Biostatistics Case Studies 2007

1. Biostatistics Case Studies 2007 Session 1: The Logic Behind Statistical Adjustment Peter D. Christenson Biostatistician http://gcrc.labiomed.org/biostat

2. Case Study J Clin Endocrin Metab 2006 Nov; 91(11):4424-32.

3. Eventual Goal:Establish Diagnostic Test for GH Administration • Potential Approaches: • Use some difference between endogenous and exogenous GH, such as isoforms. Problem is short time window. • Measure proteins or peptides that respond to GH. This study. Why preferable to GH levels themselves? • Could use a profile of several markers. • After single marker or profile is selected, need policy on sensitivity and specificity of the test.

4. Study Goal:Determine Other Relevant Subject Characteristics • Outline: • Serum IGF and collagen markers are known to be GH-responsive. • Are age, gender, BMI, ethnicity, and sport type related to the marker levels in elite athletes? • Determine the relative and combined explanatory power of these factors on the markers. • Suggest factors to be included in a doping test.

5. Not a Study Goal:Establish Reference Ranges Gender, Age Specific Gender, Stature Specific

6. Eventual Goal:Establish Reference Ranges Gender, Age, Other Specific Others could be Ethnicities IGF1 Mean Curves Other1 Other2 Other3 Other4 Female Mock-Up Other1 Other2 Other3 Other4 Male Need separate Other3 and Other4 Curves for Males? Decreasing Age

7. Eventual Goal:Use Reference Ranges for Doping Test • Issues: • Statistical significance of associations of subject characteristics with markers not so important. • Even weak associations may be included in a formula (e.g., logistic regression) or rule (e.g., CART) for Yes/No doping using markers and other factors. • Primary criteria are sensitivity and specificity of rule and their precision.

8. Back to Study Goals:Outcomes are IGF and Collagen Markers(Not Yes/No Doping) Determine the relative and combined explanatory power of age, gender, BMI, ethnicity, and sport type on the markers. Figure 2. One conclusion is lack of differences between ethnic IGF1 means, after adjustment for age, gender, and BMI (Fig 2). How are these adjustments made? * * for age, gender, and BMI.

9. Adjustment:What Specifically is It? • Standardization? • Normalization? • Stratification? • Adjustment?

10. Adjustment:For a Single Continuous Characteristic • Problem: Groups to be compared (e.g., ethnicities) have different mean ages, and age is associated with IGF1. • Solution: Make groups appear to have the same mean age. • Find regression line predicting IGF1 from age. • Move each subject parallel to the regression line to the mean age. This is the expected IGF1 if this subject had been at the mean age. • Adjusted means are means of these adjusted individual values.

11. Adjustment:For a Single Continuous Characteristic We simulate data for Caucasians and Africans only for simplicity, to demonstrate attenuation of a 155-140=15 μg/L difference to a 160-157=3 μg/L difference. 160 158 155 140

13. Adjustment:For a Single Continuous Characteristic • Typical Software (SAS): • proc glm; • class ethnic; • model igf1=ethnic age; • means ethnic; *This gives unadjusted IGF1 means; • lsmeans ethnic; *This gives adjusted IGF1 means; • run;

14. Adjustment:For a Single Continuous Characteristic From the regression: Δ=slope=ΔIGF1/ΔAge. Individual Subjects: Adjusted IGF1 = IGF1 + Δ(Age - Overall Mean Age). Groups: Adjusted IGF1 Group Mean = Group MeanIGF1 + Δ(Group Mean Age - Overall Mean Age).

15. Adjustment:For a Single Classification Characteristic • Problem: Groups to be compared (e.g., ethnicities) have different proportions of females, and gender is associated with IGF1. • Solution: Make groups appear to have the same proportion of females. • IGF1 means are adjusted to what is expected if each group had the same proportion of females. • Different proportions of subjects in each group are adjusted up or down to accomplish this.

17. Adjustment:For a Single Classification Characteristic Δ = Male IGF1 Mean - Female IGF1 Mean Individual Subjects: Adjusted IGF1 = IGF1 + Δ(IF - Overall Prop Female). where IF = 1 if Female, 0 if Male Ethnic Groups: Adjusted IGF1 Group Mean = Group MeanIGF1 + Δ(Group Prop Female - Overall Prop Female).

18. Adjustment:For a Single Classification Characteristic Caucasian: 236/590 = 0.40 Female African: 27/109 = 0.25 Combined: 263/699 = 0.38 Female Δ = Male IGF1 Mean - Female IGF1 Mean = 123 - 201 = -78 Ethnic Groups: Adjusted IGF1 Group Mean = Group MeanIGF1 + Δ(Group Prop Female - Overall Prop Female). Caucasian: 155 -78(0.40 - 0.38) = 153 African: 140 -78(0.25 - 0.38) = 150

19. Adjustment:For a Single Classification Characteristic Stratified (Subgroup) Caucasian vs. African: Male: 123 vs. 125 p=0.23 Female: 203 vs. 185 p=0.0008 Adjusted: 153 vs. 150 p=0.32 Genders Differ on Ethnic Differences: Is adjustment justified? Loses a main feature of the results. The interaction, i.e., 123-125=-2 vs. 203-185=17 has p=0.003. (Recall that this is simulated data, not actual paper results)

20. Adjustment:For Multiple Characteristics • The process is sequentially applied. • Two types of p-values: • Type I: Adjusting only for factors earlier in the sequence applied. • Type III: Adjusting for all included factors. This is most common - “independent” effect, relative to all other effects. • Figure 2: Adjusts for age, BMI, gender. Unclear which removes ethnic differences.