Data evaluation using biostatistics by different methods and statistical formulas

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Application of Biostatistics in Experimental Pharmacology:

Application of Biostatistics in Experimental Pharmacology By D.Eswar Tony M.Pharm (Pharmacology) Chalapathi Institute of Pharmaceutical Sciences(CIPS) Guntur 1

Introduction to Biostatistics:

Introduction to Biostatistics It is the branch of statistics that deals with data relating to living organisms. A Biostatistician would be involved with carrying out research, devising experiments, and providing an in depth analysis of all results. This is a great opportunity to make a difference because by carrying out this crucial research, a Biostatistician can make a difference to health care and public health. 2

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In experimental pharmacology we have to understand when to use and how to calculate and interpret different measures of central tendency (mean, median and mode) and dispersion (range, IR and standard deviation) We have to identify the types of error encountered in statistical analysis, the role of sample size and implications for decision making. Describe basic assumptions required for utilization of common statistical tests including the student’s t-test, Paired t-test, chi square analysis, wilcoxon signed rank etc 3

Types of Data:

Types of Data Nominal Sex Risk factors Ordinal Sorted by categories often with numbers denoting a rank order. Interval & Ratio Data Body temperature Body weight 4

Descriptive Vs Inferential statistics :

Descriptive Vs Inferential statistics Descriptive statistics are concerned with the presentation, organisation and summarization of data. Inferential statistics are used to generalize data from sample to a larger group of patients. 5

Frequency Distribution:

Frequency Distribution Data can be organised and presented in such a way that allows an investigator to get a visual perspective of the data. Mode Median Mean negative skew 6

Distribution of Course Grades:

Distribution of Course Grades 7

Mean,Median,Mode:

Mean,Median,Mode Mean can be defined by summation of all values divided by the number of subjects in the sample. This can be given by equation: Median is the value where half of the data points fall above and half below it. If we added one more value, the median would be calculated by taking the two middle numbers and dividing by two. Mode is the most frequently occuring number in the data set. 8

Measures of Dispersion:

Measures of Dispersion Range Interquartile range Standard deviation The range is defined as the difference between the highest and lowest values. The IR is defined as the difference between the lower quartile and upper quartile. The formula for IR is Q 3 -Q 1 9

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The SD is defined as the index of the degree of variability of study data about the mean. 10

Standard deviation:

Standard deviation Curve A Curve B 11

Hypothesis testing & Meaning of P:

Hypothesis testing & Meaning of P A Hypothesis is an unproved theory. The null hypothesis is defined as the theory that no difference exists between study groups. If a study were to compare two means, the null hypothesis (H o )=µ A =µ B Probability deals with the relative likelyhood that a certain event will occur or will not occur. The probability will always in between 0 and 1. In general the p value should not exceed 0.05 for the null hypothesis. 12

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If the change can be either in direction, µ A is not equal to µ B, a two tailed and one tailed tests are carried out. In a two-tailed test the rejection region is equally divided between the two ends of the sampling distribution. One tailed test is a test of hypothesis in which the rejection region is entirely placed at one end of the sampling distribution. The two tailed test is more conservative and thus preffered in most circunstances . 13

Statistical Tests:

Statistical Tests Student’s t-Test (paired or independent) Wilcoxon Mann-Whitney rank sum test Wilcoxon signed rank test Contingency tables (Chi-square tests) 14

Student’s t-Test :

Student’s t-Test Two types Independent Paired X and Y are the two populations. The bar above it means sample mean. The n 1 and n 2 are the sample sizes. Sp = pooled standard deviation 15

Unequal or different variances:

Unequal or different variances Welch Test Same assumptions as previous test (independence, normality) except, unequal variance Same hypotheses are used Compare to previous equal var. formula Used for data of very different sizes (Relative definition) 16

Paired Student’s t-Test:

Paired Student’s t-Test “paired t-test I used to compare the means of two populations” when the data is paired: Before-and-after Same individual is observed twice 17

Summary (t-tests):

