Data Analysis in Clinical Trials. Dr. Abha Aggarwal Deputy Director National Institute of Medical Statistics Ansari Nagar, New Delhi

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1 Data Analysis in Clinical Trials Dr. Abha Aggarwal Deputy Director National Institute of Medical Statistics Ansari Nagar, New Delhi

2 Introduction In clinical research we want the results of a trial to be accurate and reliable in order to provide a valid and unbiased assessment of true efficacy and safety of the study medication. The accuracy and reliability are usually referred to the the closeness of the results. The degree of closeness of results to the true value of patient population is termed as reliability.

3 Statistical Considerations at Planning Stage Protocol Designing Sample Size Interim Analysis and Data Monitoring Statistical and Clinical Inference Efficacy and safety assessment Statistical Data Analysis

4 DATA ANALYSIS CONSIDERATION Prespecification of the Analysis Analysis set Full Analysis Set Per Protocol Set Role of Different Analyses Set Missing Values and Outliers Data Transformation Estimation, Confidence Interval and Hypothesis Testing Adjustment of Significance and confidence Levels Subgroup Interactions and Covariates Integrity of Data and Computer Software Validity

5 Type of Data Three types of data commonly occur in clinical trials. 1. Dichotomous outcome- 0/1 values, success/failure, yes/no, dead/alive. 2. Continuous outcomes- measurements with a whole range of possibilities: wt., BP counts etc. 3. Normally Distributed Data A characteristic property of the Normal distribution is that 68% of all of its observations fall within a range of ±1 standard deviation from the mean, and a range of ±2 standard deviations includes 95% of the scores

6 Data Analysis in Clinical Trials Descriptive Statistics Inferential Statistics Descriptive methods include preparation of statistical tables, drawing diagrams & graphs and computation of statistical parameters such as percentages, average, variation and correlation & regression coefficients. Inference methods include computing confidence intervals for the estimates of parameters and various tests of statistical significance, depending upon the type of variable and the number of groups involved in the trial

7 Estimation One of the main purpose of a clinical trial is to estimate the magnitude of improvement with one treatment over the other-in terms of percentages / mean values. There are two types of estimation -Point estimate (mean, percentage) and Interval Estimate - Confidence limits

8 Confidence Limits for Proportion (p1 - p2 ):±1.96 Sqrt (A) where A = [ { p (100 - p) x {( 1/n1) + (1/n2) }}] Where p is the overall percentage of improvement in the combined groups. A= Sqrt [ (70x30)x(2/100)] A= Sqrt (42) ie; A=6.48. ie; 95% confidence Limits for the population treatment difference are 20±: 12.7 ie; 7.3 % and 32.7 %

9 P< 0.01 P-value Interpretation very strong evidence against H0 0.01<= P < 0.05 moderate evidence against H0 0.05<= P < 0.10 suggestive evidence against H0 0.10<= P little or no real evidence against H0

10 Hypotheses testing and p value Hypothesis is an assumption or statement that is made about the population regarding the efficacy safety and other outcomes of a drug. In clinical trial any scientific question is translated into hypotheses. Example; Drug A is more effective than drug B P value- is the probability that the observed results is extreme or not under the null hypotheses. We generalized the results of clinical trial.

11 STATISTICAL SIGNIFICANCE TESTS The second most important aim in a clinical trial is to see whether the observed differences in the response variable between the various treatment groups are statistically significant or not. ie; whether the difference observed is really due to the additional effect of the new drug compared to that of the standard drug or it is just due to chance ( random variation due to sampling).this is achieved by applying appropriate statistical test of significance. If the response variable is discrete, the test to be applied is Chi-square and if it is continuous, the test is Student's' t ' test / Analysis of variance or an appropriate Non- Parametric test

12 Chi-Square (²)tests Eg. Improvement rate with the Standard drug ( SD) = 60 % nl = 50 Improvement rate with the New drug ( ND ) = 80 % n2 = 50 Drug Improvement Yes No Standard New ² = 3.85, with 1 degree of fteedom (> 3.84 with 95 % confidence) ie; The difference observed in the improvement rate is not by chance and it is because of the additional effect of the new drug over the standard one. The same test can be applied in case of more than two treatments also. In case of a Cross-over / Matched Trial, the corresponding test is McNemar's' ²

13 Comparison of two groups For comparison of two groups t test is applied if the groups are independents For paired observations paired t test is applied ANOVA For more than two groups.

14 Non Parametric Test The Non- Parametric test corresponding to Student's t test ( for independent samples) is -Wilcoxon's Rank Sum Test and to One-Way Analysis of Variance is KruskalWally's One-Way Analysis of Variance.