1. Introduction to analysis DAGitty
Hein Stigum
Presentation, data and programs at:
courses
        Tid Samlet    
09:00 09:45 Continuous symmetrical :45  
10:00 10:45 (Skewed) and categorical+ intro to groups 00:45 01:30   Bivariate
11:00 11:45   Groups :45    
11:45 12:30 Lunch :45  
12:30 13:15   Groups cont :45 01:30   Groups
13:30 14:15 Plenary :45  
14:30 16:00   Regression :30 01:30   Regression
Nov-18
H.S.

2. Agenda Outcome variable decides analysis
Factors that influence analysis
Concepts
DAGitty
Bivariate analysis
Continuous symmetrical
Continuous skewed
Categorical
Multivariable analysis
Linear regression
Logistic regression
Here: emphasis on bivar
Real world: emphasis on multivariable
Need course in linear and logistic
Outcome variable decides analysis
Nov-18
H.S.

3. Factors that influence analysis
Nov-18
H.S.

4. Factors that influence analysis
Sampling
Simple random simple analysis
Stratified/clustered weighted analysis
Design
Cross-section -
Cohort survival analysis
Trad. Case-Control logistic regression
Outcome variable type
Decides analysis type
Nov-18
H.S.

5. Sampling Area 1 100.000 Population Area 2 10.000 N Random sample N=200
prevalence?
Stratified sample
N=100, 100
100
100
Disease 5%
10%
average=7.5%
Stata: survey commands ,prefix svy:
SPSS: ?
Sampling p
100/
100/10.000
Weights=1/p
1000
100
1000∗5%+100∗10%
Weighted average
=5.5%
Nov-18
H.S.

6. Sampling and analysis C E D Stratified sampling
Use weighted analysis (Stata: svy, SPSS:?)
Can ignore sampling if:
Only report prevalence by strata, not overall
Prevalences by strata are similar
Regression:
The strata act as risk factors or confounders for disease, can adjust for stratum C
stratum E D
Nov-18
H.S.

7. Risk, Rate and Odds Risk Rate Odds probability, proportion, %
Km/h, cases/person-time
2 math quatities
prop: fraction, numerator (top) is part of denominator (bottom)
ex: colds in class=2/30=7% , no dimension, 0-1
rate: change in one quantity per change in another (time),
ex: speed, drive 100 km in 2 h then average speed is 50 km/h, dimension, no upper bound
Odds: disease per healthy person
Statistical concept:
risk: probability, no dimension,
ex: flip coin
Nov-18
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8. Cohorts Closed cohort Open cohort Count persons, risk
Count person-time, rate
Closed cohort with time varying covariates
Line= follow up
Circle=event (disease)
Red line=exposed
Count person-time, rate
Nov-18
H.S.

9. Design and analysis Cross-section Cohort Traditional Case-Control -
Closed cohort risk Log-risk (or logistic)
Open cohort rate Cox-regression
Traditional Case-Control
Unmatched odds Logistic regression
Matched odds Conditional Logistic
Nov-18
H.S.

10. Datatypes Outcome variable decides analysis Categorical data
Nominal: married/ single/ divorced
Ordinal: small/ medium/ large
binary
Numerical data
Discrete: number of children
Continuous: weight
Coding 1, 2, 3, is 2 twice as much as 1
1. Set of methods for categorical data
proportion married
1. Set of methods for numerical data
average weight
Outcome variable decides analysis
Nov-18
H.S.

11. Outcome data type dictates type of analysis
Start with continuous data
Nov-18
H.S.

12. Data- and regression-types
Numerical data
Continuous (weight) Linear regression
Count (partners) Poisson regression
Categorical data
Binary (death)
Risk Linear-risk-, log-risk model
Rate Cox, Poisson
Odds logistic
Ordinal (small, med, large) ordered logistic
Multinomial (mar. status) multinomial logistic
11/18/2018
H.S.

13. Why Stata Pro Con Price Aimed at epidemiology Many methods, growing
Graphics
Structured, Programmable
Coming soon to a course near you
Con
Memory>file size
Used by leading univ, and at many summer schools
Copy tables esttab
Nov-18
Nov-18
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H.S. 13

14. Bias and precision
Concepts
Nov-18
H.S.

15. Precision and bias Measures of populations precision random error
bias systematic error
True
value
Estimate
Precision
Bias
Ignore errors at individual level
measure pop, measure sample
aim: measure as precisely and as correctly as possible
Nov-18
H.S.

16. P-values and confidence intervals
Precision
Nov-18
H.S.

17. Precision: Estimation
Population
Sample
Estimate with confidence interval
Tilfeldig utvalg
Bidrag til usikkerhet: stor spredning, lite utvalg
( | )
95% confidence interval: 95% of repeated intervals
will contain the true value
Nov-18
H.S.

