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Course Information
Meet the Teaching Team -
Course Dataset 1
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Course Dataset 2
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MODULE A1: INTRODUCTION TO STATISTICS USING R, STATA, AND SPSSA1.1 What is Statistics?
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A1.2.1a Introduction to Stata
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A1.2.2b: Introduction to R
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A1.2.2c: Introduction to SPSS
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A1.3: Descriptive Statistics
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A1.4: Estimates and Confidence Intervals
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A1.5: Hypothesis Testing
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A1.6: Transforming Variables
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End of Module A11 Quiz
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MODULE A2: POWER & SAMPLE SIZE CALCULATIONSA2.1 Key Concepts
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A2.2 Power calculations for a difference in means
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A2.3 Power Calculations for a difference in proportions
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A2.4 Sample Size Calculation for RCTs
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A2.5 Sample size calculations for cross-sectional studies (or surveys)
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A2.6 Sample size calculations for case-control studies
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End of Module A21 Quiz
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MODULE B1: LINEAR REGRESSIONB1.1 Correlation and Scatterplots
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B1.2 Differences Between Means (ANOVA 1)
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B1.3 Univariable Linear Regression
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B1.4 Multivariable Linear Regression
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B1.5 Model Selection and F-Tests
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B1.6 Regression Diagnostics
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End of Module B11 Quiz
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MODULE B2: MULTIPLE COMPARISONS & REPEATED MEASURESB2.1 ANOVA Revisited – Post-Hoc Testing
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B2.2 Correcting For Multiple Comparisons
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B2.3 Two-way ANOVA
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B2.4 Repeated Measures and the Paired T-Test
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B2.5 Repeated Measures ANOVA
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End of Module B21 Quiz
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MODULE B3: NON-PARAMETRIC MEASURESB3.1 The Parametric Assumptions
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B3.2 Mann-Whitney U Test
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B3.3 Kruskal-Wallis Test
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B3.4 Wilcoxon Signed Rank Test
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B3.5 Friedman Test
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B3.6 Spearman’s Rank Order Correlation
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End of Module B31 Quiz
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MODULE C1: BINARY OUTCOME DATA & LOGISTIC REGRESSIONC1.1 Introduction to Prevalence, Risk, Odds and Rates
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C1.2 The Chi-Square Test and the Test For Trend
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C1.3 Univariable Logistic Regression
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C1.4 Multivariable Logistic Regression
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End of Module C11 Quiz
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MODULE C2: SURVIVAL DATAC2.1 Introduction to Survival Data
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C2.2 Kaplan-Meier Survival Function & the Log Rank Test
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C2.3 Cox Proportional Hazards Regression
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C2.4 Poisson Regression
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End of Module C21 Quiz
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A Note about the Fossa Certificate
Learning Outcomes
By the end of this section, students will be able to:
- Control the association of an exposure for additional variables in a logistic regression model
You can download a copy of the slides here: Video C1.4
Video C1.4 – Controlling for Confounding in Logistic Regression (6 minutes)
C1.4 PRACTICAL: Stata
Controlling for confounders in a logistic regression
Now use the logistic command to obtain the odds ratio for prior CVD with hypertension, adjusted for HDL-C. Similar to the command in linear regression, we add additional variables after the exposure on the command line. This may be obtained as follows:
logistic prior_cvd hyperten hdlc
Note that the output gives us the odds ratio for ‘hyperten’ adjusted for ‘hdlc’ but it also gives us the odds ratios for ‘hdlc’ adjusted for ‘hyperten’.
You will run and interpret this command in the questions below.
We can control for additional variables as well by adding additional variables to the command line as we did above with ‘hdlc’. Each variable we put in the model will be controlled for all the other variables in the model. That is, if we add BMI group to this logistic regression above, we would interpret the coefficient for hypertension as ‘the association of hypertension with the odds of prior CVD, independent (or adjusted for) of HDL-C and BMI group’. BMI group would likewise be interpreted as the association of BMI group with prior CVD, once adjusted for hypertension and HDL-C.
Question C1.4b: What are the odds of having prior CVD if a participant is hypertensive, once you have adjusted for their levels of HDL-C?
