Biostatistics - slides considerations for reseaarch

biostatistics

1. Frankline M. Onchiri, Ph.D.
Seattle Children’s Research Institute (SCRI)
Statistical Considerations for
Dental and Craniofacial
Research

2. Classification of variable according to their intended use
Outcome Y
Variable that is primary focus of study. We estimate some summary
measure of the distribution of Y within groups defined by exposure/POI
Predictor of
Interest (POI)X
1
Variable that may influence size or occurrence of outcome. In RCT, this is
intervention being studied. We divide population into subpopulations based on
this variable
Effect ModifierX
2
Stratification variable: Effect modifiers define subgroups in which the
association between the response and POI is different. Effect of an exposure
differs among different subgroups of this variable.
Confounder
X
3
•Variable that is associated with predictor and, which also is associated with
outcome independent of predictor, and is NOT in causal pathway between
predictor & outcome.
•We also use these variables to divide the population into subpopulations. Each
individual in given subpopulation will have the same value of each of the C
Precision X
4
Associated with outcome variable only but whose adjustment will provide
precise estimates of association
Others X
5variables to describe the study sample
Measurements –Pre-specify covariates in protocol based on clinical and statistical reasoning

3. Statistical Role of Variables
Statistical Role
Response/outcome/
Disease
Grouping variables
Predictor/Exposure
of interest
Effect modifier /
Stratifying variable
Adjustment for covariates
Confounders
Precision variables

4. Statistical roles of variables
4
Outcome/dependent variable
/effects /dependent/disease
Confounders
•Associated with outcome and
exposure, NOT in causal
pathway between exposure
and outcome
? Association of interest TBDPrimary predictors/ risk factors
/Independent vars/Cofactors
Precision variables
•Associated with outcome only
Intermediate variable
Adjustment for covariates: Confounders, Precision variables

5. Statistical roles of variables
5
Outcome/dependent variable
/effects /dependent/disease
Cofounders
•Associated with with outcome
and exposure, NOT in causal
pathway between exposure
and outcome
? Association of interest TBDPrimary predictors/ risk factors
/Independent vars/Cofactors
Precision variables
•Associated with outcome only
Variance Inflation variables
•Associated with exposure only
Intermediate variable
Pathway (downstream
effect of exposure)
Adjustment for covariates: Confounders, Precision variables
•Think about causal relationships between variables

6. Conditions for Confounding
Exposure /
Independent Variable
Outcome /
Dependent Variable
Potential
Confounder
Every confounder must meet this criteria
Pathway (downstream
effect of exposure)
Risk factor for
exposure? (Yes)
Risk factor for
outcome? (Yes)
In causal pathway? (No)

7. Statistical/Epidemiological roles of variables: Mediating variables
Alcohol
consumption
Coronary Heart
Disease
Smoking
Age
HDL (good
cholesterol)
Risk factor for
exposure? (Yes)
Risk factor for
outcome? (Yes)
In causal pathway? (Yes)
•Modest alcohol reduces CHD risk
•Does so by raising HDL
•High levels of HDL reduce risk of CHD
•Mechanism: Modest
alcohol consumption
raises HDL levels,
which in turn reduces
risk of CHD
•So, HDL is not
confounder of
association between
alcohol and CHD

8. Statistical/Epidemiological roles of variables: Mediating variables
Maternal smoking
during pregnancy
Infant Mortality
Alcohol
Age
SES
Birthweight
Risk factor for exposure?
(Yes) Risk factor for outcome?
(Yes)
In causal pathway? (Yes)

9. Statistical/Epidemiological roles of variables: Mediating variables
Diet CHD
Economic status
Serum Cholesterol
Diabetes, HPTN
Risk factor for exposure?
(Yes) Risk factor for outcome?
(Yes)
In causal pathway? (Yes)

10. DETOUR: Measures Of Disease-exposure Association
•The chances (represented with letter p) of something happening
can be expressed as a risk or as an odds:
????????????????????????????????????????????????=
Number of persons with the disease
Total Number of people in population
=????????????

Odds=
the chances of disease occurence
the chances of disease NOT occuring
=
????????????
1−????????????