18. Precision: Testing Population Sample |
group 1
group 2
Two groups that we want to compare
So much for theory, practical analysis
p-value=P(observing this difference or more,
when the true difference is zero)
Nov-18
H.S.

19. Precision: Significance level
Birth weight, 500 newborn, observe difference
H0: boys=girls
10 gr p=0.90
50 gr p=0.40
100 gr p=0.10
130 gr p=0.04
150 gr p=0.02
Ha: boys≠girls
p<0.05
Significance level
Halvparten gutter, standard avvik=700 gr i begge grupper
Nov-18
H.S.

20. Precision: Test situations
1 sample test
Weight =10
2 independent samples
Weight by sex
K independent samples
Weight by age groups
2 dependent samples
Weight last year = Weight today
Analytic
Nov-18
H.S.

21. DAGitty
Causal graphs
Nov-18
H.S.

22. Bias: DAGs E D C2 C1 Associations Bivariate (unadjusted)
gest age D
birth weight C2
parity C1
sex
Associations Bivariate (unadjusted)
Causal effects Multivariable (adjusted)
Reasons for doing bivar: closer to data, find category codings, missing, empty cells, …
Reasons for reporting bivar: ?
Draw your assumptions before your conclusions
Nov-18
H.S.

23. DAGitty Free program to draw and analyze DAGS Nov-18 Nov-18 Nov-18
1h presentation+exercises or
Just exersises (add more)
DAGitty
Nov-18
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24. DAGitty background DAGitty Web page Draw DAGs Analyze DAGs Test DAGs
Run or download
Johannes Textor, Theoretical Biology & Bioinformatics group, University of Utrecht
Nov-18 HS

25. Interface
Nov-18 HS

26. Draw model Draw new model New variables, connect, rename
Model>New model, Exposure, Outcome
New variables, connect, rename
n new variable (or double click)
c connect (hit c over V1 and over V2 to connect)
r rename
d delete
Status (toggle on/off)
e exposure
o outcome
u unobserved
a adjusted
Draw Viatmin->Birth defects example
Draw E and D
New Age and Obesity
Connect
a-adjust, u-unobserved
Nov-18 HS

27. Export DAG Export to Word or PowerPoint
“Zoom” the DAGitty drawing first (Ctrl-roll)
Use “Snipping tool” or
use Model>Export as PDF
Without zooming
With zooming
Nov-18 HS

28. Model code Variable x y Age 1 @ 0.151, 0.840
Birth%20defects O @ 0.468,
Obesity 1 @ 0.470,
Vitamin E @ 0.145, x
Arrow list
Age Obesity Vitamin
Obesity Birth%20defects
Vitamin Birth%20defects y
May change the x and y values to align the variables
Nov-18 HS

29. Changed model code Aligning x and y coordinates (no space after ,)
Age 1 @0.1,0.8
Birth%20defects O @0.5,1.0
Obesity 1 @0.5,0.8
Vitamin E @0.1,1.0
Age Obesity Vitamin
Obesity Birth%20defects
Vitamin Birth%20defects
0.1
0.5 x
0.8
1.0
Copy, paste and Update DAG y
Nov-18 HS

30. Exercises
Nov-18 HS

31. Exercise Draw the Vitamin-Birth defects DAG
Use Obesity as an observed variable.
Interpret the “Causal effect identification”
Interpret the “Testable implications”
Add arrow from Age to Birth defects
Make obesity an unobserved variable
Nov-18 HS

32. Excercise
Draw the Statin-CHD DAG Use Lifestyle as an unobserved variable.
Interpret the “Causal effect ident.” for total effects
Interpret the “Causal effect ident.” for direct effects
Interpret the “Testable implications” C
cholesterol U
lifestyle E
statin D
CHD
Nov-18 HS

33. Effects of adjustment
Nov-18
H.S.

34. Effects of adjustment A C B E D What variables should we adjust for?
What are the effects of adjustment? E D
Variable
Adjust
Bias
Precision A B C no
bias amplification
reduce precision (collinearity)
maybe no
improve precision (model dependent)
yes
remove confounding ?
(Pearl 2011)

35. Effects of adjustment: PrecisionB
Should we adjust for B?
DAG: no bias from B, need not adjust E D
May include B to improve precision, depends on model!
E->D=1 in linear regr
C->D=2 in linear regr
D2=10% in logistic, crude E->D=1.17, adjusted E->D=1.43,
no E-C interaction
Including B: better precision
Including B: worse precision
OR not collapsible
Robinson and Jewell 1991; Xing and Xing 2010
Nov-18
H.S.

