Annualized Rate of all Infections in Participants [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Annualized Rate of Acute Serious Bacterial Infections (ASBIs) in Participants [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Annualized Rate of Episodes of Fever in Participants [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Time to First ASBI in Participants [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Duration of Infections in Participants [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Number of Days Lost From School, Work, Daycare, or to Perform Normal Daily Activities Due To Infection and/or their treatment or other Illnesses [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Number of Days on Antibiotics in Participants [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Number of Hospitalizations With Indications (Infection or other Illnesses) [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Number of Days of Hospitalization [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Number of Acute Physician Visits Due to Infection or Other Illnesses [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Maximum Concentration (Cmax) of total IgG with TAK-881 and HYQVIA at Steady-State in Participants Aged >=16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 14, 21, 28 days (post-infusion) of last infusion in each cross-over epoch]
Time to Maximum Concentration (Tmax) of total IgG with TAK-881 and HYQVIA at Steady-State in Participants Aged >=16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 14, 21, 28 days (post-infusion) of last infusion in each cross-over epoch]
Terminal half-life (t1/2) of total IgG with TAK-881 and HYQVIA at Steady-State in Participants Aged >=16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 14, 21, 28 days (post-infusion) of last infusion in each cross-over epoch]
Apparent Clearance (CL/F) of total IgG with TAK-881 and HYQVIA at Steady-State in Participants Aged >=16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 14, 21, 28 days (post-infusion) of last infusion in each cross-over epoch]
Apparent Volume of Distribution (Vz/F) of total IgG with TAK-881 and HYQVIA at Steady-State in Participants Aged >=16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 14, 21, 28 days (post-infusion) of last infusion in each cross-over epoch]
AUC0-tau; ss Per Week (AUC0-tau; ss/week) of total IgG with TAK-881 and HYQVIA at Steady-State in Participants Aged >=16 years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 14, 21, 28 days (post-infusion) of last infusion in each cross-over epoch]
Maximum Concentration (Cmax) of TAK-881 at Steady-State in Participants Aged 2 to <= 16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 21, 28 days (post-infusion)]
Time to Maximum Concentration (Tmax) of TAK-881 at Steady-State in Participants Aged 2 to <= 16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 21, 28 days (post-infusion)]
Terminal half-life (t1/2) of TAK-881 at Steady-State in Participants Aged 2 to <= 16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 21, 28 days (post-infusion)]
Apparent Clearance (CL/F) of TAK-881 at Steady-State in Participants Aged 2 to <= 16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 21, 28 days (post-infusion)]
Apparent Volume of Distribution (Vz/F) of TAK-881 at Steady-State in Participants Aged 2 to <= 16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 21, 28 days (post-infusion)]
AUC0-tau; ss Per Week (AUC0-tau; ss/week) of TAK-881 at Steady-State in Participants Aged 2 to <= 16 Years with PIDD [Time Frame: 3-Week dosing: Day 1 (pre and post-infusion), 24, 48, 72 hours and 7, 14, 21 days (post-infusion); 4-Week dosing: Day 1 (pre and post-infusion), 24, 48 and 72 hours and 7, 21, 28 days (post-infusion)]
Trough Level of Total IgG in Participants Aged 2 to <16 Years and >=16 Years with PIDD [Time Frame: Up to 27 Weeks (2 to <16 years) and 51 Weeks (>=16 years)]
Trough Level of IgG Subclasses in Participants Aged 2 to <16 Years and >=16 Years with PIDD [Time Frame: Up to 27 Weeks (2 to <16 years) and 51 Weeks (>=16 years)]
Trough Level of Antigen Specific IgG Antibodies in Participants Aged >=16 Years with PIDD [Time Frame: Up to 51 Weeks]
Number of Participants With Treatment-Emergent Adverse Events (TEAEs) [Time Frame: Up to 28 Weeks (2 to <16 years) and 52 Weeks (>=16 years)]
Number of Participants With Infusion Withdrawals, Interruptions, and Infusion Rate Reductions due to TAK-881-related TEAEs [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Number of Participants With Positive Binding Antibodies (Titer Greater than and equal to [>=] 1:160) and With Positive Neutralizing Antibodies to rHuPH20 [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Number of Infusions per Month at Full Dose With Both TAK-881 and HYQVIA in all Participants [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Duration of Infusions (minutes) at Full Dose With Both TAK-881 and HYQVIA in all Participants [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Monthly Infusion (minutes/month) Time at Full Dose With Both TAK-881 and HYQVIA in all Participants [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Number of Infusions Sites (Needle Sticks) per Infusion at Full Dose With Both TAK-881 and HYQVIA in all Participants [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Number of Infusions Sites (Needle Sticks) per Month at Full Dose With Both TAK-881 and HYQVIA in all Participant [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Maximum Infusion Rate per Site (mL/hour/site) at Full Dose With Both TAK-881 and HYQVIA in all Participants [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]
Infusion Volume per Site (mL/site) at Full Dose With Both TAK-881 and HYQVIA in all Participants [Time Frame: From start of study drug administration, up to 22 Week (2 to <16 years) and 46 Week (>=16 years)]