Please see below three references related to hazard quotient. Hope they would be helpful to you?
Volosin, Joseph S. ; Cardwell, Rick D. 2002. Relationships between Aquatic Hazard Quotients and Probabilistic Risk Estimates: What Is the Significance of a Hazard Quotient >1? Human and Ecological Risk Assessment:, 8(2): 355-368
Tannenbaum, Lawrence V. ; Johnson, Mark S. ; Bazar, Matthew. 2003. Application of the Hazard Quotient Method in Remedial Decisions: A Comparison of Human and Ecological Risk Assessments. Human and Ecological Risk Assessment 9(1): 387-401
Stoner, Kimberly A ; Eitzer, Brian D. 2013. Using a hazard quotient to evaluate pesticide residues detected in pollen trapped from honey bees (Apis mellifera) in Connecticut. PloS one, 8(10): pp.e77550
Personally, I think they are the same concept. There are caculated as ratio of the exposure estimate over an acceptable effect level, which used for lower tiered risk assessment.
In addition, you can learn more methods of risk assessment methods in the follow reference.