Lecture 18: Multivariable Models

Question 1

Review: What will happen if confounding is not controlled?

Answer 1

-We will get a biased estimate of the association of the exposure variable of interest with outcome
-ex the RR or OR for the association b/w exposure of interest and outcome will be incorrect

Question 2

Which method to control confounding will be useful in this lecture and why?

Answer 2

5. Multivariable modeling
   -bc it can be used to control for multiple potential CFVs

Question 3

What is a recap from the video shown in class?

Answer 3

-line of best fit = regression line
- But instead of y=mx+b turns where mx is slope and b is y-intercept, the notation Y= Bo +B1X1is used
EX
Y (income)= B0 (the intercept) + B1 (education)
-if B1 is a pos number: positive relationship with outcome
-if B1 is neg number: negative relationship with outcome
-if B1 = 0 no relationship

Question 4

Why do we use multivariable models?

Answer 4

-Predict the value of a dependent variable (Y) from the explanatory variables (X’s) using the optimal equation which relate Y to the X values
-Determine which explanatory variables are important predictors of the dependant variable and the extent to which they influence the dependent variable
-Study the relationship b/w the dependent variable and each of the explanatory variables while controlling for the effect of other explanatory variables
-Multiple regression allows the investigation of multiple explanatory factors at once

Question 5

What are the dependant/outcome variables (Y)?

Answer 5

-Can be continuous –> use LINEAR regression
ex body weight, milk production, blood glucose concentration

-Can be dichotomous–> use LOGISITIC regression
ex 2 possibilities pregnant or not, diseased or not

*the explanatory variables can be continuous, dichotomous or categorical with either regression approach, choice of model depends on outcome not exposure

Question 6

What are the independent/explanatory variables (X)?

Answer 6

Continuous: age, weight, gestation length (weeks)

Dichotomous (yes/no): male/female, vax/not vax, etc

Categorical: (greater or equal to 2 levels): breed, nationality, education level, age (if range: 10-20yrs)

Question 7

What should be presented in a regression model?

Answer 7

-outcome should be stated
-All explanatory variables in the model should be listed as well as their
-Unit of increase (for continuous) ex age= 1 year
-Referent category (for dichotomous/categorical variables): type of animal 0=dairy cow, 1= beef cow

For each explanatory variable:
-regression coefficient, and its standard error
-p-value and/or better yet, 95% confidence interval

-Model intercept (B0)

Question 8

What are some examples of linear regressions for continuous outcomes?

Answer 8

Standard equation: Y= B0 + B1X1 +B2X2 + B3X3….

-allows estimation of the linear effect of an explanatory variable (X), on the outcome (Y), after controlling for the potential confounding effects of the other variables in the model
-So B1 represents the average range in Y for a unit change in X1 when the other explanatory variables (X2,X3 etc) are held constant

Question 9

What are some examples of logistic regressions for dichotomous outcomes?

Answer 9

Standard equation: Y= B0 + B1X1 + B2X2 + B3X3 etc….
-Note Y is the natural log of the odds of outcome so e^coefficient = odds ratio of the outcome for a unit increase in the explanatory variable, keeping the values of the other variables in the model constant