Defined as the percentage of participants able to achieve platelet counts ≥50 000/μL (or ≥30 000/μL and \<50 000/μL and at least double from baseline) for ≥50% of 6 biweekly scheduled platelet measurements and at least 4 non-missing, biweekly visits during the last 12 weeks of the primary analysis period (PAP) in absence of rescue therapy

An AESI is an AE (serious or nonserious) of scientific and medical concern specific to the Sponsor's product or program, for which ongoing monitoring and immediate notification by the Investigator to the Sponsor is required

The Adjudication Committee will include internationally recognized independent experts in diagnosis and management of patients with IgG4-RD, blinded to participant, investigator, and site identifiers

DHR is defined as an increase of Hb by ≥2 g/dL from baseline on at least two thirds of evaluable scheduled visits between Week 12 and Week 24 (inclusive) in the PAP in the absence of rescue medication and transfusion.

Calculated from total number of clinical VOC incidents and total number of days during the observation period

Durable platelet response per guidance in regions except European Union and United Kingdom was defined as platelet counts at or above 50,000/mcL for \>=two-thirds of at least 8 non-missing weekly scheduled platelet measurements during the last 12 weeks of the 24-week blinded treatment period in the absence of rescue therapy, provided that at least 2 non-missing weekly scheduled platelet measurements were at or above 50,000/mcL during the last 6 weeks of the 24-week blinded treatment period.

Durable platelet response per guidance in European Union and United Kingdom was defined as platelet counts at or above 50,000/mcL for at least 8 out of the last 12 weeks of the 24-week blinded treatment period in the absence of rescue therapy.

Loss of Asthma Control (LOAC) event is defined as any of the following: * A 30% or greater reduction from baseline in morning peak expiratory flow (PEF) on 2 consecutive days * ≥6 additional reliever puffs of salbutamol/albuterol or levosalbutamol/levalbuterol in a 24-hour period (compared to baseline) on 2 consecutive days * Increase in ICS ≥4 times the last prescribed ICS dose (or ≥50% of the prescribed ICS dose at V2 if background therapy withdrawal completed) * Requiring use of systemic (oral and/or parenteral) steroid treatment * Requiring hospitalization or emergency room visit for asthma exacerbation

Response is defined as an increase in hemoglobin (Hb) by ≥2 g/dL from baseline and an absence of transfusion in the last 7 days, without biochemical resolution of hemolysis at the time response is achieved and an absence of rescue medications during the last 4 weeks. Complete Response is defined as hemoglobin ≥11 g/dL (women) or ≥12 g/dL (men), no evidence of hemolysis (normal bilirubin, lactate dehydrogenase (LDH) , haptoglobin, and reticulocytes), and absence of transfusion in the last 7 days and an absence of rescue medications during the last 4 weeks.

Durable response (Part B) is defined as Hb level ≥10 g/dL with an increase from baseline (Part A) of ≥2 g/dL on three consecutive scheduled visits during Week 24 to Week 50; with absence of transfusion and no rescue medication during the period of 3 consecutive visits and for at least 7 days (transfusions) and 4 weeks (rescue medication) prior to the first consecutive visit.

The EASI index is a validated investigator-administered scoring system used to measure the severity of clinical signs in atopic dermatitis (AD). Four AD disease characteristics (erythema, thickness \[induration, papulation, edema\], scratching \[excoriation\], and lichenification) were each assessed for severity by the investigator or designee on a scale of "0" (absent) through "3" (severe). In addition, the area of AD involvement were assessed as a percentage by body area of head, trunk, upper limbs, and lower limbs, and converted to a score of 0 to 6. 0: 0% of body surface area (BSA) involvement with AD; 1: 1-9%; 2: 10-29%; 2: 30-49%; 4: 50-69%; 5: 70-89% and 6: 90-100% of BSA involvement with AD. Total score ranged from 0 (minimum) to 72 (maximum); higher scores indicated greater severity of AD. Baseline was defined as the Day 1 assessment value.

Disease flare is defined as an increase in IgG4-RD responder index (RI) \>2 or initiation of rescue treatment.

The percentage of participants who achieved 2 or more consecutive platelet counts, separated by at least 5 days, of \>=50,000/ microliter (μL) and an increase of platelet count of \>=20,000/μL from baseline, by starting dose level and overall, without use of rescue medication in the 4 weeks prior to the latest elevated platelet count. 95% confidence interval (CI) was based on the Clopper-Pearson method. The average of the 2 screening results and the Cycle 1 Day 1 result were used as the baseline value.

The percentage of participants who achieved platelet counts \>=50,000/μL on at least 8 out of the last 12 weeks of the 24-week treatment period without the use of rescue medication after 10 weeks of active treatment. 95% CI was based on the Clopper-Pearson exact method.

Adverse event (AE): any untoward medical occurrence in participant or clinical study participant, temporally associated with the use of rilzabrutinib, whether or not considered related to rilzabrutinib. TEAEs: AEs that developed or worsened or became serious on or after the first dose administration of rilzabrutinib (Day 1). Any TEAEs are considered treatment-related TEAEs as per Investigator's evaluation of participant's circumstances surrounding the event, and an evaluation of any potential alternative causes to determine whether an TEAE can be considered as related to the rilzabrutinib.

AE any untoward medical occurrence in participant or clinical study participant, temporally associated with the use of rilzabrutinib, whether or not considered related to rilzabrutinib. TEAEs: AEs that developed or worsened or became serious during the treatment-emergent period, defined as any time after the first dose administration of rilzabrutinib (Day 1). Any TEAEs are considered treatment-related TEAEs as per Investigator's evaluation of participant's circumstances surrounding the event, and an evaluation of any potential alternative causes to determine whether an TEAE can be considered as related to rilzabrutinib.