Many interventional studies have found that the intervention reduced the primary end-point (a composite which includes cardiovascular mortality) without affecting total mortality. For example, the CANVAS randomized controlled clinical trial: Canagliflozin and Cardiovascular and Renal Events in Type 2 Diabetes. N Engl J Med 2017; 377:644-657. (https://www.nejm.org/doi/full/10.1056/NEJMoa1611925). “Significantly fewer participants in the canagliflozin group than in the placebo group had a primary outcome event (the composite of death from cardiovascular causes, nonfatal myocardial infarction, or nonfatal stroke): 26.9 vs. 31.5 participants with an event per 1000 patient-years (hazard ratio, 0.86; 95% CI, 0.75 to 0.97; P<0.001 for noninferiority; P=0.02 for superiority) (Figure 2 and Figure 3).” “Superiority was not shown for the first secondary outcome in the testing sequence (death from any cause; P=0.24), and hypothesis testing was discontinued. Therefore, estimates for the fatal secondary outcomes, including death from any cause (hazard ratio, 0.87; 95% CI, 0.74 to 1.01) and death from cardiovascular causes (hazard ratio, 0.87; 95% CI, 0.72 to 1.06), are not considered to be significant (Figure 2, Figure 3, and Figure 5).” Does this finding imply that the intervention increased non-cardiovascular mortality? Should non-cardiovascular mortality be analyzed as a competing risk for cardiovascular mortality?
This looks like yet another misapplication of statistical significance testing. This statement:
Many interventional studies have found that the intervention reduced the primary end-point (a composite which includes cardiovascular mortality) without affecting total mortality.
is incorrect, at least in the example shown. It is true that overall mortality was not significantly reduced while cardiovascular mortality was, but, as Andrew Gelman has written, "The difference between 'significant' and 'not significant' is not itself statistically significant". (Gelman, A, 2006, American Statistician, vol 60, p 328-333).
In this particular case, all the hazard ratios are very close.