Biostatistics in Clinical Research Peter D. Christenson Biostatistician January 12, 2005IMSD U*STAR RISE

Outline Example Statistical Issues in Clinical Research Prospective vs. Retrospective Studies Size and Power of Clinical Research Studies

Example : Statistical Issues

Statistical Aspects of Clinical Research Target population / sample / generalizability. Quantification of hypotheses, case definitions, endpoints. Control of bias; confounding. Comparison/control group. Randomization, blinding. Justification of study size: power, precision, other. Use of data from non-completers. Methods of analysis. Mid-study analyses.

Major Study Designs Prospective Follow subjects with specified characteristics and measure outcome (e.g., disease) Example: compare cholesterol between oatmeal eaters and non- eaters Compare subjects with or w/o characteristic on the outcome Typical: clinical trial Retrospective Find subjects with or w/o an outcome (e.g., disease), and measure their characteristics Example: compare oatmeal eating status between high and low cholesterol subjects Compare outcome groups on subject characteristics Typical: case-control

Example: Study Size for a Clinical Trial Consider a prospective study: 1.Randomize an equal number of subjects to treatment A (no oatmeal) or treatment B (oatmeal). 2.Follow all subjects for a month. 3.Measure X= pre-post change in cholesterol. Primary Study Aim: Does oatmeal have an effect? Do treatments A and B differ in mean X? Our Goal: How many subjects are needed to answer the primary aim?

Extreme Outcome #1 Suppose results from the study are plotted as: Obviously, B is more effective than A. AB X Each point is a separate subject.

Extreme Outcome #2 Suppose results from the study are plotted as: Obviously, A and B are equally effective. AB X Each point is a separate subject.

More Realistic Possible Outcome I Suppose results from the study are plotted as: Is the overlap small enough to claim that B is more effective? AB X Each point is a separate subject. Is the Δ large enough to be clinically relevant? Δ

More Realistic Possible Outcome II Suppose the ranges are narrower, with the same group mean difference: Now, is this minor overlap sufficient to come to a conclusion? AB X Each point is a separate subject. Δ Same Δ, but subjects in each group are more alike.

More Realistic Possible Outcome III Suppose the ranges are wider, but so is the group difference: Is the overlap small enough to claim that B is more effective? AB X Each point is a separate subject. Δ

More Realistic Possible Outcome IV Here, the ranges for X are the same as the last slide, but there are many more subjects: So, just examining the overlap isn’t sufficient to come to a conclusion, since intuitively the larger N should affect the results. AB X Each point is a separate subject.

Factors for Study Size: So Far 1.The number of subjects itself: N for each group. 2.Mean difference between treatments that is important. 3.Heterogeneity among subjects who are on the same treatment. What else?

Possible Errors in Study Conclusions Truth: H 0 : No EffectH A : Effect No Effect Effect Study Claims: Correct Error (Type I) Error (Type II) Power: MaximizeMinimize

Factors for Study Size: Final 1.The number of subjects itself: N for each group. 2.Mean difference between treatments that is important. Clinical judgment. 3.Heterogeneity among subjects who are on the same treatment. Need Std Dev from pilot study. 4.Power [Probability of correctly claiming an effect]. Usually want ≥80%. 5.Type I Error chance [Probability of incorrectly claiming an effect]. Usually want ≤5%. The next figure illustrates the inter-relationships among these factors.

Graphical Representation of Power H0H0 HAHA H 0 : true effect=0 H A : true effect=3 Effect in study=1.13 \\\ = Probability of concluding H A if H 0 is true. 41% 5% Effect (Group B mean – Group A mean) /// = Probability of concluding H 0 if H A is true. Power=100-41=59% Note greater power if larger N, and/or if true effect>3, and/or less subject heterogeneity. N=100 per Group Larger Ns give narrower curves

Online Study Size / Power Calculator

Software Output: Power with N=100 Subjects/Group Pilot data: SD= Want to Detect 3 point effect on cholesterol.

Number of Subjects and Power to Detect Oatmeal Effect of 3 Points in Cholesterol N per GroupPower 10059% 12569% 15077% 17583% 20088% 16180% Δ=3, SD=9.603, P[Incorrectly claim effect] ≤ 0.05