•Thus a risk is a proportion,
•But an odds is a ratio ; in which the numerator and denominator sum
to one

11. 11
Relationship between incidence of Lung-Cancer and drinking
Status
Have Lung
cancer
No Lung
Cancer
Total
Heavy Drinker 33 1667 1700
No drinker 27 2273 2300
Total 60 3940 4000
•Overall: Risk of lung cancer=60/4000=0.015
•Among Heavy drinkers: Risk of lung cancer= 33/1700=0.0194
•Among Non- drinkers: Risk of lung cancer= 27/2300=0.0117
•Relative Risk (RR) is ratio of two risks
•
???????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????? ????????????????????????????????????????????????????????????????????????
???????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????????????????????????????? ????????????????????????????????????????????????????????????????????????
=
0.0194
0.0117
= 1.66
•RR of Lung cancer comparing Heavy Drinkers to Non- drinkers is 1.66

12. 13
Relationship between Smoking and CHD (Case-Control)
CHD Cases Controls Total
Smokers 112 176 288
Non-smokers 88 224 312
Total 200 400 600
•Among Cases: Proportion of Smokers=112/200=56%
•Among Cases: Odds of smoking=
0.56
1−0.56
=1.273
•Among Controls: Proportion of Smokers=
176
400
= 0.44
•Among Controls: Odds of smoking=
0.44
1−0.44
=0.785
•Odds Ratio (OR) comparing Cases and Controls
•
???????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????????????????? ????????????????????????????????????????????????????????????????????????
???????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????????????????? ???????????????????????? ????????????????????????????????????????????????????????????????????????????????????????????????
=
1.273
0.785
= 1.623

13. Generally, Odds Ratio as a Cross-Product
Exposed Have
Disease
Have no
Disease
Total
Yes a b a+b
No c d c+d
Total a+c b+d a+b+c+d
•Among Exposed: Odds of disease=
????????????/(????????????+????????????)
1−????????????/(????????????+????????????)
=
????????????
????????????
•Among Unexposed: Odds of Disease =
????????????/(????????????+????????????)
1−????????????/(????????????+????????????)
=
????????????
????????????
•Odds Ratio (OR)=
???????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????? ????????????????????????????????????????????????????????????????????????
???????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????? ???????????????????????? ???????????????????????????????????????????????????????????????????????????????????????????????????????????? ????????????????????????????????????????????????????????????????????????
=
????????????/????????????
c/d
=
????????????×????????????
c×b

14. DETOUR BACK: Conditions for Confounding
Exposure /
Independent Variable
Outcome /
Dependent Variable
Potential
Confounder
Every confounder must meet this criteria
Pathway (downstream
effect of exposure)
Risk factor for
exposure? (Yes)
Risk factor for
outcome? (Yes)
In causal pathway? (No)

15. 16
Smoking as a Confounder of relationship between Lung-Cancer
and drinking
LC No LC
Heavy Drinker 24 776
No Drinker 6 194
Smokers
OR=
24×194
6×776
= 1.0
LC No LC
Heavy Drinker 9 891
No Drinker 21 2079
Non-smokers
OR=
9×2079
21×891
= 1.0
Have Lung
cancer
No Lung
Cancer
Heavy Drinker 33 1667
No drinker 27 2273
OR=
33×2273
27×1667
= 1.666
•Among SMOKERS and NON -SMOKERS: no relationship between LC and drinking since OR=1
•Observed distorted relationship between heavy drinking and LC was due to
confounding by smoking
Crude Analysis:
Stratified Analysis:

16. For smoking to be a confounding factor, 3 conditions must be met
Heavy Drinking vs. No
Drinking
Lung Cancer
Potential Confounder:
Smoking
Pathway (downstream
effect of exposure)
Is smoking Risk factor for
Heavy Drinking?
Is smoking Risk factor for L. Cancer
independent of Heavy Drinking?
In causal pathway? (No)
Smoking No
Smoking
Heavy
Drinker
a=? b=?
No drinker c=? d=?
Lung Ca No Lca
Smoking a=? b=?
No Smoking c=? d=?