C1.4b Answers
Answer C1.4b:
logistic prior_cvd i.hyperten hdlc
Logistic regression                   Number of obs =  4,293
                            LR chi2(2)   =  86.59
                            Prob > chi2  = 0.0000
Log likelihood = -2371.6353 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Pseudo R2 Â Â = 0.0179
——————————————————————————
  prior_cvd | Odds ratio  Std. err.    z   P>|z|   [95% conf. interval]
————-+—————————————————————-
 1.hyperten |  1.551415  .1191582   5.72  0.000   1.334598   1.803456
    hdlc |  .4996367  .0501632   -6.91  0.000   .4103876   .6082952
    _cons |  .6155069   .070238   -4.25  0.000   .4921515   .7697807
——————————————————————————
Note: _cons estimates baseline odds.
Here, the odds ratio for prior CVD is 1.55 times greater for participants that are hypertensive rather than normotensive, once adjusted for HDL-C (95% CI: 1.33-1.80).
C1.4 PRACTICAL: SPSS
Controlling for confounders in a logistic regression
You can control for additional variables by adding more variables to the ‘Covariates’ box within the logistic regression analysis pop up. Here we are going to use this to obtain the odds ratio for prior CVD with hypertension, adjusted for HDL-C.
Each variable we put in the model will be controlled for all the other variables in the model. That is, if we add BMI group to this logistic regression above, we would interpret the coefficient for hypertension as ‘the association of hypertension with the odds of prior CVD, independent (or adjusted for) of HDL-C and BMI group’. BMI group would likewise be interpreted as the association of BMI group with prior CVD, once adjusted for hypertension and HDL-C.
Question C1.4a: What are the odds of having prior CVD if a participant is hypertensive, once you have adjusted for their levels of HDL-C?
Answer
The output table will look like the below.
Here, the odds ratio for prior CVD is 1.55 times greater for participants that are hypertensive rather than normotensive, once adjusted for HDL-C (95% CI: 1.34-1.80).
C1.4 PRACTICAL: R
Controlling for confounders in a logistic regression
Now use the ‘glm() ‘ command to obtain the odds ratio for prior CVD with hypertension, adjusted for HDL-C. This may be obtained as follows:
model <- glm(prior_cvd ~ hypertens + hdlc, family = binomial(link = “logit”), data = df)
Note that the output gives us the odds ratio for ‘hyperten’ adjusted for ‘hdlc’ but it also gives us the odds ratios for ‘hdlc’ adjusted for ‘hyperten’.
You will run and interpret this command in the questions below.
We can control for additional variables as well by adding additional variables to the command line as we did above with ‘hdlc’. Each variable we put in the model will be controlled for all the other variables in the model. That is, if we add BMI group to this logistic regression above, we would interpret the coefficient for hypertension as ‘the association of hypertension with the odds of prior CVD, independent of (or adjusted for) HDL-C and BMI group’. BMI group would likewise be interpreted as the association of BMI group with prior CVD, once adjusted for hypertension and HDL-C.
- Question C1.4b: What are the odds of having prior CVD if a participant is hypertensive, once you have adjusted for their levels of HDL-C?
Answer
Answer C1.4a:
> model8 <- glm(prior_cvd ~ hyperten + hdlc, family = binomial(link = “logit”), data = df)
> summary(model8)
Call:
glm(formula = prior_cvd ~ hyperten + hdlc, family = binomial(link = “logit”), data = df)
Deviance Residuals:Â
  Min    1Q  Median    3Q    Max Â
-1.1004 Â -0.7844 Â -0.6978 Â 1.2748 Â 2.3248 Â
Coefficients:
      Estimate Std. Error z value Pr(>|z|)  Â
(Intercept) Â -0.4722 Â Â 0.1144 Â -4.127 3.67e-05 ***
hyperten    0.4432   0.0770  5.756 8.59e-09 ***
hdlc     -0.7038   0.1007  -6.991 2.73e-12 ***
—
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
  Null deviance: 4805.5  on 4265  degrees of freedom
Residual deviance: 4717.3 Â on 4263 Â degrees of freedom
AIC: 4723.3
Number of Fisher Scoring iterations: 4
> exp(cbind(coef(model8), confint(model8)))
Waiting for profiling to be done…
             2.5 %   97.5 %
(Intercept) 0.6236630 0.4984294 0.7805407
hyperten   1.5577272 1.3388762 1.8107175
hdlc     0.4946928 0.4055012 0.6017479Â
Here, the odds ratio for prior CVD is 1.56 times higher in those with hypertension compared to those without hypertension, after adjusting for HDL-C (OR: 1.56, 95% CI: 1.34-1.81).
This is crystal clear