Discussion 02

7/30/2019 Discussion 02

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Biostat 513

Discussion week 2

(4/8/13 – 4/12/13)



Feedback from HW 1

Question 1

• ….475 inmates were cross-classified with respect to HIV

sero-positivity and their history of intravenous drug use….

• Cross-sectional study – cannot estimate IR or IRR.

• Incorrect to say “risk of acquiring HIV infection”

• Correct – prevalence of HIV infection in this population

• Use the csi command with “or” option to estimate ORs



Measures of Association

• Recall, for two binomial probabilities p0 and

p1:

– Risk Difference: RD = p1 – p0

– Risk Ratio or Relative Risk: RR = p1/p0

– Odds Ratio: OR = [p1/(1‐p1)] / [p0/(1‐p0)]




• OR is the only appropriate measure of association for acase-control study (sampling by disease status); it isapproximately equal to the RR if disease is rare in thepopulation

•

RR, RD (and OR) all appropriate for prospective (samplingby exposure status) or cross-sectional studies – RR doesn’t provide information on absolute risk

– RR most useful when there is a clear referent group

– RR may better describe the biological or scientific effect

–

RD may better describe the public health or clinical impact“My system will double your chance of winning the lottery” v “Mysystem will increase your chance of winning the lottery by 0.000000143”




• OR is the only appropriate measure of association for acase-control study (sampling by disease status); it isapproximately equal to the RR if disease is rare in thepopulation

•




–

RD may better describe the public health or clinical impact“My system will double your chance of winning the lottery”

“My system will increase your chance of winning the lottery by0.000000143”




• OR is the only appropriate measure of association for acase-control study (sampling by disease status); it isapproximately equal to the RR if disease is rare in thepopulation.

•




–

RD may better describe the public health or clinical impact“My system will double your chance of winning the lottery” vs

“My system will increase your chance of winning the lottery by0.000000143”




• How do we choose a measure of association?

– Study design

– Scientific question of interest



Example 1

• CARE Study (Breast Cancer) – case-control

study of BC and OC use

•

Which measure of association best describesthe association between breast cancer and

oral contraceptive use?

Any OC Use None Total

BC Cases 3497 1032 4529

Controls 3658 980 4638



Example 1

• Odds Ratio

– Recall that since this is a case‐control study, we

don’t have P(disease|exposed) or

P(disease|unexposed) so, in general, we can’testimate the relative risk

– In this case, since breast cancer is rare, the OR will

be a good approximate to the RR





Example 1

• Again, because we are dealing with a case

control study, we would use the odds ratio.



Example 2

• APPROVe trial - RCT

• What measure of association best describes the

association between treatment (Vioxx) and thepresence of adenomatous polyps found bycolonoscopy during years 1‐3 of follow‐up?

Vioxx Placebo

Adenomatous Polyps

years 1‐3

460 646

None 698 596

Total 1158 1215



Example 2

• Relative Risk

– Our scientific question of interest asks us tocompare the risk of developing adenomatous

polyps in the treatment and placebo groups. – Since the disease frequency in the placebo group

is high, the OR and RR will not be close; also,upper bound on RR is ~1.9

– If we were interested in the absolute difference inrisk between the two groups, we could easilycalculate the risk difference.



Example 3

• Swedish mammography study – 15 year followupof women invited to have annual mammogram,or not

• What measure of association best summarizesthe benefit of mammograms in this population of women?

Invited Not

Died of BC 511 584

Alive/died other cause 129,239 116,676

Total 129,750 117,260



Example 3

• The RR is .80 indicating a 20% relative benefit

due to mammograms

• The RD is -0.001 suggesting that the

mammograms prevent 7 deaths per 100,000

women per year.

RD x 100,000 women / (15 years) = -6.7



Example 4

• A randomized controlled trial was carried out

to compare the effects of a single dose of

prednisone and placebo in children with acute

asthma.

Row TotalsPrednisone Placebo

Discharged Yes 20 2 22

No 47 71 118

Total 67 73 140



Example 4

The results section states “2 patients in the placebogroup (3%, 95%CI: -1 to 6%) and 20 in theprednisolone group (30%, 95%CI: 19 to 41%) were

discharged at first exam ( p < 0.0001)”. The methodssection explains that Fisher’s exact test was used forthe p-value.

• Was it necessary to use Fisher’s exact test? Was it

acceptable?• What’s wrong with the CI’s and how could you do

it better?



Example 5

• A study looks at the risk of bone fractures(over the past 5 years) in women with highcalcium levels in their drinking water versuswomen with low calcium levels.

• What is the study design?

• Which measures of association are valid?

Rate of fractures over 5 years by age andcalcium level

Age 20 - 35 Age 55 - 80 Overall(pooled)

High calcium 1.1% 11.0% 7.8%

Low calcium 3.3% 13.2% 10.0%



Example 5

• Using RR as your measure of association, is

age an effect modifier? yes

• Using RD as your measure of association, is

age an effect modifier? no !



Example 6 (optional)

Nevirapine may be given to HIV-infected women at the onsetof labor to prevent MTCT of HIV. Women are given the drugduring a prenatal visit, but may also be offered the drug whenthey present in labor (in case they lost or did not take the pillat the onset of labor).

Suppose we want to compare two different strategies of offering NVP to women but, for logistical reasons, thesestrategies can only be implemented at the clinic level. Thus,we will randomly assign each antenatal clinic and each L&Dclinic to the “T” or “C” strategy.

We want to evaluate the overall effect of the “T” strategy vsthe “C” strategy. But a difficulty is that a given woman may goto an antenatal clinic with one strategy and a L&D clinic with adifferent strategy




• List the (4) counterfactual outcomes for any givenHIV-infected woman [TT/TC/CC/CT]

• Which of these 4 counterfactuals correspond to

outcomes of real-world interest? Express thecausal effect of interest in terms of thecounterfactuals

• What key assumption do you have to make to

estimate the causal effect from the availabledata? Completely random allocation of womeninto four categories. No self-selection by women




“To adjust or not adjust, that is the question”

Consider the causal relationships

educ age

car

exposure disease Should we adjust for “car type” in studying the exposure-

disease relationship?




• Associational criteria for C being a confounder:

– C is associated with exposure

– C is associated with disease, within exposure strata

• “car type” meets the criteria for confounding

• Further, adjustment for “car type” will (likely)

change the exposure – disease odds ratio




• However, we should NOT adjust for “car type”

since it does not causally influence the

exposure or disease (it is only incidentally

associated with them)

• Only consider adjusting for factors that are

causally related to exposure or disease

• Decision to adjust for confounding depends on

the underlying causal model!

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Discussion 02