This study is being conducted to evaluate the efficacy and safety/tolerability of SCH 900222/MK-3222 in a population of participants with moderate-to-severe plaque psoriasis.

The base study consists of a screening phase of up to 4 weeks followed by a treatment period of 28 weeks, and a 20-week safety follow-up period off drug. The base study is divided into 2 sequential parts.

In Part 1 of the base study (Week 0 to Week 12), participants will be randomized to one of 4 study arms (Arm A: MK-3222 200 mg at Week 0 and Week 4 + matching placebo to etanercept twice weekly; Arm B: MK-3222 100 mg at Week 0 and Week 4 + matching placebo to etanercept twice weekly; Arm C: Matching placebo to MK-3222 at Week 0 and Week 4 + matching placebo to etanercept twice weekly; Arm D: Matching placebo to MK-3222 at Week 0 and Week 4 + etanercept 50 mg twice weekly).

In Part 2 of the base study (Week 12 to Week 28), participants in Arm A, Arm B, and Arm D will receive matching placebo to MK-3222 to maintain blinding at Week 12. Participants in Arm A and Arm B will continue to receive either MK-3222 200 mg (Arm A) or MK-3222 100 mg (Arm B) at Week 16 and Week 28 and will also receive matching placebo to etanercept once weekly through study Week 28. At study Week 12, Arm C participants will be re-randomized to receive their first dose of MK-3222 200 mg or MK-3222 100 mg, and will receive additional doses of study medication according to their re-randomized treatment assignment at Week 16 and Week 28. Participants in Arm C will also receive matching placebo to etanercept once weekly through treatment Week 28. Participants in Arm D will continue with once weekly doses of etanercept through study Week 28 in combination with matching placebo to MK-3222.

For all participants, completion of Week 28 marks completion of Part 2 and of the overall base study. Participants originally assigned to Arm D and participants who discontinue treatment prior to completing Part 2 will not be eligible to enroll in the extension. Participants that are ineligible or opt not to enter the extension study will be encouraged to complete the 20-week follow-up period.

Eligible participants that choose to enroll in the extension study will have an additional treatment period of up to 192 weeks and will be followed for an additional 20 weeks in the follow-up period. Each participant will receive MK-3222 200 mg or MK-3222 100 mg every 12 weeks up to study Week 220 according to their treatment assignment at the conclusion of Part 2 of the base study.

Inclusion Criteria

• Clinical diagnosis of moderate-to-severe plaque psoriasis for at least 6 months prior to enrollment;
• Candidate for phototherapy or systemic therapy;
• Premenopausal female participants must agree to abstain from heterosexual activity or use a medically approved method of contraception or use appropriate effective contraception as per local regulations or guidelines
• For the extension study: must have completed Part 2 of the base study
• For the extension study: must have achieved at least a PASI-50 response by the end of Part 2 of the base study

Exclusion Criteria:

• Non-plaque forms of psoriasis
• Presence or history of severe psoriatic arthritis that is well-controlled on current treatment regimen
• Women of childbearing potential that are pregnant, intend to become pregnant, or are lactating
• Participant is expected to require topical therapy, phototherapy, or systemic therapy
• Presence of any infection or history of recurrent infection requiring treatment with systemic antibiotics
• Previous use of MK-3222/SCH 900222, or other interleukin-23 (IL-23)/T- helper cell 17 (Th-17) pathway inhibitors including P40, P19, and IL-17 antagonists, or etanercept
• Latex allergy or sensitivity
• Active or untreated latent tuberculosis (TB)
• For the extension study: women of child-bearing potential that are pregnant, intend to become pregnant within 6 months of completing the trial, or that are breast feeding
• For the extension study: active or uncontrolled significant organ dysfunction or clinically significant laboratory abnormalities
• For the extension study: expected to require topical treatment, phototherapy, or systemic treatment during the extension study