therapeutics is the primary activity of the R&D of pharmaceutical industries and it involves complex network of tasks such as synthetic chemistry, in vitro/in vivo ef¿cacy, safety, preclinical and clinical research Statistical analysis has always been the foundation to establish the safety and ef¿cacy of drugs The decision to- or not to- advance preclinical drug candidates to very expensive clinical development heavily relies on statistical analysis and the resulting signi¿cance of preclinical data Recent reports attributed failure of certain drugs in clinical stages of development to improper conduct of preclinical studies and inappropriate application of statistical tools Applying appropriate statistical tools is sagacious to analysis of data from any research activity Though scientists expect computerized statistical packages to perform analyses of the data, he/she should be familiar with the underlying principles to choose the appropriate statistical tool ‘A Handbook of Applied Statistics in Pharmacology’ by Katsumi Kobayashi and K Sadasivan Pillai is a very useful book for scientists working in R&D of pharmaceuticals and contract research organizations Most of the routine statistical tools used in pharmacology and toxicology are covered perspicuously in the book The examples worked out in the book are from actual studies, hence not push a reader having less or no exposure to statistics outside his/her comfort zone Dr K.M Cherian M.S., F.R.A.C.S., Ph.D., D.Sc (Hon.), D.Sc (CHC), D.Sc (HC) Chairman & CEO Frontier Lifeline Hospitals Chennai, India Preface Scientists involved in pharmacology have always felt that statistics is a dif¿cult subject to tackle Thus they heavily rely on statisticians to analyse their experimental data No doubt, statisticians with some scienti¿c knowledge can analyse the data, but their interpretation of results often perplexes the scientists Statistics play an important role in pharmacology and related subjects like, toxicology, and drug discovery and development Improper statistical tool selection to analyze the data obtained from studies conducted in these subjects may result in erroneous interpretation of the performanceor safety- of drugs There have been several incidents in pharmaceutical industries, where failure of drugs in clinical trials is attributed to improper statistical analysis of the preclinical data In pharmaceutical Research & Development settings, where a large number of new drug entities are subjected to high-throughput in vitro and in vivo studies, use of appropriate statistical tools is quintessential It is not prudent for the research scientists to totally depend on statisticians to interpret the ¿ndings of their hard work Factually, scientists with basic statistical knowledge and understanding of the underlying principles of statistical tools selected for analysing the data have an advantage over others, who shy away from statistics Underlying principle of a statistical tool does not mean that one should learn all complicated mathematical jargons Here, the underlying principle means only ‘thinking logically’ or applying ‘common sense’ The authors of this book, with decades of experience in contract research organizations and pharmaceutical industries, are fully cognizant of the extent of literacy in statistics that the research scientists working in pharmacology, toxicology, and drug discovery and development would be interested to learn This book is written with an objective to communicate statistical tools in simple language Utmost care has been taken to avoid complicated mathematical equations, which the readers may ¿nd dif¿cult viii A Handbook of Applied Statistics in Pharmacology to assimilate The examples used in the book are similar to those that the scientists encounter regularly in their research The authors have provided cognitive clues for selection of an appropriate statistical tool to analyse the data obtained from the studies and also how to interpret the result of the statistical analysis Contents Foreword Preface v vii Probability Probability and Possibility Probability—Examples Probability Distribution Cumulative Probability Probability and Randomization 1 3 Distribution History Variable Stem-and-Leaf Plot Box-and-Whisker Plot 6 Mean, Mode, Median Average and Mean Mean Geometric Mean Harmonic Mean Weighted Mean Mode Median 11 11 11 12 12 13 13 14 Variance, Standard Deviation, Standard Error, Coef¿cient of Variation Variance Standard Deviation (SD) Standard Error (SE) Coef¿cient of Variation (CV) When to Use a Standard Deviation (SD)/Standard Error (SE)? 