It always amazes me that people (not just Gore Vidal) can't get numbers and history straight. Usually this is for propaganda purposes. For example, because the Philippine-American war of 1899-1902 is often labeled as a 'bad war" and a "war of conquest" both Filipino and US losses are exaggerated to make it seem more bloody and awful then it really was. So here are the actual US losses from the US army records:
Killed in battle (includes died of Wounds) - 1,004
Died of Disease - 2,572
Other Deaths -589
Total - 4,165.
Total Served: 100,000 (often quoted as 124,000 or so, but that includes men who went twice or more from the US to the Philippines).
Total Filipino Losses:
Killed in Battle - 12,000-16,000 (even the 12,000 is probably an exaggeration).
Civilian Deaths due to Disease, Famine, Battle - 200,000
How many of the 200,000 were due to the war and how many to due to the Cholera epidemic of 1902 is unknown.
The usual end time for the war is stated as June 1902. But there was very little fighting from June 1901 to June 1902. The US army lists 100 men killed in battle from July 1901 to June 1902. Of those 50 killed in one massacre on Samar in August 1901.