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22 - 10 - 2014
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Regression analysis: Introduction

We used correlation analysis in order to reveal association between two variables. With correlation analysis we can understand presence of association and its strength; however, we cannot study functional dependence between variables. Functional dependency is studied in regression analysis. In correlation two variables are treated as equal, however in regression one (or several) variables are considered independent (predictor) and another variable – dependent (outcome).

Regression analysis is one of the methods of prognosis: by values of already measured predictors we may predict value of an outcome variable:

Methods of prognosis 

Linear regressions are used for continuous outcome; among these regressions simple (or univariate) is used to study relation between one dependent and one predictor variables and multiple (multivariate) regression is used to study relation between one dependent and multiple predictor variables:

Types of regression analysis

For binary outcomes logistic regression is used. This is very common type of outcome, it can indicate presence or absence of some parameter (virulent/non-virulent strain, sensitive/resistant, etc.); it may also indicate result of some process (e.g., result of treatment – favourable/unfavourable outcome of disease). Because of this, logistic regression also has become popular method in recent times. Logistic regression actually is used not only for describing relationship between variables but first of all for prognosis of values of dependent variable, particularly to assess probability of dependent variable to fall into some class (e.g., strain is more likely to be virulent or non-virulent, outcome of disease in individual patient is more likely to be favourable or not, etc.), because of this logistic regression will be discussed in the chapter with prognosis methods.

When outcome belongs to time-to-event type (survival data) cox proportional hazards regression is used. This regression is the most popular in medicine, where it assesses survival of patients during particular time.

Regression analysis nowadays is commonly used in different microbiological studies. The table below shows some selected examples on application of different types of regression in microbiology.

Selected examples on application of regression analysis in microbiological studies

Dependent variable

Predictor variables

Method of regression


Molecular cluster of Mycobacterium tuberculosis in Switzerland

Cavitary disease, sex, and age

Logistic regression

Fenner et al., 2012

Attributable mortality in patients with complicated bacteremia caused by methicillin-resistant Staphylococcus aureus

Acute Physiology and Chronica health Evaluation Score-II (APACHE-II), vancomycin area under the concentration-time curve (AUC)/MIC ratio

Classification and regression tree analysis (CART), logistic regression

Brown et al., 2012

Mortality in patients with Pseudomonas aeruginosa bacteremia

Carbapenem resistance

Cox regression

Peña et al., 2012

Outcome in patients with Clostridium difficile infection

Sex, age, severity of comorbidity

Poisson regression

Wenisch et al., 2012

Diagnostic performance in diagnosis of Toxoplasma gondii infection

Peptides mimicking epitopes from T. gondii antigens

Logistic regression

Maksimov et al., 2012

Presence of complications in patients with pulmonary hydatidosis


Logistic regression

Santivañez et al., 2012

Hepatitis A virus inactivation rates in contaminated green onions

Storage temperature

Linear regression

Sun et al., 2012

Outcomes in patients with bloodstream infections caused by extended-spectrum beta lactamase-producing pathogens

Intensive care unit stay, presence of a central line prior to positive culture, presence of a rapidly fatal condition at the time of admission, recent prior hospitalization, empiric carbapenem therapy, receipt of empiric cefepime, etc.

Logistic regression

Chopra et al., 2012

Nucleoside reverse transcriptase inhibitor susceptibility

HIV-1 reverse transcriptase mutations

Least-squares regression

Melikian et al., 2012

Nephrotoxicity associated with colistin use

Body mass index, diabetes, the length of hospitalization in days prior to receipt of colistin, age, etc.

Logistic regression

Gauthier et al., 2012

MIC distribution analysis for posaconazole, itraconazole, and voriconazole for A. fumigatus isolates

Mutations in the cyp51A gene

Nonlinear regression

Meletiadis et al., 2012

Outcomes in patients with bacteremia due to vancomycin-resistant Enterococcus

Bacteremia due to vancomycin-resistant E. faecalis and E. faecium

Logistic regression

Hayakawa et al., 2012

28-day mortality and clinical response in patients with methicillin-resistant Staphylococcus aureus pneumonia

Age, APACHE II score, AIDS, cardiac disease, vascular disease, diabetes, SCCmec type II, Panton-Valentine leukocidin negativity, higher vancomycin MIC, etc.

Multivariate regression

Haque et al., 2012

The risk of in vitro resistance to pyrimethamine in Plasmodium falciparum

Mutations F423Y in the pfmdr2 gene, N51I, C59R, and S108N in the pfdhfr gene

Logistic regression

Briolant et al., 2012

Antibiotic effect

Antibiotic concentration

Sigmoidal regressions, biphasic regressions

Garcia et al., 2012

Acquisition of multidrug-resistant Proteus mirabilis isolates responsible for bloodstream infections; impact on mortality of such infections

Admission from a long-term care facility, previous therapy with fluoroquinolones or oxyimino-cephalosporins, urinary catheterization, previous hospitalization, etc.

Multivariate regression analysis

Tumbarello et al., 2012

Concentrations of protozoa and indicator bacteria (Escherichia coli and total coliform)

Wetland type, seasonality, rainfall, and various water quality parameters

Longitudinal Poisson regression

Hogan et al., 2012

Outcome in patients with HIV-associated tuberculous meningitis

Mycobacterium tuberculosis drug resistance, bacterial lineage, and host vaccination status

Cox multiple regression models

Tho et al., 2012

Area under the concentration-time curve from 0 to 12 h (AUC0-12) of antituberculosis drugs

Age, sex, weight, drug dose/kilogram, CD4+ lymphocyte count, treatment schedule, and concurrent antiretrovirals

Multilevel linear mixed-effects regression

McIlleron et al., 2012

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