## 10.4 Tests for ORs

A study examined the mortality rates of lower-limb amputation, and factors that may be associated with mortality .

As part of the study, the researchers recorded the five-year mortality rate (the number of amputees who died within five years of amputation) and whether or not the person used an artificial limb.

The RQ was:

For this type of amputees, is the odds of being alive after five years the same for those who used an artificial limb, and those who did not?

A total of 105 subjects were used: 35 died within five years, and 70 were still alive after five years.

In addition, 65 subjects used an artificial limb, and 40 did not.

1. After five years, 49 people using an artificial limb were alive.

Construct the $$2\times 2$$ table (Table 10.1) displaying the number of people alive or dead after five years (in columns, say) and whether or not they used an artificial limb or not (in rows).

TABLE 10.1: Five-year mortality for artifical limb users
Used artificial limb
Did not use artificial limb
Total 105
1. For a person using an artificial limb, compute the odds of being alive after five years.

For a person not using an artificial limb, compute the odds of being alive after five years.

Then compute the odds ratio, complete Table 10.2, and carefully explain what the OR means.

2. Write down the 95% CI for the population OR using the software output (jamovi: Fig. 10.4; SPSS: Fig. 10.5).

3. Perform a hypothesis test to compare the odds of being alive after five years for both groups (jamovi: Fig. 10.4; SPSS: Fig. 10.5):

1. Write the hypotheses.
2. Write down the value of $$\chi^2$$.
3. What $$z$$-score is this approximately equivalent to?
4. What is the approximate $$P$$-value using the 68--95--99.7 rule?
5. What is the exact $$P$$-value as reported by software?
6. Write a conclusion.
TABLE 10.2: Five-year mortality and use of an artificial limb: Numerical summary
Percentage alive
Odds of being alive
Sample
after 5 years after 5 years size
Use artificial limb
Did not use artifical limb
Odds ratio

### References

Singh RK, Prasad G. Long-term mortality after lower-limb amputation. Prosthetics and Orthotics International. 2016;40(5).