That’s the subject of a 2006 paper by Bo Honore and Adriana Lleras-Muney. From the abstract:

In 1971 President Nixon declared war on cancer. Thirty years later, many have declared the war a failure: the age-adjusted mortality rate from cancer in 2000 was essentially the same as in the early 1970s. Meanwhile the age-adjusted mortality rate from cardiovascular disease fell dramatically. Since the causes underlying cancer and cardiovascular disease are likely to be correlated, the decline in mortality rates from cardiovascular disease may in part explain the lack of progress in cancer mortality.

If more people are surviving cardiovascular disease then more will die of cancer.  So if there were really no progress in cancer treatment then cancer mortality would in fact be increasing.  By how much?  That counterfactual question gets at the true benefits of the war on cancer.

In the case of white males, the probability of surviving past age 75 increased by about 19.5 percentage points, from 56.1% in 1970 to 75.6% in 2000. From row 3 [of table 4 in the paper] we see that, in the absence of cancer progress, this probability would have been between 66% and 73.8% in 2000. Therefore from this vantage point progress in cancer ranges from 2 to 10.6 percentage points and accounts for somewhere between 10% and 55% of the total increase in survival.

They identify bounds on cancer progress for other groups as well.  The published paper is gated, here is a 2005 working paper version.