Introduction to Biostatistics for Clinical and Translational Researchers

1. Introduction to Biostatistics for Clinical and Translational Researchers KUMC Departments of Biostatistics & Internal Medicine University of Kansas Cancer Center FRONTIERS: The Heartland Institute of Clinical and Translational Research

2. Course Information • Jo A. Wick, PhD • Office Location: 5028 Robinson • Email: jwick@kumc.edu • Lectures are recorded and posted at http://biostatistics.kumc.edu under ‘Events & Lectures’

3. Objectives • Understand the role of statistics in the scientific process and how it is a core component of evidence-based medicine • Understand features, strengths and limitations of descriptive, observational and experimental studies • Distinguish between association and causation • Understand roles of chance, bias and confounding in the evaluation of research

4. Course Calendar • July 5: Introduction to Statistics: Core Concepts • July 12: Quality of Evidence: Considerations for Design of Experiments and Evaluation of Literature • July 19: Hypothesis Testing & Application of Concepts to Common Clinical Research Questions • July 26: (Cont.) Hypothesis Testing & Application of Concepts to Common Clinical Research Questions

5. “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.” Albert Einstein (1879-1955)

6. Vocabulary

7. Basic Concepts • Statistics is a collection of procedures and principles for gathering data and analyzing information to help people make decisions when faced with uncertainty. • In research, we observe something about the real world. Then we must infer details about the phenomenon that produced what we observed. • A fundamental problem is that, very often, more than one phenomenon can give rise to the observations at hand!

8. Example: Infertility Suppose you are concerned about the difficulties some couples have in conceiving a child. • It is thought that women exposed to a particular toxin in their workplace have greater difficulty becoming pregnant compared to women who are not exposed to the toxin. • You conduct a study of such women, recording the time it takes to conceive.

9. Example: Infertility • Of course, there is natural variability in time-to-pregnancy attributable to many causesaside from the toxin. • Nevertheless, suppose you finally determine that those females with the greatest exposure to the toxin had the most difficulty getting pregnant.

10. Example: Infertility • But what if there is a variable you did not consider that could be the cause? • No study can consider every possibility.

11. Example: Infertility • It turns out that women who smoke while they are pregnant reduce the chance their daughters will be able to conceive because the toxins involved in smoking effect the eggs in the female fetus. • If you didn’t record whether or not the females had mothers who smoked when they were pregnant, you may draw the wrong conclusion about the industrial toxin.

12. Example: Infertility Lurking (Confounding) Variable →Bias ? ? Type I Error!

13. Example: Infertility Lurking (Confounding) Variable → “Noise” ? ? Type II Error!

14. The Role of Statistics • The conclusions (inferences) we draw always come with some amount of uncertainty due to these unobserved/unanticipated issues. • We must quantify that uncertainty in order to know how “good” our conclusions are. • This is the role that statistics plays in the scientific process. • P-values (significance levels) • Level of confidence • Standard errors of estimates • Confidence intervals • Proper interpretation (association versus causation)

15. The Role of Statistics Scientists use statistical inference to help model the uncertainty inherent in their investigations.

16. Evidence-based Medicine Evidence-based practice in medicine involves • gathering evidence in the form of scientific data. • applying the scientific method to inform clinical practice, establishment or development of new therapies, devices, programs or policies aimed at improving health.

17. Types of Evidence Scientific evidence: “empirical evidence, gathered in accordance to the scientific method, which serves to support or counter a scientific theory or hypothesis” • Type I: descriptive, epidemiological • Type II: intervention-based • Type III: intervention- and context-based

18. Evidence-based Medicine • Evidence-based practice results in a high likelihood of successful patient outcomes and more efficient use of health care resources.

19. The Scientific Method

20. Clinical Evaluation

21. Types of Studies • Purpose of research • To explore • To describe or classify • To establish relationships • To establish causality • Strategies for accomplishing these purposes: • Naturalistic observation • Case study • Survey • Quasi-experiment • Experiment Ambiguity Control

22. Generating Evidence Complexity and Confidence

23. Observation versus Experiment • A designed experiment involves the investigator assigning (preferably randomly) some or all conditions to subjects. • An observational study includes conditions that are observed, not assigned.

24. Example: Heart Study • Question: How does serum total cholesterol vary by age, gender, education, and use of blood pressure medication? Does smoking affect any of the associations? • Recruit n = 3000 subjects over two years • Take blood samples and have subjects answer a CVD risk factor survey • Outcome: Serum total cholesterol • Factors: BP meds (observed, not assigned) • Confounders?

