药学学报

Regulatory region	General chapter / guidance / guideline
China	General requirements for preparations < 0111 Preparations for inhalation > (Pharmacopoeia of the People's Republic of China 2020, Volume Ⅳ)^[25] General requirements for preparations < 0106 Nasal preparations > (Pharmacopoeia of the People's Republic of China 2020, Volume Ⅳ)^[26]
	Technical guideline on the investigation of human bioequivalence of chemical drug generic drugs with pharmacokinetic parameters as the end-point (2016-03-18)^[3] Guideline on the study of bioequivalence for generic orally inhaled products (OIP) (2020-12-16)^[4]
	Technical guideline on quality control of inhaled preparations (2007-11-21)^[21]
	Guideline on statistical approaches to investigating bioequivalence (2018-10-17)^[27]
United States	< 5 > Inhalation and nasal drug products-general information and product quality tests (United States Pharmacopeia, USP43/NF38)^[28] < 601 > Inhalation and nasal drug products: aerosals, spays, and powers—performance quality tests (United States Pharmacopeia, USP2021)^[29] Code of federal regulations title 21, PART 320^[30] Guidance for industry: statistical approaches to establishing bioequivalence (2001-01)^[31] Guidance for industry: bioavailability and bioequivalence studies for orally administered drug products – general considerations draft guidance (2002-07)^[32] Guidance for industry: metered dose inhaler (MDI) and dry powder inhaler (DPI) products - quality considerations draft guidance (2018-04)^[33] Guidance for industry: nasal spray and inhalation solution, suspension, and spray drug products-chemistry, manufacturing and controls documentation (2002-07)^[34]
	Guidance for industry: bioavailability and bioequivalence studies for nasal aerosols and nasal sprays for local action (2003-04)^[22]
European Union	Preparations for inhalation. European Pharmacopoeia (EP10.0)^[35] Nasal preparations. European Pharmacopoeia (EP10.0)^[36] Directive 2001/83/EC of the European Parliament and of the Council of 6 November 2001 on the Community Code Relating to Medicinal Products for Human Use^[37] Guideline on the investigation of bioequivalence (CPMP/EWP/QWP/1401/98 Rev. 1/Corr)^[24] Guideline on the requirements for clinical documentation for orally inhaled products (OIP) including the requirements for demonstration of therapeutic equivalence between two inhaled products for use in the treatment of asthma and chronic obstructive pulmonary disease (COPD) in adults and for use in the treatment of asthma in children and adolescents (CPMP/EWP/4151/00 Rev. 1) [2009-01-22]^[2]
	Guideline on the pharmaceutical quality of inhalation and nasal products (EMEA/CHMP/QWP/49313/2005 Corr). (2006-06-21)^[23]

Regulatory region	General chapter / guidance / guideline
China	General requirements for preparations < 0111 Preparations for inhalation > (Pharmacopoeia of the People's Republic of China 2020, Volume Ⅳ)^[25] General requirements for preparations < 0106 Nasal preparations > (Pharmacopoeia of the People's Republic of China 2020, Volume Ⅳ)^[26]
	Technical guideline on the investigation of human bioequivalence of chemical drug generic drugs with pharmacokinetic parameters as the end-point (2016-03-18)^[3] Guideline on the study of bioequivalence for generic orally inhaled products (OIP) (2020-12-16)^[4]
	Technical guideline on quality control of inhaled preparations (2007-11-21)^[21]
	Guideline on statistical approaches to investigating bioequivalence (2018-10-17)^[27]
United States	< 5 > Inhalation and nasal drug products-general information and product quality tests (United States Pharmacopeia, USP43/NF38)^[28] < 601 > Inhalation and nasal drug products: aerosals, spays, and powers—performance quality tests (United States Pharmacopeia, USP2021)^[29] Code of federal regulations title 21, PART 320^[30] Guidance for industry: statistical approaches to establishing bioequivalence (2001-01)^[31] Guidance for industry: bioavailability and bioequivalence studies for orally administered drug products – general considerations draft guidance (2002-07)^[32] Guidance for industry: metered dose inhaler (MDI) and dry powder inhaler (DPI) products - quality considerations draft guidance (2018-04)^[33] Guidance for industry: nasal spray and inhalation solution, suspension, and spray drug products-chemistry, manufacturing and controls documentation (2002-07)^[34]
	Guidance for industry: bioavailability and bioequivalence studies for nasal aerosols and nasal sprays for local action (2003-04)^[22]
European Union	Preparations for inhalation. European Pharmacopoeia (EP10.0)^[35] Nasal preparations. European Pharmacopoeia (EP10.0)^[36] Directive 2001/83/EC of the European Parliament and of the Council of 6 November 2001 on the Community Code Relating to Medicinal Products for Human Use^[37] Guideline on the investigation of bioequivalence (CPMP/EWP/QWP/1401/98 Rev. 1/Corr)^[24] Guideline on the requirements for clinical documentation for orally inhaled products (OIP) including the requirements for demonstration of therapeutic equivalence between two inhaled products for use in the treatment of asthma and chronic obstructive pulmonary disease (COPD) in adults and for use in the treatment of asthma in children and adolescents (CPMP/EWP/4151/00 Rev. 1) [2009-01-22]^[2]
	Guideline on the pharmaceutical quality of inhalation and nasal products (EMEA/CHMP/QWP/49313/2005 Corr). (2006-06-21)^[23]

