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.

A B

XEach point is a separate subject.

Extreme Outcome #2

Suppose results from the study are plotted as:

Obviously, A and B are equally effective.

A B

XEach 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?

A B

XEach 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?

A B

XEach 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?

A B

XEach 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.

A B

XEach 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:

H0: No Effect HA: Effect

No Effect

Effect

Study Claims:

Correct

CorrectError (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

H0

HA

H0: true effect=0

HA: true effect=3

Effect in study=1.13

\\\ = Probability of concluding HA if H0 is true.

41%

5%

Effect (Group B mean – Group A mean)

/// = Probability of concluding H0 if HA 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

www.stat.uiowa.edu/~rlenth/Power

Online Study Size / Power Calculator

Software Output: Power with N=100 Subjects/Group

Pilot data: SD=9.603. Want to Detect 3 point effect on cholesterol.

Number of Subjects and Power to Detect Oatmeal Effect of 3 Points in

Cholesterol

N per Group Power

100 59%

125 69%

150 77%

175 83%

200 88%

161 80%

Δ=3, SD=9.603, P[Incorrectly claim effect] ≤ 0.05