Hi Okie,
Here is my take on your rose. First there is quite a bit of dead that needs to be removed. Also I doubt this is a bush that is on its own roots; if not then the graft portion is below the soil line.
Go ahead and lower the soil line around the rose, I would even create a furrow or depression for deeper watering. Then remove all the dead branches.
Leave what is left up top; this bush obviously needs all the leaf it can muster.
Next you need to apply some Epsom Salts. I find the Epsom Salts promotes the growth of new offshoots at the graft point. This will (hopefully) encourage new branches.
Then you need to Fertilize for Spring. Most folks think that during winter a plant is in dormancy and is not doing anything, but that is contrary to the truth. All plants utilize the winter to grow up to 90% of its newest root growth; taking advantage of not having to support blooms and new leaf growth. So by winter's end your bush will be ready for some fertilizer to get the new growth started. My recommendation is a fertilizer designed specifically for roses with a systemic pesticide. This will keep thrips and aphids off of your bush.
By one or two seasons from now Then I would bring all the canes (primary branches) down to about 12-18 inches tall; but do not do this in the Fall, do not do this in the Winter, but wait until just about the time the bush is going to break dormancy. Here in the desert Southwest we normally do our pruning on or around February 14th (Valentine's Day=Heart=Roses). This makes it easy to remember. Then you will get a new healthy start in creating a fabulous bushy bush loaded with the largest blooms you have ever seen.
GoodLuck! I think you will really see a difference before long.
Take care, Ron
ps, the reason I wait until Spring to do any pruning is because pruning done in the Fall and Winter might leave you with canes that could succumb to disease and freezing. It is best to allow your bushes to carry over until Spring just before they break dormancy. This way the plant will be focused on the new growth and overcome any hazards, and you can identify and remove those that do not make it. Some folks like a neat and tidy garden before Winter sets in, with me I find I have less loss if I wait until Spring.