### Interpretation of Regression Models

Interpretation of Regression Models

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Module 5 – SLP

UNIVARIATE VERSUS BIVARIATE ANALYSES; REGRESSION

Interpret the two models that appear below, and address the following additional questions as they pertain to each:

1. What about confounding? Which of the variables are potential confounders?

2. Compare and contrast matching on potential confounders versus including them in a regression model.

BMI (1 unit) = 1.3 + 2.4 (diabetes) + 2.3 (family history diabetes) + 1.7 (gender) + 1.4 (age) + 1.7 (race) + 2.6 (income) + 3.4 (height), p<0.05

Allergies = 4.5 + 3.8 (Family History Allergies) + 2.1 (gender) + 1.4 (age) + 0.8 (race) + 1.5 (weight), p<0.05

SLP Assignment Expectations

Length: SLP assignments should be at least 2 pages (500 words) in length.

References: At least two references must be included from academic sources (e.g. peer-reviewed journal articles). Required readings are included. Quoted material should not exceed 10% of the total paper (since the focus of these assignments is critical thinking). Use your own words and build on the ideas of others. When material is copied verbatim from external sources, it MUST be enclosed in quotes. The references should be cited within the text and also listed at the end of the assignment in the References section (APA format recommended).

Organization: Subheadings should be used to organize your paper according to question

Format: APA format is recommended for this assignment. See Syllabus page for more information on APA format.

Grammar and Spelling: While no points are deducted for minor errors, assignments are expected to adhere to standards guidelines of grammar, spelling, punctuation, and sentence syntax. Points may be deducted if grammar and spelling impact clarity.

The following items will be assessed in particular:

• Achievement of learning outcomes for SLP assignment.

• Relevance—all content is connected to the question.

• Precision—specific question is addressed; statements, facts, and statistics are specific and accurate.

• Depth of discussion—points that lead to deeper issues are presented and integrated.

• Breadth—multiple perspectives and references, multiple issues/factors considered/

• Evidence—points are well-supported with facts, statistics, and references.

• Logic—presented discussion makes sense; conclusions are logically supported by premises, statements, or factual information.

• Clarity—writing is concise, understandable, and contains sufficient detail or examples.

• Objectivity—use of first person and subjective bias are avoided.

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Module 5 – Background

UNIVARIATE VERSUS BIVARIATE ANALYSES; REGRESSION

Collier, W. Independent & Dependent Variables. University of North Carolina at Pembroke. Retrieved from http://www.uncp.edu/home/collierw/ivdv.htm

Health Knowledge. Confounding, interactions, methods for assessment of effect modification. Retrieved from http://www.healthknowledge.org.uk/public-health-textbook/research-methods/1a-epidemiology/confounding-interactions-methods

Lowry, Richard. Simple Logistical Regression. VassarStats: Website for Statistical Computation. http://www.vassarstats.net/logreg1.html

Ludford, Pamela J. University of Minnesota, College of Science and Engineering. Linear Regression. Retrieved from http://www-users.cs.umn.edu/~ludford/Stat_Guide/Linear_Regression.htm

McDonald, John H. Logistic Regression. Handbook of Biological Statistics. Retrieved from http://udel.edu/~mcdonald/statlogistic.html

National Science Digital Library’s Computation Science Education Research Desk: Univariate Data and Bivariate Data. Retrieved from http://www.shodor.org/interactivate/discussions/UnivariateBivariate/

National Science Digital Library’s Computation Science Education Research Desk: Graphing and Interpreting Bivariate Data. Retrieved from http://www.shodor.org/interactivate/discussions/GraphingData/

Penn State. STAT507 Epidemiological Research Methods: 3.5 – Bias, Confounding, and Effect Modification. Retrieved from https://onlinecourses.science.psu.edu/stat507/node/34

PowerPoint Presentation Regarding How to Control for Confounding: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CDkQFjAB&url=http%3A%2F%2Fcphp.sph.unc.edu%2Ffocus%2Fvol4%2Fissue1%2F4-1AdvancedData_slides.ppt&ei=6jkFUq-nMYjw2QWrjYHIBA&usg=AFQjCNEx5DfK5SDgjc_kyaMo1uFkl8zQIA&sig2=887k52Cs6-jotuMeo0iDJQ&bvm=bv.50500085,d.b2I

University of Pennsylvania. Stratification and Matching in Design. Retrieved from http://www.cceb.upenn.edu/pages/localio/EPI521/2007/part4.pdf

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Module 5 – Home

UNIVARIATE VERSUS BIVARIATE ANALYSES; REGRESSION

Modular Learning Outcomes

Upon successful completion of this module, the student will be able to satisfy the following outcomes:

• Case

o Distinguish between univariate and multivariate analysis.

o Distinguish between dependent and independent variables.

o Distinguish between logistic and linear regression.