36. Why plot data?
Nov-18
H.S.

37. Problem example Lunch meals per week
Table of means (around 5 per week)
Linear regression
Nov-18
H.S.

38. Problem example 2 Iron level by sex
Both linear and logistic regression
Opposite results
(boys: higher mean, but more deficiency)
Iron level in blood
Nov-18
H.S.

39. Bivariate analysis 1 Continuous symmetric outcome: Birth weight Nov-18
H.S.

40. Distribution drop if weight<2000 kdensity weight kdensity weight
Nov-18
H.S.

41. Central tendency and dispersion
Mean and standard deviation:
Mean with confidence interval:
Std Dev for Data
Std Err for Estimate
*550=2500
3600+2*550=4700
Nov-18
H.S.

42. Compare groups, equal variance?
Not equal
Compare boys and girls
Focus on means or focus on low tail gives opposite results!!
Nov-18
H.S.

43. 2 independent samples Are birth weights the same for boys and girls?
Density plot
Scatterplot
Scatter to see linear/no-linear effect, look for outliers
Density to see equal variance
Nov-18
H.S.

44. 2 independent samples test
ttest weight, by(sex) unequal unequal variances
ttest var1==var2 paired test
Nov-18
H.S.

45. K independent samples Is birth weight the same over parity?
Density plot
Scatterplot
Scatter to see linear/no-linear effect, look for outliers
Density to see equal variance
(possibly a bit larger variance in the 2-7 (red) group)
Nov-18
H.S.

46. K independent samples test
equal means?
Equal variances?
Nov-18
H.S.

47. Continuous by continuous
Does birth weight depend on gestational age?
Scatterplot
Scatterplot, outlier dropped
Nov-18
H.S.

48. Continuous by continuous tests
Cut gestational age up in groups, then use T-test or ANOVA or
Use linear regression with 1 covariate
Nov-18
H.S.

49. Test situations 1 sample test 2 independent samples
ttest weight =10
2 independent samples
test weight, by(sex)
K independent samples
oneway weight parity
2 dependent samples (Paired)
ttest weight_last_year == weight_today
1: ttest weight=10
4: ttest weight0=weight1 (assumes paired test)
Nov-18
H.S.

50. Continuous skewed outcome: Number of sexual partners
Bivariate analysis 2
Nov-18
H.S.

51. Distribution kdensity partners if partners<=50 Nov-18 H.S.
Lower 75% fractile here than on next page because partner>50 are dropped here
Nov-18
H.S.

52. Central tendency and dispersion
Median and percentiles:
cci binomial exact; conservative confidence interval
normal normal, based on observed centiles
meansd normal, based on mean and standard deviation
Nov-18
H.S.

53. 2 independent samples
Do males and females have the same number of partners?
Scatterplot
Density plot
Scatter to see linear/no-linear effect, look for outliers
Density to see equal variance
Unequal variance! Test somewhat problematic
N=400, quite skewed, probably need nonparametric tests.
If N is large, and/or not very skewed, the means will still follow a normal distribution and standard (parametric) test will do
Nov-18
H.S.

54. 2 independent samples test
equal medians?
Nov-18
H.S.

55. K independent samples Do partners vary with age? Scatterplot
Density plot
Scatter to see linear/no-linear effect, look for outliers
Problems with unequal variance
Density difficult to read, no apparent differences
Nov-18
H.S.

56. K independent samples test
equal medians?
Probably a cohort effect rather than an age effect
Nov-18
H.S.

57. Table of descriptives
Nov-18
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58. Table of tests Remarks: If unequal variance in ANOVA:
Use linear regression with robust variance estimation
If N is large:
may use parametric tests
Categorical ordered:
use nonparametric tests
Mann-Whithey U=Wilcoxon rank sum
Nov-18
H.S.

59. Categorical outcome: Being bullied
Bivariate analysis 3
Nov-18
H.S.

60. Frequency and proportion
Proportion with CI:
Proportion:
May standardize, adjust for clusters, use bootstrap or jacknife est
May weigth if stratified sample
Nov-18
H.S.

61. Proportion, confidence interval
x=”disease”
n=total number
proportion:
standard error:
confidence interval:
How much increase n to get half the standard error?
Nov-18
H.S.

62. Crosstables Are boys bullied as much as girls? equal proportions?
Nov-18
H.S.

63. Ordered categories, trend
equal proportions?
Nov-18
H.S.

64. Table of tests Remarks: If unequal variance in ANOVA:
Use linear regression with robust variance estimation
If N is large:
may use parametric tests
Categorical ordered:
use nonparametric tests
Mann-Whithey U=Wilcoxon rank sum
Nov-18
H.S.