17. 18
Smoking as a Confounder of relationship between Lung-Cancer
and drinking
LCNo LC Total
smokers
Heavy Drinker24776 800
No Drinker 6 194 200
Smokers
OR=
24×194
6×776
= 1.0
LCNo LC Total
NonSmokers
Heavy Drinker9 891 900
No Drinker 212079 2100
Non-smokers
OR=
9×2079
21×891
= 1.0
Have Lung
cancer
No Lung
Cancer
Heavy Drinker 33 1667
No drinker 27 2273
OR=
33×2273
27×1667
= 1.666
•Among SMOKERS and NON -SMOKERS: no relationship between LC and drinking since OR=1•Observed distorted relationship between heavy drinking and LC was due to confounding by
smoking
Crude Analysis:
Stratified Analysis:

18. For smoking to be a confounding factor, 3 conditions must be met
Heavy Drinking vs. No
Drinking
Lung Cancer
Potential Confounder:
Smoking
Pathway (downstream
effect of exposure)
Is smoking Risk factor for
Heavy Drinking?
Is smoking Risk factor for L. Cancer
independent of Heavy Drinking?
In causal pathway? (No)
Smoking No
Smoking
Heavy
Drinker
a=800 b=900
No drinker c=200 d=2100
Lung Ca No Lca
Smoking a=6 b=194
No Smoking c=21 d=2079
OR=
800×2100
200×900
= 9.33
OR=
6×2079
21×194
= 3.06

19. Does smoking meet definition of Confounder?
Heavy Drinking vs. No
Drinking
Lung Cancer
Potential Confounder:
Smoking
Pathway (downstream
effect of exposure)
Is Smoking Risk factor for exposure?
Yes: Drinking is associated with
smoking: OR=9.33
Is Smoking Risk factor for outcome
(Lca)?
YES: Smoking is associated with
Lung cancer: OR=3.06
In causal pathway? (No)

20. Effect Modification
•Effect modification: variation relationship between exposure and
outcome due to actions of another variable (called effect modifier)
–stratum-specific measures of disease- exposure
associations are appreciably different from each other
•Strength of association between exposure and Disease depends on
an effect modifier
– association is MODIFIED by third factor.

21. Effect Modification
CASES
(D+)
CONTROLS
(D-)
E+ 10 10
E- 5 20
CASES
(D+)
CONTROLS
(D-)
E+ 10 30
E- 15 20
CASES (D+)CONTROLS (D-)
Exposed 20 40
Not
Exposed
20 40
Crude/Un- adjusted
OR= ad/bc=20*40/20*40=1.0
Stratum 2
OR=0.44
Stratum 1
OR=4.0
Crude Analysis:
Stratified Analysis:

22. Conducting Analysis by Subgroups- Stratified analysis
DiseaseNo Disease
Exposed 450 75
Unexposed 760 1975
DiseaseNo Dis
Exposed 370 10
Unexposed 400 280
DiseaseNo Dis
Exposed 80 65
Unexposed 360 1695
OR= 5.8
OR= 25.9
Overall OR=15.6
Stratum 1: Hep. B+ virus Stratum 2: No Hep. B Virus
Crude
Stratified
Evaluating relationships between exposure and outcome in strata
homogeneous with respect to a confounder.

23. Effect Modification
•Effect modification is not bias or confounding and when found it
provides information for the nature of an association
•Effect modification does not violate internal validity of the study
•It requires stratified analysis for different levels of the interacting
factor (like sex or age group).

24. Homework Questions: Q1
1.To measure the effect of exercise on heart disease, investigators in a 1961 study compared the
incidence of the disease for two large groups of people who worked on the London bus system:
drivers and conductors. Conductors get a lot more exercise than the drivers since they walk
around all day collecting fares while the drivers just sit. The age distributions of the two groups
were the same. The study found the incidence of heart disease was substantially lower among
the conductors.
a.How do you classify this study? (observational vs interventional? Cohort, case-control,
cross- sectional or clinical trial?)
a.The investigators seem to have been worried that age would be a confounding factor in
their study. Was this the case?
(i)Yes, age was a confounding factor.
(ii)No, age was not a confounding factor.
(iii)There is not enough information to determine whether age is a confounding factor