• SLP

o Interpret the results of a regression analysis, both linear and logistic

o Discuss the concept of confounding, and note potential confounders in a hypothetical study.

o Assess the merits of matching on confounders versus adjusting for confounders by including them in a regression model.

• Discussion

o Identify confounders for known diseases.

Module Overview

Univariate versus Multivariate Analysis

Univariate analysis looks at how two variables relate to one another. Often time, it examines whether there is an association between a potential risk factor or background characteristic (e.g. smoking, gender, exercise) with an outcome or disease (e.g. lung cancer, breast cancer, diabetes). The analysis only involves the disease (or outcome) with the potential risk factor (or exposure). Multivariate analysis, on the other hand, examines more than one potential risk factor at the same time, and their potential association to the disease or outcome. For instance, one could examine the effects of smoking, gender, age, obesity, and diabetes together against a potential association with cardiovascular disease.

National Science Digital Library’s Computation Science Education Research Desk: Univariate Data and Bivariate Data. Retrieved from http://www.shodor.org/interactivate/discussions/UnivariateBivariate/

National Science Digital Library’s Computation Science Education Research Desk: Graphing and Interpreting Bivariate Data. Retrieved from http://www.shodor.org/interactivate/discussions/GraphingData/

Dependent versus Independent Variables

In these cases, the outcome or disease status is the dependent variable, whereas any potential exposure or risk factor is an independent variable. Multivariate analysis most often looks at one dependent variable (disease or outcome status) and more than one independent variable (e.g. gender, race, income, medical history, etc.).

Collier, W. Independent & Dependent Variables. University of North Carolina at Pembroke. Retrieved from http://www.uncp.edu/home/collierw/ivdv.htm

Confounder

A confounder is a variable that is linked with a disease (or outcome) and is related with the risk factor (or exposure), that changes the relationship between the exposure and outcome. For instance, let’s say that obesity is a potential risk factor for diabetes. Then consider a third variable, a family history of diabetes, that is also a potential risk factor for diabetes, and is related to obesity. If the addition of the third variable (family history of diabetes) changes the relationship between obesity and diabetes, then the third variable (family history of diabetes) is a confounder in this situation.

Resources

PowerPoint Presentation Regarding How to Control for Confounding: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CDkQFjAB&url=http%3A%2F%2Fcphp.sph.unc.edu%2Ffocus%2Fvol4%2Fissue1%2F4-1AdvancedData_slides.ppt&ei=6jkFUq-nMYjw2QWrjYHIBA&usg=AFQjCNEx5DfK5SDgjc_kyaMo1uFkl8zQIA&sig2=887k52Cs6-jotuMeo0iDJQ&bvm=bv.50500085,d.b2I

University of Pennsylvania. Stratification and Matching in Design. Retrieved from http://www.cceb.upenn.edu/pages/localio/EPI521/2007/part4.pdf

Penn State. STAT507 Epidemiological Research Methods: 3.5 – Bias, Confounding, and Effect Modification. Retrieved from https://onlinecourses.science.psu.edu/stat507/node/34

Health Knowledge. Confounding, interactions, methods for assessment of effect modification. Retrieved from http://www.healthknowledge.org.uk/public-health-textbook/research-methods/1a-epidemiology/confounding-interactions-methods

Logistical and Linear Regression

Unlike univariate analysis, regression models allow researchers to examine more than one independent variable at a time against a dependent variable. This means that confounders or demographic variables may be studied alongside the exposure and outcome variables, to adjust for any potential bias that may arise due to background characteristics (e.g. difference by gender or race or income, etc.). Depending on the outcome variable, logistical regression is used for binary outcomes (e.g. disease status of “yes” or “no,” mortality data, etc.) whereas linear regression is used for continuous outcomes (e.g. blood pressure, bone mass density, fasting blood glucose, etc.). Logistical and Linear models can be interpreted as follows:

Lung Cancer = 4.5 + 2.4 (smoking) + 1.7 (gender) + 2.3 (age) + 0.7 (race), p<0.05

After controlling for gender, age, and race, those with a history of smoking are 2.4 times more likely to have lung cancer than those who do not smoke (p<0.05). In this statement, lung cancer is the dependent variable, history of smoking is the independent variable of interest (the exposure), and gender, age, and race are the confounders. This is a logistical regression model, where the dependent variable is binary: lung cancer versus no lung cancer.

BMI (1 unit) = 3.9 + 3.4 (high fasting glucose) + 1.5 (gender) + 1.3 (age) + 2.7 (race), p<0.05

After controlling for gender, age, and race, a one unit increase in BMI is 3.4 times more likely in those with a high fasting glucose level than those with a lower fasting glucose level. In a linear regression model, the dependent variable is continuous and results are measured in units. The dependent variable here is body mass index (BMI) and the independent variable is fasting glucose levels (high versus low), and the potential confounders are gender, age, and race.

