Current clinical strategies to assess benefits from hearing aids (HAs) are based on self-reported questionnaires and speech-in-noise (SIN) tests; which require behavioural cooperation. Instead, objective measures based on Auditory Brainstem Responses (ABRs) to speech stimuli would not require the individuals' cooperation. Here, we re-analysed an existing dataset to predict behavioural measures with speech-ABRs using regression trees. Ninety-two HA users completed a self-reported questionnaire (SSQ-Speech) and performed two aided SIN tests: sentences in noise (BKB-SIN) and vowel-consonant-vowels (VCV) in noise. Speech-ABRs were evoked by a 40 ms [da] and recorded in 2x2 conditions: aided vs. unaided and quiet vs. background noise. For each recording condition, two sets of features were extracted: 1) amplitudes and latencies of speech-ABR peaks, 2) amplitudes and latencies of speech-ABR F0 encoding. Two regression trees were fitted for each of the three behavioural measures with either feature set and age, digit-span forward and backward, and pure tone average (PTA) as possible predictors. The PTA was the only predictor in the SSQ-Speech trees. In the BKB-SIN trees, performance was predicted by the aided latency of peak F in quiet for participants with PTAs between 43 and 61 dB HL. In the VCV trees, performance was predicted by the aided F0 encoding latency and the aided amplitude of peak VA in quiet for participants with PTAs ≤ 47 dB HL. These findings indicate that PTA was more informative than any speech-ABR measure, as these were relevant only for a subset of the participants. Therefore, speech-ABRs evoked by a 40 ms [da] are not a clinical predictor of behavioural measures in HA users.