Study type	Regulatory agent	Dosage form	In vitro study	Statistical metric
Delivered dose from OIDP	FDA	Inhalation suspension MDI/DPI	Mean delivered dose Single actuation content at beginning (B), middle (M), and end (E) life stages using 3 flow rates	PBE PBE
	EMA		The targeted delivered dose should be similar	ABE Within ±15% difference
Particle size distribution for OIDP	FDA	Inhalation suspension MDI DPI	Comparative drug particle and agglomerate particle size distribution in nebulized aerosol at the specified flow rate per RLD labeling Aqueous droplet size distribution by a laser diffraction method APSD at the B and E life stages at one flow rates APSD at the B and E life stages at three flow rates	ABE PBE PBE PBE
	EMA		APSD comparison (including FPM and upper stages) performed per impactor stage or justified group of stages (at least 4 groups of stages are expected). Data should be obtained with a range of clinically relevant flow rates of the target patient population.	ABE: in vitro difference should be indicated and justified, e.g., ± 15%
Others	FDA	Inhalation suspension	Comparative mean nebulization time Comparative drug particle and agglomerate particle size distribution in the suspension Comparative unit dose content of drug in the ampules	ABE ABE ABE
	FDA EMA	MDI	Spray pattern at B life stage at two distances Plume geometry at B life stage Priming and repriming Inhaled volume The active substance is in the solid state (powder, suspension): crystalline structure and/or polymorphic form aerosol particle behaviour (e.g. hygroscopic effect, plume dynamic and geometry)	PBE ABE 90%-111% PBE ABE within ± 15%

Study type	Regulatory agent	Dosage form	In vitro study	Statistical metric
Delivered dose from OIDP	FDA	Inhalation suspension MDI/DPI	Mean delivered dose Single actuation content at beginning (B), middle (M), and end (E) life stages using 3 flow rates	PBE PBE
	EMA		The targeted delivered dose should be similar	ABE Within ±15% difference
Particle size distribution for OIDP	FDA	Inhalation suspension MDI DPI	Comparative drug particle and agglomerate particle size distribution in nebulized aerosol at the specified flow rate per RLD labeling Aqueous droplet size distribution by a laser diffraction method APSD at the B and E life stages at one flow rates APSD at the B and E life stages at three flow rates	ABE PBE PBE PBE
	EMA		APSD comparison (including FPM and upper stages) performed per impactor stage or justified group of stages (at least 4 groups of stages are expected). Data should be obtained with a range of clinically relevant flow rates of the target patient population.	ABE: in vitro difference should be indicated and justified, e.g., ± 15%
Others	FDA	Inhalation suspension	Comparative mean nebulization time Comparative drug particle and agglomerate particle size distribution in the suspension Comparative unit dose content of drug in the ampules	ABE ABE ABE
	FDA EMA	MDI	Spray pattern at B life stage at two distances Plume geometry at B life stage Priming and repriming Inhaled volume The active substance is in the solid state (powder, suspension): crystalline structure and/or polymorphic form aerosol particle behaviour (e.g. hygroscopic effect, plume dynamic and geometry)	PBE ABE 90%-111% PBE ABE within ± 15%

Test	BA and BE study measure	BE measure for statistical evaluation	Lifestage B (beginning), M (middle), E (end)	Statistical evaluation for BE
Single actuation content through container life	Drug mass per single actuation	Same as previous column	B, M, E (aerosols) B, E (sprays)	PBE
Droplet size distribution by laser diffraction	D₁₀, D₅₀, D₉₀, span at 2 distances	D₅₀, span	B, E	PBE
Drug in small particles/droplets by cascade impactor	Drug mass below upper stage	Same as previous column	B (sprays)	PBE modified to be one- sided with respect to the mean comparison
Particle/droplet size distribution by cascade impactor	Drug mass on individual accessories, stages, etc	Deposition profile	B (aerosols)	Profile analysis
Drug particle size distribution by microscopy for suspensions	Drug CMD; extent of agglomerate	Same as previous column	B	Not applicable
Spray pattern	Automated analysis: area ovality ratio at 2 distances or manual analysis: D_max, ovality ratio at 2 distances	Qualitative - shape comparison Quantitative - same as previous column	B	PBE for area and ovality ratio (automated analysis) or D_max and ovality ratio manual analysis
Plume geometry	Height, width, and cone angle of one side view at one delay time	Width and cone angle of one side view at one delay time	B	Point estimates
Priming and repriming	Drug mass per single actuation at first primed or reprimed actuation	Same as previous column for priming, and repriming if in precursor product (R) labeling	B (priming) lifestage not specified (repriming)	Point estimate relative to label claim if in precursor product (R) labeling