Additional Resources

Lowry, Richard. Simple Logistical Regression. VassarStats: Website for Statistical Computation.http://www.vassarstats.net/logreg1.html

Ludford, Pamela J. University of Minnesota, College of Science and Engineering. Linear Regression. Retrieved from http://www-users.cs.umn.edu/~ludford/Stat_Guide/Linear_Regression.htm

McDonald, John H. Logistic Regression. Handbook of Biological Statistics. Retrieved from http://udel.edu/~mcdonald/statlogistic.html

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**SAMPLE ANSWER**

**Introduction**

Both univariate and bivariate or multivariate analyses are used in determining the relationship between two or more variables (Arsham, 2012; Chatterjee, 2012). For instance, in univariate analysis the relationship between two variables i.e. an independent variable against a dependent variable is examined, whereas bivariate and multivariate analysis the analysis between one dependent variable and two or more that two independent variables respectively is examined in what is known as multiple linear or logistical regression model (Babbie, 2009; Warne, Ramos & Ritter, 2012). In the regression models considered in this assignment, the disease status or outcome is the dependent variable, while the potential risk factors or exposures are the independent variables.

**Interpretation of Regression Models**

Unlike in univariate analysis, logistical and linear regression models allow the examination of more than one independent variable at once against a dependent variable (Arsham, 2012). In the logistical and linear regression models considered in this case or scenario, the disease status or outcome is the dependent variable, while the potential risk factors or exposures are the independent variables (Chatterjee, 2012). Thus, since the logistical and linear regression models represent multivariate analysis, the relationship between examined is between one dependent variable (outcome status or disease) and more than one or multiple independent variables (e.g. age, gender, race, weight, height, medical/family history, income, etc.). Interpretation of the models is as follows:

** ****Model 1 Interpretation**

BMI (1 unit) = 1.3 + 2.4 (diabetes) + 2.3 (family history diabetes) + 1.7 (gender) + 1.4 (age) + 1.7 (race) + 2.6 (income) + 3.4 (height), p<0.05

After controlling for family history diabetes, gender, age, race, income, and height, a BMI’s increase in one unit is 2.4 times more likely in those with diabetes than those without diabetes. Considering that in a linear regression model, the measurement of the dependent variable results is done in units and also it is continuous. For instance, in this regression model the body mass index (BMI) is the dependent variable and the independent variable is diabetes (presence versus absence), and the potential confounders are family history diabetes, gender, age, race, income, and height.

**Model 2 Interpretation **

Allergies = 4.5 + 3.8 (Family History Allergies) + 2.1 (gender) + 1.4 (age) + 0.8 (race) + 1.5 (weight), p<0.05

After controlling for gender, age, race and weight, those with a family history allergies are 3.8 times more likely to have allergies than those without family history allergies (p<0.05). In this statement, allergies is the dependent variable (the outcome or disease), whereas family history allergies is the independent variable of interest (the risk factor or exposure), and gender, age, race, and weight are the confounders. As a result, it means this regression model is a logistical regression model, in which the representation of the dependent variable is form of a binary data i.e. allergies versus no allergies.

**Questions **

**Confounding in Regression Models**

Confounding is the presence of variables linked with an outcome (or disease) and related with the exposure (or risk factor) in a regression model, that changes how the exposure relates to the outcome (Chatterjee, 2012; Chvatal, 2013). For example, in model 1 the potential confounders are family history diabetes, gender, age, race, income, and height, while in model 2 the potential confounders are gender, age, race, and weight.

**Comparing and contrasting the matching on potential confounders versus their inclusion in a regression model**

Potential confounders changes how the exposure relate to the outcome in a regression model. For instance, before controlling for potential confounders (matching) in model 1, a BMI’s increase in one unit is 1.3 times more likely in those with diabetes than those without diabetes but after controlling for potential confounders (inclusion in regression model) a BMI’s increase in one unit increased to 2.4 times more likely in those with diabetes than those without diabetes. In model 2 before controlling for potential confounders (matching), those with a family history allergies are 4.5 times more likely to have allergies than those without family history allergies (p<0.05) but after controlling for potential confounders (inclusion in regression model) the likelihood of those with a family history allergies to have allergies than those without family history allergies dropped to 3.8 times (p<0.05).

**References**

Arsham, H. (2012). Foundation of Linear Programming: A Managerial Perspective from Solving System of Inequalities to Software Implementation, *International Journal of Strategic Decision Sciences*, 3(3), 40-60.

Babbie, E. R. (2009). *The Practice of Social Research*, (12^{th} ed.). New York, NY: Wadsworth Publishing.

Chatterjee, S. (2012).* Regression analysis by example. *Hoboken, NJ: John Wiley & Sons Inc.* *

Chvatal, V. (2013). *Linear Programming*. New York, NY: W. H. Freeman and Company.

Warne, R. L., Ramos, T., & Ritter, N. (2012). Statistical Methods Used in Gifted Education Journals, 2006–2010. *Gifted Child Quarterly, *56(3), 134–149.

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