Confounding And Interaction

Dr. L. JeyaseelanDepartment 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 Placebo

Cure

No Cure

120 (60%)80

60 (60%)40

Total 200 100

2 = 0.00

Female

Drug Placebo

Cure

No Cure

30 (30%)70

60 (30%)140

Total 100 200

2 = 0.00

Hypothetical Example (Cont.)

PooledDrug 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

DFig 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

639320 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

Nn 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 NadRO 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 2

2

MH

The pooled estimate of the odds ratio is given by:

11.1

2392 * 197

4764 * 176

23923 * 17

476293 * 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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