Stratification and Adjustment

Stratification

• Direct and indirect adjustment

• Mantel-Haenszel

Objectives

• To discuss the purpose and assumptions of stratification

• Discuss and calculate direct and indirect adjustment

• To discuss and calculate Mantel-Haenszel statistics

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

Assumptions

• Stratification– 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

Example of Simple Stratified Analysis

Crude and Stratified Analyses

All Cases and Controls - Crude Associations

Lung CA No Lung CA O.R.Alcohol yes 110 75

no 70 80

Stratified Analysis by Smoking status

For SmokersLung CA No Lung CA O.R.

Alcohol yes 90 35no 55 50

For Non-SmokersLung CA No Lung CA O.R.

Alcohol yes 20 40no 15 30

Simple Stratified AnalysisAll Cases and Controls - Crude Associations

Died Survived O.R.Women 350 200Men 150 250

Stratified Analysis by Smoking status

< 35 years oldDied Survived O.R.

Alcohol Women 150 75Men 50 50

35 to 65 years oldDied Survived O.R.

Alcohol Women 100 50Men 50 75

> 65 years oldDied Survived O.R.

Alcohol Women 100 75Men 50 125

Simple Stratified Analysis – Multiple Strata

Simple Adjustment

• Direct and indirect adjustment– 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

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

Method for calculating direct adjustment

Adjusted AR and RR

• Adjusted AR = I*A – I*B

• Adjusted RR = I*A

A*B

Example of homogeneity of AR but heterogenity of RR

Example of homogeneity of RR but heterogeneity of AR

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.

Method for calculating Indirect Adjustment

Comparisons of SMRs for different study groups may be inappropriate

Mantel-Haenszel for adjusted measures of association

Mantel-Haenszel Adjusted Rate Ratio

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)

Table 3. Factors associated with Maternal-Child Separation

Sep

(n=253)

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 .02

Boys 51.8 43.8 .07

HIV + child 3.6 1.9 .23

Table 4. Factors associated with Mat-Child Separation in Multivariate

Logistic Regression (N=522)

SA 3.50 (2.35-5.21)**

HIV+ mom .38 ( .21- .68)**

> 5 yrs 1.59 (1.07 - 2.36)*

Boys v.s. girls 1.45 ( .99-2.11)