16 16 18 19 19 20 y  y =D =E =F Regression Analysis b1 = CD  BE AC  B b2 = AE  BD AC  B 81 Once the slopes are derived, a can be calculated using the formula: y = a + b1 x1+ b2 x Multiple correlation coef¿cient can be computed using the formula: R= 6yy ' ¦ y y '2 , where R = Multiple correlation coef¿cient; y = Actual value; y’= Predicted y (calculated using the regression equation, y = a + b1 x 1+ b2 x 2; ê Ư y u Ư y' ằ 6yy ' = ôƯ yy '  n ẳ Ư y =Ư y 2  (¦ y ) n ; ¦ y' ¦ y'  (¦ y ' ) n Signi¿cance of the multiple regression equation can be checked by ANOVA (Table 10.5) Polynomial Regression Linear regression does not hold good, when the data of your dependent variable follows a curved line, rather than a straight line Transforming the y or x or both the variables to their logarithms, reciprocals, square roots etc., may straighten certain curves, but not all Another way to solve this issue is to use a curvilinear regression equation Polynomial regression equation is an example of curvilinear regression equation, which is used to predict toxicological variables (Vogt, 1989) Given the complexity of the calculations in polynomial regression analysis, it is not being included in the coverage of this book The purpose of touching upon polynomial 82 A Handbook of Applied Statistics in Pharmacology Table 10.5 Signi¿cance of multiple regression equation by ANOVA Source of variation Total SS for Y Degrees of freedom n–1 Reduction due to regression (Residual SS) k Error n–k–1 SS ¦y ¦ y' 2 Mean SS  (¦ y )  (¦ y ' ) - n ¦ Y '2  n ê Ư y u Ư y ' ằ ô Ư yy '  n ẳ (Ư Y ' ) n /k ê Ư y u ¦ y ' º» « ¦ yy '  n ¬ ¼ /n–k–1 k is the number of independent variables F value is calculated by dividing Reduction due to regression (Residual SS) with error regression analysis, is to create awareness that before carrying out linear regression analysis one should ensure that the trend of the association between the two variables is linear Misuse of Regression Analysis Use of a regression equation is considered to be inappropriate for estimating an independent variable, rather than a dependent variable (Williams, 1983) It is important to understand the nature of the data before choosing a regression model This can be easily done by plotting the data, which will help understanding the nature of the data and selecting appropriate regression model One should not ¿t a straight line using a linear regression equation for a ‘nonlinear data’ References Ambrosius, W.T (2007): Topics in Biostatistics Humana Press Inc., New Jersey, USA Bailey, N.T.J (1995): Statistical Methods in Biology Cambridge University Press, Cambridge, UK Chan, Y.H (2004): Biostatistics 201: Linear regression analysis Singapore Med J., 45 (2), 55–61 Cornbleet, P.J and Gochman, N (1979): Incorrect least-squares regression coef¿cients in method-comparison analysis Clin Chem., 25, 432–438 Crow, J.F (1993): Francis Galton: Count and measure, measure and count Genetics, 135, 1–4 DuPont, W.D (2002): Statistical Modeling for Biomedical Researchers Cambridge Univ Press, Cambridge, U.K Regression Analysis 83 Farnsworth, D.L (1990): The effect of a single point on correlation and slope Internat J Math Math Sci., 13(4), 799–806 Glaister, P (2005): Robust linear regression using Theil’s method J Chem Educ., 82(10), 1472–1473 Vittinghoff, E., Glidden, D.N., Shiboski, S.C and McCulloch, C.E (2005): Statistics for Biology and Health Springer Science+Business Media, Inc., New York, USA Vogt, N.B (1989): Polynomial principal component regression: An approach to analysis and interpretation of complex mixture relationships in multivariate environmental data Chemometrics Intelligent Lab Systems, 7(1-2), 119–130 Williams, G.P (1983): Improper use of regression equations in earth sciences Geology, 11(4), 195–197 Yoshimura, I (1987): Statistical Analysis of Toxicological Data Scientist Inc., Tokyo, Japan 11 Multivariate Analysis Analysis of More than Two Groups Student’s t-test is used to test the equality of the means from two different populations (Rothmann, 2005) Use of Student’s t-test for comparing more than two groups can cause Type I error This can be better understood from the example below: Absolute weight of the liver of female mice in a 13-week repeated dose administration study is given in Table 11.1 Table 11.1 Liver weight (g) of female mice in a 13-week repeated dose administration study Group N Mean ± SD Tukey’s multiple range test A B C A 10 1.083±0.057 B 10 1.098±0.077 NS C 10 1.154±0.050 NS NS D 10 1.273±0.062 S S S NS—Not signi¿cant; S—Signi¿cant (P