Test	BA and BE study measure	BE measure for statistical evaluation	Lifestage B (beginning), M (middle), E (end)	Statistical evaluation for BE
Single actuation content through container life	Drug mass per single actuation	Same as previous column	B, M, E (aerosols) B, E (sprays)	PBE
Droplet size distribution by laser diffraction	D₁₀, D₅₀, D₉₀, span at 2 distances	D₅₀, span	B, E	PBE
Drug in small particles/droplets by cascade impactor	Drug mass below upper stage	Same as previous column	B (sprays)	PBE modified to be one- sided with respect to the mean comparison
Particle/droplet size distribution by cascade impactor	Drug mass on individual accessories, stages, etc	Deposition profile	B (aerosols)	Profile analysis
Drug particle size distribution by microscopy for suspensions	Drug CMD; extent of agglomerate	Same as previous column	B	Not applicable
Spray pattern	Automated analysis: area ovality ratio at 2 distances or manual analysis: D_max, ovality ratio at 2 distances	Qualitative - shape comparison Quantitative - same as previous column	B	PBE for area and ovality ratio (automated analysis) or D_max and ovality ratio manual analysis
Plume geometry	Height, width, and cone angle of one side view at one delay time	Width and cone angle of one side view at one delay time	B	Point estimates
Priming and repriming	Drug mass per single actuation at first primed or reprimed actuation	Same as previous column for priming, and repriming if in precursor product (R) labeling	B (priming) lifestage not specified (repriming)	Point estimate relative to label claim if in precursor product (R) labeling

E_q = point estimate	H_q = confidence bound	U_q= (H_q - E_q)²
$ {E}_{\mathrm{D}}={\widehat{\mathrm{\Delta }}}^{2} $	$ {H}_{D}={\left(\left\|\widehat{\mathrm{\Delta }}\right\|+{t}_{1-\alpha , {n}_{T}\cdot {l}_{T}+{n}_{R}\cdot {l}_{R}-2}{\left(\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{{n}_{\mathrm{T}}\cdot {l}_{\mathrm{T}}\cdot m}+\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{{n}_{\mathrm{R}}\cdot {l}_{\mathrm{R}}\cdot m}\right)}^{1/2}\right)}^{2} $	$ {U}_{\mathrm{D}} $
$ E1=\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m} $	$ H1=\frac{\left({l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}-1\right)\cdot E1}{{\chi }_{{l}_{T}\cdot {n}_{T}-1, \alpha }^{2}} $	$ U1 $
$ E2=\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m} $	$ H2=\frac{{l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}\left(m-1\right)\cdot E2}{{\chi }_{{l}_{T}\cdot {n}_{T}\cdot (m-1), \alpha }^{2}} $	$ U2 $
$ E3s=-\left(1+{\theta }_{p}\right)\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m} $	$ H3s=\frac{\left({l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}-1\right)\cdot E3s}{{\chi }_{{l}_{R}\cdot {n}_{R}-\mathrm{1, 1}-\alpha }^{2}} $	$ U3s $
$ E4s=-(1+{\theta }_{p})\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m} $	$ H4s=\frac{{l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}\left(m-1\right)\cdot E4s}{{\chi }_{{l}_{R}\cdot {n}_{R}\cdot (m-1), 1-\alpha }^{2}} $	$ U4s $

