The purpose and fundamentals of statistics

European Patients Academy on Therapeutic Innovation The Purpose and Fundamentals of Statistics in Clinical Trials The purpose and fundamentals of statistics European Patients Academy on Therapeutic Innovation Basics of hypothesis testing: Null and alternative hypothesis Sample size

Bias Type I and Type II error Significance Power Confidence intervals Trial design types 2 What is hypothesis testing? European Patients Academy on Therapeutic Innovation A statistical hypothesis is an assumption about a population parameter (a measurable characteristic of a

population). Hypothesis testing is the evaluation done by a researcher in order to either confirm or disprove a hypothesis. Hypothesis tests typically examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected. Samples should be representative of the population, however, hypothesis testing on samples can never guarantee a hypothesis completely - only say that it has a certain probability to be true or false. 3 Null and alternative hypothesis European Patients Academy on Therapeutic Innovation

Null hypothesis (H0) - formulated to capture our current situation. A null hypothesis in a clinical trial might be that the new medicine is no better than the current treatment. Alternative hypothesis (H1) - formulated to capture what we want to show by doing the trial. An alternative hypothesis in a clinical trial might be that the new medicine is better than the current treatment. 4 Type I and Type II error European Patients Academy on Therapeutic Innovation

Null hypothesis is true Null hypothesis is false Reject the null hypothesis Type I error False positive Correct outcome True positive

Fail to reject the null hypothesis Correct outcome True negative Type II error False negative 5 Sample size European Patients Academy on Therapeutic Innovation

Sample size is the total number of participants required for a trial. It is based on the principles of statistical hypothesis testing: 1. Magnitude of the effect expected 2. Variability in the variables being analysed 3. Desired probability 6 Sampling error European Patients Academy on Therapeutic Innovation A randomly selected study sample may not be representative of the true population.

By using larger study samples the severity of sampling error can be reduced. 7 Bias European Patients Academy on Therapeutic Innovation Bias is the intentional or unintentional adjustment in the design and/or conduct of a clinical trial, and analysis and evaluation of the data that may affect the results. An example of bias: when examining patients, a doctor looks more favourably towards patients receiving the actual medicine instead of the placebo.

8 Significance level European Patients Academy on Therapeutic Innovation Significance level is the probability of committing a type I error. Factors that affect significance level are: The power of the test Size of sample 9

Power European Patients Academy on Therapeutic Innovation The probability of not committing a type II error is called the 'power' of the hypothesis test. Factors that can increase the power: Increasing sample size Higher significance level 10 Confidence interval European Patients Academy on Therapeutic Innovation

The 'confidence interval' is used to express the degree of uncertainty associated with a sample statistic. 11 Common hypothesis tests European Patients Academy on Therapeutic Innovation There are several types of statistical tests that can be used for hypothesis testing: z-test: used to test hypothesis about a population mean when the population variance is known. t-test: tells if there is a significant difference between two sets of

data. Chi-squared test: used to determine if two variables are related. 12