statistical analysis SAS

This activity focuses on fitting logistic regression models to determine whether the relationships between incidence of cardiovascular disease and predictors of interest are statistically significant.

This activity aligns with the healthcare and life sciences industry. It uses data from a clinical study conducted to identify characteristics contributing to cardiovascular disease.

Table of Contents Framingham Heart Study: Statistical Analysis 1 Purpose 1 SAS Software 1 Industry Alignment 1 Activity Notes and Requirements 3 Learning Objectives 3 Estimated Completion Time 3 Experience Level 3 Prerequisite Knowledge 3 Software 3 Content Knowledge 3 Additional Notes 3 Data Source 4 Introduction 4 Description of variables 4 Framingham Heart Study: Descriptive Analysis Activity 5 Part 1: Data Setup 5 Part 2: Statistical Analysis of Relationships Between CHD Outcome and Predictors 5 Appendix 9 Appendix A: Access Software 9 Appendix B: Data Information 9 Appendix C: Helpful Documentation 9 Appendix D: Recommended Learning 9

This activity is designed to practice statistical analyses appropriate for a binary outcome. The objectives are to:

· Fit a logistic regression model.

· Compute and interpret odds ratios and associated confidence intervals.

· Fit several logistic regression models using backwards and forwards model selection techniques and identify a best fitting model.

This activity will take students approximately 3 hours to complete.

To complete this activity students should have the following levels of experience:

· Intermediate skill in SAS programming

· Intermediate skill in statistics

Students should have experience with the following:

Students should have experience/knowledge with the following concepts:

· Logistic regression models incorporating one or more predictors.

· Odds ratios and their interpretation.

· Model selection techniques such as forwards and backwards selection.

· Comparing models using the Akaike information criteria (AIC)

This activity pairs well with the following activities in the Academic Hub:

· Framingham Heart Study: Data Preparation, Industry Applied Activity

· Framingham Heart Study: Descriptive Analysis, Industry Applied Activity

The variables contained in this dataset are:

Before beginning this activity, create a SAS library called HEARTLIB and store the MYHEART dataset in this library. If you have not previously completed the Framingham Heart Study: Data Preparation, Industry Applied Activity, make sure to familiarize yourself with the MYHEART dataset prior to attempting Part 2.

The Framingham Heart Study aimed to identify characteristics contributing to cardiovascular disease. Numerous potential predictors were collected as well as whether the patient was diagnosed with coronary heart disease. This activity focuses on fitting and comparing logistic regression models to determine whether the relationships between incidence of cardiovascular disease and predictors of interest are statistically significant. These statistical analyses are conducted in two stages. You will first fit univariate logistic regression models relating incidence of CHD to each predictor. Following these analyses, you will fit several multivariate logistic regression models to determine the best set of predictors which together model incidence of CHD.

1. Construct a univariate logistic regression model with CHD=1 as the outcome and one of several categorical variables as the predictor.

a. Use HEARTLIB.MYHEART as the input dataset.

b. Construct a univariate model for each of these predictors:

i. BP_Status

ii. Smoking_StatusNew

iii. Weight_StatusNew

iv. Chol_StatusNew

v. Sex_New

c. Note the AIC model fit statistic for each model.

d. Compute odds ratios and associated 95% confidence interval for odds of CHD=1 for all pair-wise comparisons of levels of each predictor. For example, for BP_Status, compare High vs Normal, High vs. Optimal, and Normal vs. Optimal. Designate CHD=0 as the reference level so that all odds ratios are comparing the odds of CHD=1 in the numerator to the odds of CHD=0 in the denominator.

e. After completing parts a-d, answer these questions:

i. Which model had the lowest AIC value, indicating the best fitting model?

ii. Which pairwise combinations of variable levels have odds ratios that show the levels are statistically different from each other in incidence of CHD?

iii. Which variable had the largest pairwise odds ratio comparing any two of its levels?

iv. What do you conclude about the univariate relationships between CHD and the categorical predictors of interest?

