1. Stratification and Adjustment

2. Stratification
Direct and indirect adjustment
Mantel-Haenszel

3. Objectives To discuss the purpose and assumptions of stratification
Discuss and calculate direct and indirect adjustment
To discuss and calculate Mantel-Haenszel statistics

4. Stratification and Multivariate Modeling
Stratification and Multivariate modeling are the analytic tools used to control for confounding
Stratification allows for assessment of confounding and effect modification
Multivariate analyses are used to carry out statistical adjustment

5. Assumptions Stratification Adjustment
Strata must be meaningfully and properly defined
Strata must be homogenous within stratum
Adjustment
Simple techniques such as direct and indirect adjustment and Mantel-Haenszel assume that the association are homogenous across strata and there is not interaction
Multivariate regression techniques are more mathematically complex models and each has it’s own set of assumptions

6. Example of Simple Stratified Analysis

7. Crude and Stratified Analyses

8. Simple Stratified Analysis

9. Simple Stratified Analysis – Multiple Strata

10. Simple Adjustment Direct and indirect adjustment Mantel-Haenszel
Direct (compare rates by using a standardized population)
Indirect (compare rates applying a standard rate and SMRs)
Mantel-Haenszel
A weighted average measure of association

11. Direct Adjustment
For each stratum of the suspected confounding variable, the incidence is calculated n the two study groups
A standard population is identified
The expected number of cases in each stratum of the standard population is calculated by multiplying stratum specific rates in study group to number of subjects in the standard population
Overall expected cases in the standard population divided by the total number of individuals in the standard population are standardized rates and can be compared

12. Method for calculating direct adjustment

13. Adjusted AR and RR
Adjusted AR = I*A – I*B
Adjusted RR = I*A
A*B

14. Example of homogeneity of AR but heterogenity of RR

15. Example of homogeneity of RR but heterogeneity of AR

16. Indirect Method
For each study group, the ratio of the total number of observed events to the number of expected events (if the rates in the study group were the “standard” rates) provides an estimate of the factor-adjusted relative risk or rate ratio.
Useful when stratum-specific risk or rates are missing or when study groups are small.
Should be used to compare more than one study group to the source of reference rates.

17. Method for calculating Indirect Adjustment

18. Comparisons of SMRs for different study groups may be inappropriate

19. Mantel-Haenszel for adjusted measures of association

21. Mantel-Haenszel Adjusted Rate Ratio

22. Limitations of Stratification-based methods of adjustment
Can be used to adjust for several covariates simultaneously, adjustment is carried out only for the association between one independent variable and one outcome at a time
Can adjust for categorical covariates only
When data is sparse the methods are not useful (i.e. can not calculate stratum-specific rates if the sample size is 0)

23. Table 3. Factors associated with Maternal-Child Separation
Not Sep
(n=269)
P-value SA
49.0
24.2
.0001
HIV+ mom
84.2
90.7
.02
> 5 yrs
70.8
61.0
Boys
51.8
43.8
.07
HIV + child
3.6
1.9
.23

24. Table 4. Factors associated with Mat-Child Separation in Multivariate Logistic Regression (N=522)
3.50 ( )**
HIV+ mom
.38 ( )**
> 5 yrs
1.59 ( )*
Boys v.s. girls
1.45 ( )