Psoriatic arthritis (PsA) is a long-term inflammatory disease that affects the joints and skin.

The purpose of this study is to check how safe zasocitinib is, how well it is tolerated and how well it works in adults with PsA over a longer period of time.

Adults who completed the 1-year (52-week) treatment period in one of the parent studies (TAK-279-PsA-3001 [NCT06671483] or TAK-279-PsA-3002 [NCT06671496]) may be able to join this continuation study (also called long-term extension or LTE study). All participants in this continuation study, will receive zasocitinib (lower or higher dose), once a day (QD).

Each participant can be in this study for approximately 2 years (108 weeks). This includes a treatment period of up to 2 years (104 weeks) and a 1-month (4-week) follow-up period to monitor a participant's health.

Inclusion Criteria:

1. The participant is aged 18 years or older at the time of signing the informed consent form (ICF). In South Korea, the age requirement for adult participants is >=19 years of age.
2. The participant has completed the 52-week treatment period in one of the parent studies (TAK-279-PsA-3001 or TAK-279-PsA-3002) independent of treatment assignment, and without meeting the criteria for permanent discontinuation of trial intervention defined in the parent studies.
3. The participant must be deemed by the investigator to benefit from continued or newly initiated (that is, for participants randomized to active comparator in parent study TAK-279-PsA-3001) zasocitinib therapy.

Exclusion Criteria:

1. Any participant who is deemed by the investigator to be not benefiting from the trial intervention based upon lack of improvement or worsening of their symptoms in the respective parent study.
2. Any participant who met the criteria for permanent discontinuation of trial intervention defined in the parent studies (TAK-279-PsA-3001 or TAK-279-PsA-3002).
3. The participant has developed any disease(s) that might confound the evaluations of benefit of zasocitinib therapy since enrollment in the respective parent study, including but not limited to rheumatoid arthritis, axial spondyloarthritis (this does not include a primary diagnosis of PsA with spondylitis), systemic lupus erythematosus, Lyme disease, gout, or fibromyalgia.
4. The participant has developed evidence of a concomitant comorbid skin condition that, in the opinion of the investigator, would interfere with the study assessments, such as evidence of non-plaque PsO (erythrodermic, pustular, predominately guttate PsO, inverse, or drug-induced PsO).

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.