It's understandable, but grammatically it doesn't quite hang together. "the convincing of the presentation" is not right, you can't "respond to" an "intention to prescribe", and "to start or increase prescribing" is also awkward IMO. ) My suggestion: Following the visits of salesmen, doctors were asked to rate the persuasiveness of the presentation, the quality of information presented, the value of the visit in terms of knowledge gained, and the likelihood that they would start prescribing the salesman's products or prescribe them more frequently.
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