LESSON   13

Options for controlling for confounders

Design options

Randomization

RCT only

Groups are similar (on both measured and unmeasured factors)

Restriction

Easy, inexpensive

Generalizability

Matching – most freq with case-control studies

Gain precision

Number of controls per case

Matched analyses

Analysis options

Stratified analysis

Mathematical modeling

Mathematical Modeling

Introduction to Mathematical Modeling

A mathematical model is a mathematical expression that describes how an outcome variable can be predicted from explanatory variables.

Linear regression – usually a continuous outcome variable (e.g., blood pressure, antibody level, weight); predictor variables can be categorical or continuous.

The Logistic Model

In epidemiology many times the outcome variable is dichotomous. When the dependent variable is dichotomous, the most popular mathematical model is a non-linear model called the logistic model.

Table 14-2.  Example Data 1: Hypothetical cohort study of the relationship between smoking and coronary heart disease (CHD) stratified on sex

Females

 Smoker Non-Smoker CHD 5 8 13 No CHD 45 142 187 50 150 200 Risk 10.0% 5.3%

Odds Ratio for females (ORf) = 2.0 (0.6, 6.3)

Males

 Smoker Non-Smoker CHD 300 50 350 No CHD 300 150 450 600 200 800 Risk 50.0% 25.0%

Odds Ratio for males (ORm) = 3.0 (2.1, 4.3)

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Summary information

Directly adjusted OR = 2.9 (2.1, 4.1)

Mantel-Haenszel OR = 2.9 (2.1, 4.1)

Chi-square p-value (MH) p-value < .001

Table 14-9.  Example data 1: Hypothetical cohort study of the relationship between smoking and coronary heart disease (CHD) controlling for the sex of the individual, logistic regression model

There were  363 type  1.0's  (model gives log odds of this type) and 637 type   .0's.

Log likelihood   = -575.0730

Likelihood ratio =  158.1036 2 df  (P = .0000)

Dependent Variable =        CHD

Standard

Coefficient  Error    Coef/SE "P value"

CONSTANT   -3.0336       .2997    -10.1211  .0000

SMOKE       1.0618       .1733      6.1277  .0000

SEX         1.9643       .3045      6.4505  .0000

95.0-% confidence limits

Coefficient             Odds ratio

lower           upper  lower           upper

limit           limit  limit           limit

SMOKE   .7222  1.0618  1.4015 2.0590  2.8916  4.0611

SEX    1.3675  1.9643  2.5612 3.9254  7.1302 12.9513