The research about this is all over the board, and tends to reflect the bias of whoever paid for it. There are pros and cons to either decision.
An article by Laura Sanborn titled Long-Term Health Risks and Benefits Associated with Spay / Neuter in Dogs Reviews medical research and gives both sides of the problem. It's about 12 pages long, and leaves you confused. If you trust your vet, talk with him.
SUMMARY
An objective reading of the veterinary medical literature reveals a complex situation with respect to the long-
term health risks and benefits associated with spay/neuter in dogs. The evidence shows that spay/neuter
correlates with both positive AND adverse health effects in dogs. It also suggests how much we really do
not yet understand about this subject.
On balance, it appears that no compelling case can be made for neutering most male dogs, especially
immature male dogs, in order to prevent future health problems. The number of health problems associated
with neutering may exceed the associated health benefits in most cases.
On the positive side, neutering male dogs
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eliminates the small risk (probably <1%) of dying from testicular cancer
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reduces the risk of non-cancerous prostate disorders
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reduces the risk of perianal fistulas
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may possibly reduce the risk of diabetes (data inconclusive)
On the negative side, neutering male dogs
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if done before 1 year of age, significantly increases the risk of osteosarcoma (bone cancer); this is a
common cancer in medium/large and larger breeds with a poor prognosis.
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increases the risk of cardiac hemangiosarcoma by a factor of 1.6
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triples the risk of hypothyroidism
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increases the risk of progressive geriatric cognitive impairment
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triples the risk of obesity, a common health problem in dogs with many associated health problems
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quadruples the small risk (<0.6%) of prostate cancer
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doubles the small risk (<1%) of urinary tract cancers
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increases the risk of orthopedic disorders
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increases the risk of adverse reactions to vaccinations
For female dogs, the situation is more complex. The number of health benefits associated with spaying may
exceed the associated health problems in some (not all) cases. On balance, whether spaying improves the
odds of overall good health or degrades them probably depends on the age of the female dog and the
relative risk of various diseases in the different breeds.
The basic rules of thumb appear to be to S/N if you do not intend to breed the dog. Wait until the dog has matured before having the operation.