1

Applied biostatistics

Francisco Javier Barón LópezDpto. Medicina PreventivaUniversidad de Málaga – Españabaron@uma.es

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Multivariate analysis

Generally used to study: the effect of one variable

Numerical dichotomous, or qualitative by using multiple binary variables.

On another variable Numerical: Multiple linear regression Binary: Logistic regression

Controlling for the effect of a few other variables Control variables Covariates Confusion

The usual multivariate model in Health sciences

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Multivariate model Outcome

Interesting variable

Co

vari

ates age

sex

…

Does [interesting variable] influence [Outcome variable] when [adjusting/controlling/taking into account] covariates1, covariates2,…?

Numerical outcome: Multiple linear regression

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Multivariate model:

Linear regression

model

Numericoutcome

Interesting variable

Co

vari

ates age

sex

…

Estimate±std.error; pEstimate; CI 95%; p

We are NOT (very) interested in the significance of covariates.

•Estimate>0, Increasing effect •Estimate<0, Decreasing effect•Estimate=0, No effect

Binary logistic regression

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Multivariate model:

Linear regression

model

Binaryoutcome

Interesting variable

Co

vari

ates age

sex

…

OR; pOR; CI 95%; p

0/1

The estimates now are: Odds Ratios (OR)•OR>1, Increased risk •OR<1, Decreased risk•OR=1, No effect

Dummy variables

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Multivariate model Outcome

Qualitative interesting variable with3+ levels

Co

vari

ates age

sex

…

We must encode the qualitatives non binary variables using only binary variables. How?

Encoding dummy variables

Categoria laboral

•Administativo•dummySeguridad=0•dummyDirectivo=0

•Seguridad:•dummySeguridad=1•dummyDirectivo=0

•Directivo:•dummySeguridad=0•dummyDirectivo=1

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Dummy variables

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Multivariatemodel

Outcome

Qualitative interesting variable with3+ levels

Co

va

ria

tes

…

Coding qualitative variables using dummy variables

Multivariatemodel

Outcome

Dummy 1

Co

va

ria

tes

…

Dummy 2

…