The barbell method is a combination of prescriptive strength training combined with HIIT (High Intensity Interval Training) Conditioning work.
I choice this combination due to its effects on all the individual markers of sick ageing. Those being:
Poor Body Composition (Too much fat or not enough muscle, resulting in a decline in general health)
Increase Risk of Inflammatory Diseases (Diabetics, coronary heart disease, high blood pressure, raised cholesterol)
Loss of Strength (and independence when you can't get yourself out of a chair and self-esteem with it)
Reduced Flexibility (further loss of independence due to inability to dress yourself)
Inadequate Cardiovascular Endurance (unable to play or meaningfully interact with the grand children)
While indeed cardiovascular training deals with the first and last of these, it not only fails to improve flexibility and strength it actively reduces both of them. Even body composition change is only fat loss and no increase in lean muscle.
A prescriptive strength training programme on the other hand has a positive effect on all these factors, even some positive effect on cardiovascular endurance. Add to this HIIT Training and all factors are well covered.