Summary (t-tests) T-test Unpaired Paired Equal Variance Unequal Variance Paired subjects (variance may or may not differ) Paired t-Test Unpaired t-test Welch Test 18

Non-Parametric:

Non-Parametric Paired vs. Unpaired Types: Wilcoxon Mann-Whitney Rank Sum Test Wilcoxon signed rank test 19

Wilcoxon Mann-Whitney Rank Sum Test:

Wilcoxon Mann-Whitney Rank Sum Test T-statistic applied to the ranks, not data Intended for not-normal (non-parametric), but independent Hypothesis H 0 – “the two populations being compared have identical distributions” H A – “populations differ in location i.e. (median)” 20

Wilcoxon Mann-Whitney Rank Sum Test (continued, example):

Wilcoxon Mann-Whitney Rank Sum Test (continued, example) Fastest - T H H H H H T T T T T H – Slowest Consider a race between 6 Hares and 6 Tortoisses. From the perspective of the Toirtoises, there is one that beats 6 hares, but the second, third, fourth, and fifth beat only one hair. The U value in this case = 6+1+1+1+1+1 = 11. WMW Rank Sum Test – solely concerns the relative positions/value, not the exact ones. 21

Contingency Tables:

Contingency Tables Categorical variables Cross-classification Set up table 22

The X2 Test:

The X 2 Test Perform in this case Take row totals 23

McNemar’s Test:

McNemar’s Test Categorical data from paired observations “…cases matched with controls on variables such as sex, age, and so on, or observations made on the same subjects on two occasions. Hypothesis H 0 : populations do not differ 24

McNemar’s Test :

McNemar’s Test a + b = a +c and c + d = d + b X 2 = 25

Overall Summary of Tests:

Overall Summary of Tests data Quantitative Ordinal or Nominal X 2 Test t-test (perhaps) Independent Independent Paired Paired McNemar’s X 2 Test Pearson X 2 Test Equal Variance Unequal Variance Variance doesn’t matter Unpaired t-test Welch (modified t-) test Paired t-test 26

Analysis of Variance (ANOVA) Is a technique whereby the total variation present in a data set is partitioned or segregated into several components :

Analysis of Variance (ANOVA) Is a technique whereby the total variation present in a data set is partitioned or segregated into several components 27

For example, if four drug levels with their six possible combinations are to be compared, and each comparison is made by using Alpha = .05, -there is a 5% chance that each comparison will falsely be called significant; :

For example, if four drug levels with their six possible combinations are to be compared, and each comparison is made by using Alpha = .05, -there is a 5% chance that each comparison will falsely be called significant; 28

PowerPoint Presentation:

So the recommended use of ANOVA protects the researcher against error inflation by first asking if there are differences at all among means of the groups . Some basic concepts in experimental designs are the minimum requirements to appreciate the approach of ANOVA in estimating and testing the hypotheses about - population means or about - population variances. 29

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It may be pointed out that when experiments are designed with the analysis in mind,researchers can, before conducting experiments, identify those sources of variation that they consider important and choose a design that will allow them to measure the extent of the contribution of these sources to total variation. 30

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The Completely Randomized Design (CRD) are used in Pharmacological experimentations, requiring the application of - One-way and - Two-way Analyses of Variance, respectively . 31

Conclusion:

Conclusion In Every case of our life statistics plays a major role for better gaining and accurate results. Mainly comparison is important now-a-days for better output and this was achieved by a good evaluation using different statistical methods. A Biostatistician have to be well aware of all these methods and able to apply when different results were generated. 32

References:

References Guyatt G, jaeschke R, Heddle N, Cook D, Shannon H, Walter S, Hypothesis testing. CMAJ 1995;152:27-32. Gaddis GM, Gaddis ML. Introduction to biostatistics : part 5 statistical inference techniques for hypothesis testing with non parametric data. Ann Emerg Med 1990;19:153-8. De Muth JE. Basic statistics and pharmaceutical statistical applications. New york : Mark Dekker Inc., 1999:115-48 33

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