Often people will first find a spread between the derivative products and the base one. This spread, is likely to be a reflection of the marginal cost of refining that last unit of the derivative product. Therefore it is likely to depend on demand relative to supply of refining capacity: If there's a new refinery for this product coming online, then you'd expect the spread to fall. If the demand for construction goods that use this refined product is increasing, then you'd expect and increase in the spread.
Often several plastics and refined produces are substitutes of each other, like natural gas and gasoline are somewhat substitutable for each other. I would use the recent price of the other refined products to predict the price of polyethylene or polyurethane or its spread w/respect to crude oil.
This wikipedia article has more on the spread and how people think it is determined.