25. Example: Diabetes • Question: Will a new treatment help overweight people with diabetes lose weight? • N = 40 obese adults with Type II (non-insulin dependent) diabetes (20 female/20 male) • Randomized, double-blind, placebo-controlled study of treatment versus placebo • Outcome: Weight loss • Factor: Treatment versus placebo

26. How to Talk to a Statistician? • “It’s all Greek to me . . .” • Καλημέρα

27. Why Do I Need a Statistician? • Planning a study • Proposal writing • Data analysis and interpretation • Presentation and manuscript development

28. When Should I Seek a Statistician’s Help? • Literature interpretation • Defining the research questions • Deciding on data collection instruments • Determining appropriate study size

29. What Does the Statistician Need to Know? • General idea of the research • Specific Aims and hypotheses would be ideal • What has been done before • Literature review! • Outcomes under consideration • Study population • Drug/Intervention/Device • Rationale for the study • Budget constraints

30. “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.” Albert Einstein (1879-1955)

31. Vocabulary • Hypotheses: a statement of the research question that sets forth the appropriate statistical evaluation • Null hypothesis “H0”: statement of no differences or association between variables • Alternative hypothesis “H1”: statement of differences or association between variables

32. Disproving the Null • If someone claims that all swans are white, confirmatory evidence (in the form of lots of white swans) cannot prove the assertion to be true. • Contradictory evidence (in the form of a single black swan) makes it clear the claim is invalid.

33. The Scientific Method Revise H Evidence supports H Evidence inconsistent with H

34. Hypothesis Testing • By hypothesizing that the mean response of a population is 26.3, I am saying that Iexpect the mean of a sample drawn from that population to be ‘close to’ 26.3:

35. Hypothesis Testing • What if, in collecting data to test my hypothesis, I observe a sample mean of 26? • What conclusion might I draw?

36. Hypothesis Testing • What if, in collecting data to test my hypothesis, I observe a sample mean of 27.5? • What conclusion might I draw?

37. Hypothesis Testing • What if, in collecting data to test my hypothesis, I observe a sample mean of 30? • What conclusion might I draw? ?

38. Hypothesis Testing • If the observed sample mean seems odd or unlikely under the assumption that H0 is true, then we reject H0 in favor of H1. • We typically use the p-value as a measure of the strength of evidence againstH0.

39. What is a P-value? A p-value is the area under the curve for values of the sample mean more extremethan what we observed in the sample we actually gathered. A p-valuethe probability of getting a sample mean as favorable or more favorable to H1than what was observed, assuming H0 is true. The tail of the distribution it is in is determined by H1. If H1 states that the mean is greater than 26.3, the p-value is as shown. If H1 states that the mean is less than 26.3, the p-value is the area to the left of the observed sample mean. Null distribution If H1 states that the mean is different than 26.3, the p-value is twice the area shown, accounting for the area in both tails. Observed sample mean p-value

40. Vocabulary • One-tailed hypothesis: outcome is expected in a single direction (e.g., administration of experimental drug will result in a decrease in systolic BP) • Two-tailed hypothesis: the direction of the effect is unknown (e.g., experimental therapy will result in a different response rate than that of current standard of care)

41. Vocabulary • Type I Error (α): a true H0 is incorrectly rejected • “An innocent man is proven GUILTY in a court of law” • Commonly accepted rate is α = 0.05 • Type II Error (β): failing to reject a false H0 • “A guilty man is proven NOT GUILTY in a court of law” • Commonly accepted rate is β = 0.2 • Power (1 – β): correctly rejecting a false H0 • “Justice has been served” • Commonly accepted rate is 1 – β = 0.8

42. Decisions

43. Statistical Power • Primary factors that influence the power of your study: • Effect size: as the magnitude of the difference you wish to find increases, the power of your study will increase • Variability of the outcome measure: as the variability of your outcome decreases, the power of your study will increase • Sample size: as the size of your sample increases, the power of your study will increase

44. Statistical Power • Secondary factors that influence the power of your study: • Dropouts • Nuisance variation • Confounding variables • Multiple hypotheses • Post-hoc hypotheses

45. Hypothesis Testing • We will cover these concepts more fully when we discuss Hypothesis Testing and Quality of Evidence

46. Descriptive Statistics

47. Field of Statistics

48. Field of Statistics

49. Field of Statistics • Descriptive statistics • Summarizing and describing the data • Uses numerical and graphical summaries to characterize sample data • Inferential statistics • Uses sample data to make conclusions about a broader range of individuals—a population—than just those who are observed (a sample)

50. Field of Statistics • Experimental Design • Formulation of hypotheses • Determination of experimental conditions, measurements, and any extraneous conditions to be controlled • Specification of the number of subjects required and the population from which they will be sampled • Specification of the procedure for assigning subjects to experimental conditions • Determination of the statistical analysis that will be performed