Measures of Effect in 2x2 Tables

Question 1

How do we calculate a risk ratio?

Answer 1

Risk of poor outcome in group a / Risk of poor outcome in group b

Question 2

How do we interpret risk ratios?

Answer 2

= 1 means same risk
>1 means increased risk
<1 means reduced risk

Question 3

What is the convention for risk ratios in clinical trials?

Answer 3

New, active or experimental treatment /conventional, placebo or control

Question 4

What is the odds ratio?

Answer 4

The odds ratio (OR) is the ratio between the odds of the outcome in the active group and the odds of the outcome in the control group.

Question 5

What additional step is required when calculating confidence intervals for risk ratios?

Answer 5

Calculate the standard error of the ln risk ratio (avoids answers with negative risk ratios which are meaningless)

Question 6

Following using the ln risk ratio, how do we get back to the original risk ratio scale?

Answer 6

Anti-log of the final answer

Question 7

How do we calculate a risk ratio with a confidence interval of 95%?

Answer 7

exp( ln(RR) +/- 1.96 * SE(lnRR) )

Question 8

How can we calculate risk ratio confidence intervals using the error factor method?

Answer 8

See formula

Question 9

How can we describe the sampling distribution of the ln risk ratio when n is sufficiently large (>10)?

Answer 9

We can say that it is approx normal therefore we can calculate a confidence interval with the formula we know from previous calculations

The same can be said about odd ratios

Question 10

What happens to the risk ratio as the overall risk increases?

Answer 10

It becomes less extreme.

Question 11

What is the number needed to treat?

Answer 11

The “number needed to treat” (NNT) is 1/risk difference.

Question 12

How do we interpret NNT?

Answer 12

The lower the number the better

Question 13

What is the number needed to harm?

Answer 13

For adverse events. Calculated the same way as NNT but larger numbers are better (i.e. more rare)

Question 14

Why do some researchers prefer odds ratios?

Answer 14

The interpretation of the results does not depend on the occurence or non-occurence of an event is used as the outcome. Therefore

Question 15

Statistically speaking, why might odds be more useful?

Answer 15

Confidence interval formula approximations are better for smaller sample sizes than risk ratios

Question 16

Why is it important to identify confounders?

Answer 16

Skews data if not recognised - leading to false assumptions

Techniques can be used to adjust for confounders

Secondary analyses such as looking for characteristics associated with worse outcomes are susceptible to confounding

Question 17

What three variables must we consider in assessing a potential confounder?

Answer 17

Exposure of interest
Outcome of interest
Confounder

Question 18

What are the three criteria of confounders?

Answer 18

1. An independent risk factor for the outcome of interest
2. Associated with the exposure of interest
3. Not a causal pathway between exposure and outcome

Question 19

Define the causal pathway

Answer 19

The causal pathway is the sequence of events that leads to an outcome being affected by an exposure

Question 20

How do stratified tables help to adjust for confounders?

Answer 20

Start with the unstratified table (crude table)

Divide groups into strata to explore the confounder

Calculate X2 and P-value of each strata to find significance

If the P-values are both more significant than the crude table then the confounder is confirmed

Question 21

What technique can we use to account for a confounding factor?

Answer 21

Mantel-Haenszel method

Question 22

How does the Mantel-Haenszel method work?

Answer 22

It is a weighting method of calculating the overall risk ratio adjusted for the effect of the confounder depending on whether it is a positive or negative confounder

Question 23

How does the Mantel-Haenszel method weight its calculation?

Answer 23

It gives more weight to the group with the larger sample size

Question 24

Where else can the Mantel-Haenszel method be employed in potential confounder identification?

Answer 24

Chi-squared testing

Question 25

Is there a statistical test for confounding?

Answer 25

No

Question 26

How are confounders adjusted for in RCTs?

Answer 26

Randomisation breaks the relationship between exposure and confounder

Question 27

Can the influence of confounders be total mitigated in RCTs?

Answer 27

No, weak relationships between treatment and potential confounders can still exist by chance - often called baseline imbalance. Therefore RCTs may present both adjusted and non-adjusted data to evidence baseline imbalance

Question 28

What are the potential effects of confounding?

Answer 28

1. May be significant before adjusted and then non-significant after
2. THe association may remain significant but with a less significant p-value
3. The strata may show opposing results i.e. effect modifiers (common ones include gender). This phemonema is usually of interest in sub-group analyses. This can be tested for with an interaction test.
4. The confounder may mask or partially hide an association that exists. As in RITA-3

Question 29

Does adjustment techniques like Mantel-Haenszel method always eliminate confounders?

Answer 29

No, it is possible for there to be residual confounding.

Question 30

What technique is optimal when dealing with multiple potential confounders?

Answer 30

Multiple regression to simultaneously adjust for multiple confounders both discrete and continuous.