5.6 Optional: Percentages and odds

This question is optional; for example, if you need more practice, or you are studying for the exam.

Endotracheal intubation (ETI) is a method for maintaining an open airway or as a method for administering certain drugs for ill patients.

ETI is widely used for airway management of children in the out-of-hospital setting, but for many years little evidence was available on the effect of using ETI. Table 5.2 comes from a study (Gausche et al. 2000) of using different types of endotracheal intubation on children. Use the table to answer the questions that follow.

TABLE 5.2: Airway management data
	BVM group		ETI group
	Number	%	Number	%
Normal, no change from baseline	39	(10%)	33	(8%)
No change from baseline	33	(8%)	25	(6%)
Mild disability	20	(5%)	27	(6%)
Moderate disability	6	(1%)	7	(2%)
Severe disability	10	(2%)	6	(1%)
Coma/vegetative	15	(4%)	12	(3%)
Death	281	(70%)	306	(74%)
Total	404		416

Among people treated with BVM ('ball valve mask'), compute the percentage that died (to the nearest percent).
Among the people treated with BVM, what are the odds that someone died? Explain which one of the following calculations is correct, and explain what the other calculations compute, and hence why they are wrong.

281/(404-281) = 2.28 (404-281)/404 = 0.304 281/404 = 0.696 (281+306) / ( 404+416) = 0.716 281/306 = 0.918
Among people treated with ETI, the odds that someone died is 2.78. What does this mean?

A patient treated with ETI has a 2.78% chance of dying. 2.78% of patients treated with ETI in the study died. For patients treated with ETI, about 278 die for every 100 that survive. For patients treated with ETI, about 278 live for every 100 that die.
How many times greater is the odds that a person treated with ETI died compared to the odds that a person treated with BVM died?

References

Gausche M, Lewis RJ, Stratton SJ, Haynes BE, Gunter CS, Goodrich SM, et al. Effect of out-of-hospital pediatric endotracheal intubation on survival and neurological outcome: A controlled clinical trial. Journal of the American Medical Association. 2000;283(6):783–90.