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Background: Encouraged by the success of pretrained Transformer models in many natural language processing tasks, their use for International Classification of Diseases (ICD) coding tasks is now actively being explored. In this study, we investigate three types of Transformer-based models, aiming to address the extreme label set and long text classification challenges that are posed by automated ICD coding tasks. Methods: The Transformer-based model PLM-ICD achieved the current state-of-the-art (SOTA) performance on the ICD coding benchmark dataset MIMIC-III. It was chosen as our baseline model to be further optimised. XR-Transformer, the new SOTA model in the general extreme multi-label text classification domain, and XR-LAT, a novel adaptation of the XR-Transformer model, were also trained on the MIMIC-III dataset. XR-LAT is a recursively trained model chain on a predefined hierarchical code tree with label-wise attention, knowledge transferring and dynamic negative sampling mechanisms. Results: Our optimised PLM-ICD model, which was trained with longer total and chunk sequence lengths, significantly outperformed the current SOTA PLM-ICD model, and achieved the highest micro-F1 score of 60.8%. The XR-Transformer model, although SOTA in the general domain, did not perform well across all metrics. The best XR-LAT based model obtained results that were competitive with the current SOTA PLM-ICD model, including improving the macro-AUC by 2.1%. Conclusion: Our optimised PLM-ICD model is the new SOTA model for automated ICD coding on the MIMIC-III dataset, while our novel XR-LAT model performs competitively with the previous SOTA PLM-ICD model.