Confounding And Interaction
Dr. L. Jeyaseelan
Department Of Biostatistics
CMC, Vellore
Case Study
Is goiter related to high altitudes?
• A group of researchers presented data showing rate of goiters between two areas that were different in altitudes.
• There was a higher rate of goiter among people who lived in counties located at high altitudes.
• Hence the researchers concluded that living at high altitudes was a factor associated with presence of goiter.
PDQ Epidemiology
Is goiter related to high altitudes?
Distance to
reach high
altitudes
Iodine evaporates before reaching high altitudes….
Definition
What looks like a causal relationship between a supposed hazard and a disease may be due to another factor not taken into consideration. This additional factor is called a confounder, something that confuses the correct interpretation of data.
GAMBLING CANCER
SMOKINGALCOHOL
OTHER FACTORS
Unobservedassociation
Truecausation
Hypothetical Example
Male
Drug Placeb
o
Cure
No
Cure
120
(60%)
80
60
(60%)
40
Total 200 100
2 = 0.00
Female
Drug Placeb
o
Cure
No
Cure
30 (30%)
70
60
(30%)
140
Total 100 200
2 = 0.00
Hypothetical Example (Cont.)
Pooled
Drug Placebo
CureNo Cure
150 (50%)150
100 (33.3%)200
Total 300 300
2 = 17.14 (p < 0.0001)
BASIC CONCEPTS IN ASSESSMENT OF RISK
Situations in which F is a confounder for a disease- exposure association. ( ) non- causal association; ( ) causal association.The letters E Exposure F Potential matching factor (confounder) D Disease
Fig A. Indirect association between exposure and disease that is due to the factor F.
Example: Association between drinking alcoholic beverages (E) and Lung cancer (D) would likely be explained in terms of an association between alcohol intake and cigarette smoking (F).
F
E
D
Fig A
James. J. Schlesselman, 1982
Situation in which matching on a factor F is proper
Fig B. E and F individually alter the risk of disease and are also associated. Failure to match or otherwise control for F in this instance would result in a biased assessment of the individual effect of E.
F
E
D
Fig B
Example: Use of oral contraceptives and cigarette smoking are both risk factors for myocardial infarction.
Note: OC use and smoking are positively associated, so that failure to adjust for the effect of smoking (F) results in an overestimate of the effect of the OC use (E) on the risk of a myocardial infarction.
James. J. Schlesselman, 1982
Situations in which F is not a confounder for a disease-exposure association.
E
F
D
Fig C
E
F
D
Fig D
Fig C Example: A case control study of venous thromboembolism and blood group O provides an example of avoiding unnecessary matching. Although age and sex are characteristics that bear a strong relationship to disease, they are practically unrelated to the factors is necessary
Fig D Example: Hospital based case control study on Myocardial infarction (MI) and oral contraceptives.
James. J. Schlesselman, 1982
Situations in which F is not a confounder for a disease-exposure association.
E
F
D
E
D
F
James. J. Schlesselman, 1982
Confounding:
Apparent association is due to another variables
- Apparent lack of association could result from failure to control for the effect of some other factor.
Example:
The following table shows the recent oral Contraceptive (OC) use (last use within the month before admission) among 234 cases of MI and 1742 controls.
OC MI ControlYes 29 135No 205 1607
Odds ratio = 1.68 (Shapiro et al 1979)
Age Recent OC use
MI Control OR
25 - 29 30 - 34 35 - 39 40 - 44 45 - 49
Yes No
Yes No
Yes No
Yes No
Yes No
4 2
9 12
4 33
6 65
6 93
62 224
33
390
26 330
9 62
5
301
7.2
8.9
1.5
3.7
3.9 Total 234 1742
Table: age-specific Relation of MI to Recent oral Contraceptive (OC) use
Table : Summary of Examples Showing Confounding and/or Interaction in Randomly Sampled Data
ADJUSTED VS. CRUDE Example
Study (Effect Measure)
Stratum 1 Estimate
Stratum 2 Estimate
Crude Estimate
Confounding And Interaction No Confounding and No Interaction Confounding and No interaction Strong Interaction, Confounding Irrelevant
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Follow-up (RR) Follow-up (RR) Case-control (OR) Follow-up (RR) Follow-up (RR) Case-control (OR) Follow-up (RR) Follow-up (RR) Case-control (OR) Follow-up (RR) Follow-up (RR) Case-control (OR) Follow-up (RR) Follow-up (RR) Case-control (OR)
1.02 1.74 0.96 4.00 1.00 1.83 4.00 1.00 1.83 1.01 3.00 0.83 1.07 3.00 0.36
1.86 3.00 0.45 4.00 1.00 1.83 4.00 1.00 1.83 1.03 3.00 0.83 9.40 0.33 6.00
4.00 1.00 1.83 4.00 1.00 1.83 4.00 1.00 1.83 4.00 1.00 1.83 4.00 1.00 1.83
Page (246); David G. Kleinbaum 1982
MANTEL-HAENSZEL METHOD OF COMBINING 2 * 2 TABLES
Amount of Care One-month Survival Status Dead Alive
Total
Less
More
20
6
373
316
393
322
Total 26 689 715
The null hypothesis of interest is:
H0 : PLESS = PMORE Vs Ha : PLESS P MORE
95% CI (1.11 to 6.71 )
² = 5.26 > 3.84Reject H0
2.73 322
6
393
20 ˆ RR
However, these data were collected in two clinics and then combined. The data for the individual clinics are shown below together with some summary statistics.