65. Multivariable analysis 1
Continuous outcome: Linear regression, Birth weight
Multivariable analysis 1
Nov-18
H.S.

66. Regression idea Nov-18 H.S. X=gest, Y=weigth
straigth line: y=constant +slope times x
beta0=constant or intercept, beta1=reg. coef. Or slope, y=dep. continous, x=..
Nov-18
H.S.

67. Model and assumptions Model Association measure Assumptions Robustness
1 = increase in y for one unit increase in x1
Assumptions
Independent errors
Linear effects
Constant error variance
Robustness
influence
In GLM b-s and betas are coefficients
In some fields (and in SPSS) b-s are coefs and betas are standardizes coefs
Nov-18
H.S.

68. Workflow DAG Scatterplots Bivariate analysis Regression
Model estimation
Test of assumptions
Independent errors
Linear effects
Constant error variance
Robustness
Influence E
gest age D
birth weight C2
parity C1
sex
Model fitting
Adjust if cofactor is confounder, problems cofacor has missing, cofactor has error, cofactor is in causal path
Test of assumptions
Stata: Estimation remains in memory. Post estimation commands
Normally do assumtions first, then influence.
Note leverage value of outlier
Nov-18
H.S.

69. Categorical covariates
2 categories OK
3+ categories
Use “dummies”
“Dummies” are 0/1 variables used to create contrasts
Want 3 categories for parity: 0, 1 and 2-7 children
Choose 0 as reference
Make dummies for the two other categories
generate Parity1 = (parity==1) if parity<.
generate Parity2_7 = (parity>=2) if parity<.
Nov-18
H.S.

70. Create meaningful constant
Expected birth weight at:
gest= 0, sex=0, parity=0, not meaningful
gest=280, sex=1, parity=0
Sex is coded 1=boys and 2=girls

71. Model estimation
Nov-18
H.S.

72. Test of assumptions Plot residuals versus predicted y
Independent residuals?
Linear effects?
constant variance?
Dependent residuals if many children from same mother Or
Nov-18
H.S.

73. Violations of assumptions
Dependent residuals
Use mixed models or GEE
Non linear effects
Add square term
Non-constant variance
Use robust variance estimation
Linear mixed models: xtmixed
Nov-18
H.S.

74. Influence
Beta changes from 6 to 16 when removing influential outlier
Nov-18
H.S.

75. Measures of influence Measure change in: Predicted outcome Deviance
Remove obs 1, see change
remove obs 2, see change
Measure change in:
Predicted outcome
Deviance
Coefficients (beta)
Delta beta
Nov-18
H.S.

76. Delta beta for gestational age
If obs nr 539 is removed, beta will change from 6 to 16
Nov-18
H.S.

77. Removing outlier Full model Outlier removed
One outlier affected two estimates
Final model
Nov-18
H.S.

78. Multivariable analysis 2
Binary outcome: Logistic regression, Being bullied
Multivariable analysis 2
Nov-18
H.S.

79. Ordered categories and model
Interval versus ordered scale:
Interval scale
Ordered scale 1 2 3
low
medium
high
Categories
Regression model 2
Logistic
3-7
Ordinal logistic
>7
Linear (treat as interval)
Nov-18
H.S.

80. Logistic model and assumptions
Association measure
Odds ratio in y for 1 unit increase in x1
Assumptions
Independent errors
Linear effects on the log odds scale
Robustness
influence
Nov-18
H.S.

81. Being bullied We want the total effect of country on being bullied.
The risk of being bullied depends on age and sex.
The age and sex distribution may differ between countries.
Should we adjust for age and sex? C1
age E
country D
bullied C2
sex
Noncausal open=biasing path
No, age and sex are mediating variables
Nov-18
Nov-18
Nov-18
H.S.
H.S. 81 81 81

82. Logistic: being bullied
Roughly:
Same risk of being bullied in Island as in Sweden.
2 times the risk in Norway
as in Sweden.
3 times the risk in Finnland
Prevalence of being bullied=17%
OR RR
ORRR if outcome is rare
OR>RR (further from 1) if the outcome is common
Nov-18
H.S.

83. Summing up DAGs Plots Bivariate analysis Multivariable analysis
State prior knowledge. Guide analysis
Plots
Linearity, variance, outliers
Bivariate analysis
Continuous symmetrical Mean, T-test, anova
Continuous skewed Median, nonparametric
Categorical Freq, cross, chi-square
Multivariable analysis
Continuous Linear regression
Binary Logistic regression
Model fitting
Adjust if cofactor is confounder, problems cofacor has missing, cofactor has error, cofactor is in causal path
Test of assumptions
Stata: Estimation remains in memory. Post estimation commands
Normally do assumtions first, then influence.
Note leverage value of outlier
Nov-18
H.S.