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I forgot to mention that besides using supplements there are some other avenues of treatment for arthritis available now through veterinary clinics…there are now k-laser treatments and adequan injections (directly into the joint) that are much safer and can also be far more effective than an anti-inflammatory alone.  Many times dogs getting these treatments no longer take an anti-inflammatory or they can be on a significantly reduced dose.  Ask your vet about k-laser treatments and adequan (I think this is spelled incorrectly) injections. 

Alanine Aminotransferase: 8.2 to 57 u/L
Alkaline Phosphatase: 10.6 to 101 u/L
Aspartate Aminotransferase: 8.2 to 57 u/L
Gamma Glutamyltransferase: 1.0 to 9.7 u/L
Serum Bilirubin: 0.1 to 0.6 mg/dL

Even if your vet is not inclined to require a regular blood panel or liver panel for dogs that are on an anti-inflammatory (many do not have a system in place to flag these dogs) the most valuable regular veterinary procedure any dog or cat owner can have done on a regular basis, either yearly or every six months depending upon the age and condition of the pet, is a comprehensive blood panel covering all organs and which includes a urinalysis and thyroid test.  In my experience this is far more important than going for annual vaccinations.  Most pets do not need that vaccination at all because they already have more than adequate levels of antigens in their blood from the vaccinations they received in their first through 2nd years of life. 
But to address your question of how to help dogs with arthritis without compromising their health through the use of anti-inflammatories…
(I should mention that I regularly use rimadyl and think it has extremely beneficial results – but blood work must be monitored.)
There are supplements that are regularly recommended for dogs to support improvement in arthritic joints as well as pain relief.  Here are my favorites.  Each of these has specific directions on the labels for how much to administer based on the weight of your dog.  A canine orthopedist can tell you that dogs are much more responsive to the use of these supplements (glucosamine, chondroitin, and others) than humans are.  Unlike humans, canines can regenerate cartilage.  These supplements are aimed at achieving two goals – improvement of the physical joint and reduction of inflammation and pain.  So here are my favorite supplements for arthritic seniors at Sheltie Rescue of Utah:

Vetri-Science Glyco-Flex III – this is for advanced and pretty bad arthritis.  I like the pricing I get on this from http://KVVet.com. ( I also buy items numbered 2 and 3 below from KVVet.com.) There are formulas labeled Glyco-Flex II and probably a I.  I don’t know how to decide when it’s time to graduate from one to the next. 
Cosequin DS (which stands for “double strength”) I like to use this with dogs with mild arthritic issues or possibly even moderate arthritic issues.  This is what I use for dogs who are not yet at the Glyco-Flex III level of need.
Welactin – this is a fish oil supplement high in omega-3 fatty acids.  This has a known anti-inflammatory effect and thus contributes to a reduction in pain.  It has other benefits as well including being very good for the skin and coat which often suffer from lack of adequate nutritional support as dogs (or humans) age.
Pain Away – Joint & Back Pain Relief – this is a 100% human grade product.  A 4oz container goes a LONG way and cost me $12.99.  The container states “This product is designed to reduce joint & back pain and to rebuild damaged tissue associated with arthritis and other inflammatory diseases.”  This product is distributed by Healthline Nutrition in Vancouver, WA.  Their website is http://cssilverhl.com
In support of these supplements I think it’s extremely important to feed your pets the highest quality food you can.  While many diseases arise from genetic predispositions – the disposition doesn’t have to be realized.  Just as in human health, providing the body with the tools to combat disease is an important component of better health.  In the last 10 years we have seen a jump in the longevity of dogs that come to us which I believe is associated with both improvements in dog food overall as well as improvements in veterinary care.
I am an avid dispenser of vitamins both for me and our dogs.  My favorite vitamin for adult dogs is Vetri-Science Canine Plus for adult dogs.  For seniors, I like Vetri-Science Canine Plus for Seniors.  For seniors with few or no teeth or painful mouth conditions I use (often in conjunction with a crushed Canine Plus for Seniors tablet) a powdered vitamin formula called Young At Heart which I buy at http://JeffersPet.com.  The same company that makes Young At Heart also makes a powdered supplement called Show Stopper which many people who show their dogs in the show ring, swear by. 

Sharon – I hope this is somewhat helpful to you.  The pain of loss from whatever cause is an agony that is hardly bearable.  Thinking that a treatment that was administered contributed to that loss would leave me wracked with even more pain and tremendous guilt.  Kidney disease is a creeping disease that, as you found with Mattie, can be detected early.  Signs of kidney disease may not show up on some tests until a significant portion of the kidney is unable to function normally.  Rimadyl may have had a contributory role but its impact is NOT primarily on the kidneys and I doubt that it was the primary culprit in Chloe’s situation.  Rimadyl may actually have provided her with pain relief from some of the effects of kidney disease as well as pain relief from her arthritis. Even with advanced insight, as with Mattie, you generally cannot do anything more than slow down the progression of this disease.  ( I have friends who had dogs that were diagnosed with kidney disease and with special supplements which I need to dig up or re-discover – actually seemed to have eliminated it.  But these are rare exceptions.)
I would also note that while a low protein diet is the mantra for pets with kidney disease, there is still controversy over that with some people feeling that providing adequate protein levels is more important than the stress that the processing of the protein, puts on the kidneys. 
ps I do not get any compensation from the companies or webstores mentioned.  If I did, I wouldn’t be going nuts finding ways to raise funds to pay the vet bills incurred by our rescued Shelties.  I’m definitely all for universal health care for both people and pets.