Clinic 1 Dead Alive
Total
Clinic 2 Dead Alive
Total
Less Care
More Care
3
4
176
293
179
297
17 2
197
23
214
25 Total 7 469 476
19 220 239
1.35 P̂
1.68 P̂
0.08
1.24 ˆ
More
less
2
RR
Conclusion is s that there is no association between amount of prenatal care and one-month infant survival. This contradicts our previous conclusion. Why?
8.00 P̂
7.94 P̂
0.00
0.99 ˆ
More
less
2
RR
Suitable methods have been suggested by Mantel and Haenszel
1. To test the null hypothesis that on the average there is no association.
2. To measure the average strength of the association.
The formulas for the individual tables is
v
2 e) - a( 2MHX
)1(
n n n n
N
n n
2NEENDD
ED
NNv
eWhere
XMH2 approximately has the chi-square distribution with 1 d.f.
With indicating summation over all strata or tables.
With the continuity correction,
vX MH
22 ] 0.5 - e - a [
N)(bc
)( ˆ Nad
RO MH
The pooled estimate of the odds ratio is given by:
With indicating summation over all strata or tables.
Example: For the prenatal care data:
6217.1475 * 476
297 * 179 * 469 * 7 v
2.6323 476
179 * 7 e
3 a
2
1.6450 238 * 239
25 * 214 * 220 * 19 v
17.0126 239
214 * 19 e
17 a
2
Clinic 1
Clinic 2
0.039 1.6450) (1.6217
] 17.0126) (2.6323 - 17) (3 [ X
22
MH
The pooled estimate of the odds ratio is given by:
11.1
239
2 * 197
476
4 * 176239
23 * 17
476
293 * 3
ˆ
MHRO
Case Study
Characteristic 3 day treatment (n=1095)
5 day treatment (n=1093)
Mean (SD) Age (months) 17.0 (13.3) 16.9 (13.0)
Mean (SD) height (cm) 74.8 (10.98) 74.8 (10.75)
Mean (SD) weight (kg) 8.7 (2.49) 8.7 (2.4)
Mean (SD)duration of illness days) 4.7 (3.43) 4.5 (3.12)
Mean (SD) temperature (oC) 37.1 (0.66) 37.2 (0.67)
Mean (SD) respiratory rate (breath / minute):2 – 11 months old12 – 59 months old
56.447.3
(5.02)(5.58)
56.047.9
(4.54)(6.1)
Male 685 (62.6) 676 (61.8)
Age (months):2 – 1112 – 59
479616
(43.7)(56.3)
475618
(43.5)(56.5)
Weight for height z score*:-2 to -1-3 - 2
300188
(27.4)(17.2)
303183
(27.7)(16.7)
Table1: Baseline characteristics of 2188 children with non-severe pneumonia randomised to 3 days or 5 days of treatment with amoxicillin. Values are numbers (percentages) of patients unless stated otherwise
Characteristic 3 day treatment (n=1095)
5 day treatment (n=1093)
Duration of illness (days): 3 3
538557
(49.1)(50.9)
540553
(49.4)(50.6)
Fever 833 (76.1) 850 (77.8)
Cough 1081 (98.7) 1078 (98.6)
Difficulty in breathing 417 (38.1) 387 (35.4)
Vomiting 135 (12.3) 141 (12.9)
Diahorrea 71 (6.5) 55 (5.0)
Excess respiratory rate (breaths / minute) 10 10
903192
(82.5)(17.5)
881212
(80.6)(19.4)
Wheeze present 140 (12.8) 147 (13.4)
Adherence to treatment: At day 3 At day 5
1031937
(94.2)(85.6)
1026928
(93.9)(84.9)
RSV Positive 252 (23.0) 261 (23.9)
Table1 (Cont….)
*Z score given as number of standard deviations from normal value. †Rate above the age specific cut off RSV=respiratory syncytial virus.
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