The reduction in the transcription ratio of the gene is as a result of mutations at its promoter region or near its proximity. Promoter region is the area, which binds the RNA (ribonucleic acid) polymerase enzyme and other cofactors that are essential in transcribing a specific gene.
Any change in the sequence of the promoter of the gene would hinder the chances of these transcribing proteins to attach to the promoter region. This is the main reason why there is a decrease in the relative transcription rate in the β-globulin gene as a result of mutation.