Download - Stratification and Adjustment. Stratification Direct and indirect adjustment Mantel-Haenszel
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Stratification and Adjustment
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Stratification
• Direct and indirect adjustment
• Mantel-Haenszel
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Objectives
• To discuss the purpose and assumptions of stratification
• Discuss and calculate direct and indirect adjustment
• To discuss and calculate Mantel-Haenszel statistics
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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
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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
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Example of Simple Stratified Analysis
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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
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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
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Simple Stratified Analysis – Multiple Strata
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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
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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
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Method for calculating direct adjustment
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Adjusted AR and RR
• Adjusted AR = I*A – I*B
• Adjusted RR = I*A
A*B
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Example of homogeneity of AR but heterogenity of RR
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Example of homogeneity of RR but heterogeneity of AR
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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.
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Method for calculating Indirect Adjustment
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Comparisons of SMRs for different study groups may be inappropriate
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Mantel-Haenszel for adjusted measures of association
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Mantel-Haenszel Adjusted Rate Ratio
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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)
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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
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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)