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 ‘Educational Opportunities’

3. Course Objectives • Understand the role of statistics in the scientific process • 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 • June 29: Descriptive Statistics and Core Concepts • July 6: Hypothesis Testing • July 13: Linear Regression & Survival Analysis • July 20: Clinical Trial & Experimental Design

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

6. Basic Concepts

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 Suppose you are concerned about the difficulties some couples have in conceiving a child. • Of course, there is natural variability in time-to-pregnancy attributable to many causes aside 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 Suppose you are concerned about the difficulties some couples have in conceiving a child. • 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. The Role of Statistics • The conclusions we draw—the inferences we make—always come with some amount of uncertainty. • 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.

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

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

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

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

17. What Does the Statistician Need to Know? • General idea of the research • What has been done before • Rationale for the study • Budget constraints

18. 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

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

20. 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.

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

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

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

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

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

26. 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.

27. 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

28. 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)

29. 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

30. Decisions

31. Hypothesis Testing • We will cover these concepts more fully on July 6 when we discuss Hypothesis Testing

32. 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

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

34. 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

35. Design of Experiments • We will cover these concepts more fully on July 20 when we discuss Design of Experiments

36. Descriptive Statistics

37. Field of Statistics

38. Field of Statistics

39. 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)

40. 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

41. Descriptive Statistics • Descriptive statistics is one branch of the field of Statistics in which we use numerical and graphical summaries to describe a data set or distribution of observations.

42. Types of Data • All data contains information. • It is important to recognize that the hierarchy implied in the level of measurement of a variable has an impact on (1) how we describe the variable data and (2) what statistical methods we use to analyze it.

43. Levels of Measurement • Nominal: difference • Ordinal: difference, order • Interval: difference, order, equivalence of intervals • Ratio: difference, order, equivalence of intervals, absolute zero discrete qualitative continuous quantitative

44. NOMINAL ORDINAL INTERVAL RATIO Types of Data Information increases

45. Ratio Data • Ratio measurements provide the most information about an outcome. • Different values imply difference in outcomes. • 6 is different from 7. • Order is implied. • 6 is smaller than 7.

46. Ratio Data • Intervals are equivalent. • The difference between 6 and 7 is the same as the difference between 101 and 102. • Zero indicates a lack of what is being measured. • If item A weighs 0 ounces, it weighs nothing.

47. Ratio Data • Ratio measurements provide the most information about an outcome. • Can make statements like: “Person A (t = 10 minutes) took twice as long to complete a task as Person B (t = 5 minutes).” • This is the only type of measurement where statements of this nature can be made. • Examples: age, birth weight, follow-up time, time to complete a task, dose

48. Interval Data Interval measurements are one step down on the “information” scale from ratio measurements. • Difference and order are implied and intervals are equivalent. • BUT, zero no longer implies an absence of the outcome. • What is the interpretation of 0C? 0K? • The Celsius and Fahrenheit scales of temperature are intervalmeasurements, Kelvin is a ratio measurement.

49. Interval Data Interval measurements are one step down on the “information” scale from ratio measurements. • You can tell what is better, and by how much, but ratios don’t make sense due to the lack of a ‘starting point’ on the scale. • 60F is greater than 30F, but not twice as hot since 0F doesn’t represent an absence of heat. • Examples: temperature, dates

50. Ordinal Data • Ordinal measurements are one step down on the “information” scale from interval measurements. • Difference and order are implied. • BUT, intervals are no longer equivalent. • For instance, the differences in performance between the 1st and 2nd ranked teams in basketball isn’t necessary equivalent to the differences between the 2nd and 3rd ranked teams. • The ranking only implies that 1st is better than 2nd, 2nd is better than 3rd, and so on . . . but it doesn’t try to quantify the ‘betterness’ itself.