2. Construct a univariate logistic regression model with CHD=1 as the outcome and one of several continuous variables as the predictor.

a. Use HEARTLIB.MYHEART as the input dataset.

b. Construct a univariate model for each of these predictors:

i. Diastolic

ii. Systolic

iii. Smoking

iv. MRW

v. Cholesterol

c. Previous descriptive analyses show a quadratic relationship between the logit of CHD and each of Diastolic, Systolic, MRW, and Cholesterol. Given this, include linear and quadratic terms in the models including the predictors Diastolic, Systolic, MRW, and Cholesterol. Include only a linear term in the model including the predictor Smoking.

d. State the AIC model fit statistic for each model.

e. Compute odds ratios and associated 95% confidence intervals for the following predictor values and units. Designate CHD=0 as the reference level so that all odds ratios are comparing the odds of CHD=1 in the numerator to the odds of CHD=0 in the denominator.

i. At Diastolic= 80, 90, and 100 compared to a 10-unit increase.

ii. At Systolic= 120, 130, and 140 compared to a 10-unit increase.

iii. At Smoking=0 compared to a 5-unit increase.

iv. At MRW=100 and 150 compared to a 25-unit increase.

v. At Cholesterol=150 and 200 compared to a 50-unit increase.

f. After completing parts a-e, answer these questions:

i. Which model had the lowest AIC value, indicating the best fitting model?

ii. Which computed odds ratios showed statistically significant relationships?

iii. What do you conclude about the univariate relationships between CHD and the continuous predictors of interest?

g. After completing question 1, parts a-d, and question 2, parts a-e, answer these questions:

i. Considering models fit in both questions 1 and 2, compare the AIC for the model for each continuous predictor generated in question 2 to the model for its associated categorical predictor(s) generated in question 1. For example, compare the AICs from the models for BP_Status, Diastolic, and Systolic. Which model has the lowest AIC? In general, do models with continuous or categorical predictors fit better?

ii. Over all models fit in questions 1 and 2, which model and associated predictor had the lowest AIC?

3. Perform stepwise model selection to fit a multivariate logistic regression model with the best set of predictors for modeling the incidence of CHD.

a. Use HEARTLIB.MYHEART as the input dataset.

b. Include in the set of predictor variables the variable Sex_New as well as all continuous predictors examined in question 2.

c. Make sure to include the quadratic predictors included in models for question 2.

d. Use significance level as the criteria to determine which variables enter or leave the model. Use 0.05 as the significance level to enter the model and 0.05 as the significance level to stay in the model.

e. Make sure to note the AIC of the final model.

f. Which predictors are included in the final model?

4. Repeat question 3 using backwards model selection.

a. Which predictors are included in the final model when using backwards model selection? Are these different than the predictors selected via stepwise model selection?

b. Compare the AIC values of the final models generated in questions 3 and 4. Which one has the lower AIC? How do these AIC values compare to the AIC values of the models generated in questions 1 and 2?

c. Overall, what do you conclude from the best models obtained in questions 3 and 4 about the most important predictors of CHD?

Congratulations- you have completed a statistical analysis of the predictors of coronary heart disease! Additional analyses of interest in the actual Framingham heart study include a survival analysis of predictors of time to coronary heart disease as well as longitudinal analyses of data collected over the 32 biennial exams in the study.

The original cohort of the Framingham Heart study consisted of 5,209 men and women between the ages of 28 and 62 living in Framingham, Massachusetts. The first visit of data collection for participants in this cohort occurred between 1948 and 1953, and participants were assessed every two years thereafter through April 2014—almost 7 decades! Important links between cardiovascular disease and high blood pressure, high cholesterol levels, cigarette smoking, and many other health factors were first established using its data.

The complete Framingham Heart Study data consists of hundreds of datasets taken over time at 32 biennial exams and has led to over 3000 (wow!) published journal articles. To simplify analyses for illustrative purposes, the SASHELP.HEART dataset includes a snapshot of selected primary study variables taken at one of the biennial exams.

Below are helpful links to documentation regarding the procedures used in the activity.