26. Homework Questions: Q1
1.To measure the effect of exercise on heart disease, investigators in a 1961 study compared the
incidenceofthediseasefortwolargegroupsofpeople who worked on the London bus system:
driversandconductors. Conductors get a lot more exercise than the drivers since they walk
around all day collecting fares while the drivers just sit.Theagedistributionsofthetwogroups
werethesame. The study found theincidenceofheartdisease was substantially lower among
the conductors.
a.How do you classify this study? (observational vs interventional? Cohort, case-control,
cross- sectional or clinical trial?)
a.The investigators seem to have been worried that age would be a confounding factor in
their study. Was this the case?
(i)Yes, age was a confounding factor.
(ii)No, age was not a confounding factor.
(iii)There is not enough information to determine whether age is a confounding factor

27. Homework Question 2
In your opinion, is smoking status an effect modifier, confounder, neither,
or both? Justify your answer in three sentences or less?

28. 30
Homework Question 2: Role of Smoking in relationship between
Oral Cleft and drinking
Oral CleftControl
Alcohol Drinker46 14
Teetotaler 32 43
Smokers
OR=
46×43
32×14
= 4.42
Oral CleftControl
Alcohol Drinker 18 18
Teetotaler 4 25
Non-smokers
OR=
18×25
4×18
= 6.25
Oral Cleft Control
Alcohol Drinker 64 32
Teetotaler 36 68
OR=
75×79
22×21
= 3.78

29. 31
Role of Smoking in relationship between Oral Cleft and drinking
(Does smoking meet conditions for Confounding?)
•Criteria 1: Be risk factor for exposure: Is smoking related to Drinking?
Smoke Nonsmoker
Alcohol drinkers 60 36
Teetotalers 75 29
Smoking status
OR=0.644
•Criteria 2 : Be independent risk factor for disease: Is smoking related to
Oral Cleft independent of drinking status?
Among Alcohol Drinkers
Oral CleftControl
Smoke 46 14
Not smoke 18 18
OR=3.29
Among teetotalersOral CleftControl
Smoke 32 43
Not smoke 4 25
OR=4.65

30. For smoking to be a confounding factor, 3 conditions must be met
Alcohol driking vs. No
Drinking
Oral Cleft
Potential Confounder:
Smoking
Pathway (downstream
effect of exposure)
Is smoking Risk factor for
Alcohol Drinking?
Is smoking Risk factor for Oral cleft
independent of Heavy Drinking?
In causal pathway? (No)
Smoking No
Smoking
Alcohol
Drinker
a=60 b=36
No drinker c=75 d=29
Oral
Cleft
No oral
Cleft
Smoking a=32 b=194
No Smoking c=4 d=25
OR=
60×29
75×36
= 0.644
OR=
32×25
4×194
= 4.65

31. Homework Question 3
3.A case-control study was conducted to determine if Helicobacter pylori (H. pylori)
increased the risk of gastric cancer (stomach cancer). Vitamin C is a well-
established anti-oxidant and therefore may have anti-cancer properties. The
authors reported that the risk of gastric cancer was 1.71 times greater among
people with detectable H. pylori compared to people without detectable H pylori.
They then stratified by vitamin C use and observed an OR of 4.68 among low
vitamin C users, and an OR of 0.72 among high vitamin C users
a.In the results section the authors state, “The OR difference between the
two strata [of vitamin C use] was statistically significant (p- value=0.02).”
What does this p- value indicate?
b.Is vitamin C use an effect-modifier of the relation between H pylori and
gastric cancer? Why or why not?
c.Would you control for the use of vitamin C in your analysis, or would you
stratify by this variable?

32. 34
Homework Question 3: Role of Smoking in relationship between
Oral Cleft and drinking
Oral CleftControl
H. Pylori a
1 b
1
No H. Pylori c
1 d
1
Low Vitamin C users
OR=
a
1
×d
1
c
1
×b
1
= 4.68
Gastric CaControls
H. Pylori a
2 b
2
No H. Pylori c
2 d
2
OR=
a
2
×d
2
c
2
×b
2
= 0.72
Gastric Ca Controls
H. Pylori a b
No H. Pylori c d
OR=
????????????×????????????
c×b
= 1.71
High Vitamin C users
Statistical test comparing 4.68 vs. 0.72 resulted in p- value=0.02
Crude Analysis:
Stratified Analysis:

33. Homework Question 4
4.Vitamin D has a well-known role in calcium regulation and bone metabolism. Significant sources of vitamin D
include foods, endogenous vitamin D made by skin cells after sunlight exposure, and vitamin supplements.
Recent laboratory studies suggest that vitamin D may also be involved in modulating cell growth and blood-
vessel formation, both of which are important in cancer.
In 1992– 1998, a multi-national collaborative study in Europe recruited about 520,000 cancer-free adults
from the general population or through screening programs. At recruitment, all participants donated a blood
sample and completed a standardized dietary questionnaire. Occurrence of cancer was then monitored
through population-based cancer registries and death certificates in each country. By 2003, 1,248
participants had developed oral cancer. Each of them was matched to a study participant of the same age,
gender, and area of residence who was known to be alive and had not developed oral cancer. Stored blood
samples and questionnaire data were then analyzed to compare the two groups. The results showed
significantly lower blood vitamin D levels among those who developed oral cancer than among those who
did not. However, essentially no differences were found with regard to dietary intake of foods high in vitamin
D.
a.Classify the study design. (1 point)
b.The results for blood levels of vitamin D differed from the results for self-reported dietary intake of
vitamin D. Could this difference be due to recall bias in the self-reported dietary data? Explain briefly.
(1 point)
c. The study results were considered encouraging by cancer control experts, because blood level of
vitamin D may be a potentially modifiable risk factor for oral cancer. What type of study design might
best establish whether raising a person’s blood level of vitamin D reduces his or her risk of oral cancer?
(2 points)

34. Homework Question 5
5.Guillain-Barr´e syndrome (GBS) is a rare but potentially serious form of muscle paralysis that is
known to be triggered by certain viral illnesses and some vaccines. In 2008, a group of Taiwanese
investigators mounted a study to determine whether flare- ups of herpes zoster infection
(“shingles”) can also trigger GBS. Taiwan’s national health insurance system covers almost all of
the country’s population. From national health insurance data, researchers found that a total of
315,595 individuals had been diagnosed with herpes zoster infection on a medical visit during
2003– 2005. For each herpes zoster victim, three comparison persons were chosen at random
from among national health insurance enrollees who were of similar age and gender and who had
made a medical visit on the same date for some other reason besides herpes zoster infection.
During the two months following their index medical visit, 78 people in the herpes zoster group
and 14 people in the comparison group were diagnosed with GBS, according to national health
insurance records. Assume for present purposes that no participants died, disenrolled, or
emigrated from Taiwan during those two months. How would you classify the basic study design?

35. Homework Question 6
6.(BONUS, OPTIONAL) The tables below show the association periodontitis and CVD according to
a hypothetical susceptibility factor
CVD+ CVD-
Periodontitis (E+) 240 960
No Periodontitis (E-) 360 2440
Among patients without susceptibility factor:
CVD+ CVD-Total
Periodontitis (E+)200 600 800
No Periodontitis (E-)200 10001200
Among patients without susceptibility factor:
CVD+ CVD- Total
Periodontitis (E+)40 360 400
No Periodontitis (E-)160 1440 1600
Determine from the data if the susceptibility factor an Effect Modifier, Confounder, or both? Justify
your answer by show of calculations (Hint: remember definition of confounder)

36. 38
Homework BONUS Question: Role of Susceptibility factor in
relationship between Periodontitis and CVD
CVD+ CVD-
Periodontitis 200 600
No Periodontitis200 1000
Stratum 1:
Susceptibility factor
OR=
200×1000
200×600
= 1.5
Oral CleftControl
Periodontitis 40 360
No Periodontitis 160 1440
Stratum 2:
No Susceptibility factor
OR=
40×1440
160×360
= 1.00
CVD+ CVD-
Periodontitis 240 960
No Periodontitis 360 2440
Crude OR=
240×2440
360×960
= 1.56
Crude Analysis:
Stratified Analysis:

37. Limitations of Stratified analysis
•Inability to control simultaneously for multiple confounding variable
•To adjust for multiple confounders, a regression model is used
•Linear regression when outcome is continuous
•Logistic regression when outcome is binary categorical