E_q = point estimate	H_q = confidence bound	U_q= (H_q - E_q)²
$ {E}_{\mathrm{D}}={\widehat{\mathrm{\Delta }}}^{2} $	$ {H}_{D}={\left(\left\|\widehat{\mathrm{\Delta }}\right\|+{t}_{1-\alpha , {n}_{T}\cdot {l}_{T}+{n}_{R}\cdot {l}_{R}-2}{\left(\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{{n}_{\mathrm{T}}\cdot {l}_{\mathrm{T}}\cdot m}+\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{{n}_{\mathrm{R}}\cdot {l}_{\mathrm{R}}\cdot m}\right)}^{1/2}\right)}^{2} $	$ {U}_{\mathrm{D}} $
$ E1=\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m} $	$ H1=\frac{\left({l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}-1\right)\cdot E1}{{\chi }_{{l}_{T}\cdot {n}_{T}-1, \alpha }^{2}} $	$ U1 $
$ E2=\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m} $	$ H2=\frac{{l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}\left(m-1\right)\cdot E2}{{\chi }_{{l}_{T}\cdot {n}_{T}\cdot (m-1), \alpha }^{2}} $	$ U2 $
$ E3s=-\left(1+{\theta }_{p}\right)\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m} $	$ H3s=\frac{\left({l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}-1\right)\cdot E3s}{{\chi }_{{l}_{R}\cdot {n}_{R}-\mathrm{1, 1}-\alpha }^{2}} $	$ U3s $
$ E4s=-(1+{\theta }_{p})\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m} $	$ H4s=\frac{{l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}\left(m-1\right)\cdot E4s}{{\chi }_{{l}_{R}\cdot {n}_{R}\cdot (m-1), 1-\alpha }^{2}} $	$ U4s $

E_q = point estimate	H_q = confidence bound	U_q = (H_q - E_q)²
$ {E}_{\mathrm{D}}={\widehat{\mathrm{\Delta }}}^{2} $	$ {H}_{D}={\left(\left\|\widehat{\mathrm{\Delta }}\right\|+{t}_{1-\alpha , {n}_{T}\cdot {l}_{T}+{n}_{R}\cdot {l}_{R}-2}{\left(\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{{n}_{\mathrm{T}}\cdot {l}_{\mathrm{T}}\cdot m}+\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{{n}_{\mathrm{R}}\cdot {l}_{\mathrm{R}}\cdot m}\right)}^{1/2}\right)}^{2} $	$ {U}_{\mathrm{D}} $
$ E1=\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m} $	$ H1=\frac{\left({l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}-1\right)\cdot E1}{{\chi }_{{l}_{T}\cdot {n}_{T}-1, \alpha }^{2}} $	$ U1 $
$ E2=\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{T}}{m} $	$ H2=\frac{{l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}\left(m-1\right)\cdot E2}{{\chi }_{{l}_{T}\cdot {n}_{T}\cdot (m-1), \alpha }^{2}} $	$ U2 $
$ E3c=-\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m} $	$ H3c=\frac{\left({l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}-1\right)\cdot E3c}{{\chi }_{{l}_{R}\cdot {n}_{R}-\mathrm{1, 1}-\alpha }^{2}} $	$ U3c $
$ E4c=-\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m} $	$ H4c=\frac{{l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}\left(m-1\right)\cdot E4c}{{\chi }_{{l}_{R}\cdot {n}_{R}\cdot (m-1), 1-\alpha }^{2}} $	$ U4c $

E_q = point estimate	H_q = confidence bound	U_q = (H_q - E_q)²
$ {E}_{\mathrm{D}}={\widehat{\mathrm{\Delta }}}^{2} $	$ {H}_{D}={\left(\left\|\widehat{\mathrm{\Delta }}\right\|+{t}_{1-\alpha , {n}_{T}\cdot {l}_{T}+{n}_{R}\cdot {l}_{R}-2}{\left(\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{{n}_{\mathrm{T}}\cdot {l}_{\mathrm{T}}\cdot m}+\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{{n}_{\mathrm{R}}\cdot {l}_{\mathrm{R}}\cdot m}\right)}^{1/2}\right)}^{2} $	$ {U}_{\mathrm{D}} $
$ E1=\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m} $	$ H1=\frac{\left({l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}-1\right)\cdot E1}{{\chi }_{{l}_{T}\cdot {n}_{T}-1, \alpha }^{2}} $	$ U1 $
$ E2=\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{T}}{m} $	$ H2=\frac{{l}_{\mathrm{T}}\cdot {n}_{\mathrm{T}}\left(m-1\right)\cdot E2}{{\chi }_{{l}_{T}\cdot {n}_{T}\cdot (m-1), \alpha }^{2}} $	$ U2 $
$ E3c=-\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m} $	$ H3c=\frac{\left({l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}-1\right)\cdot E3c}{{\chi }_{{l}_{R}\cdot {n}_{R}-\mathrm{1, 1}-\alpha }^{2}} $	$ U3c $
$ E4c=-\frac{\left(m-1\right)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m} $	$ H4c=\frac{{l}_{\mathrm{R}}\cdot {n}_{\mathrm{R}}\left(m-1\right)\cdot E4c}{{\chi }_{{l}_{R}\cdot {n}_{R}\cdot (m-1), 1-\alpha }^{2}} $	$ U4c $

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 106	H_D = 0.113 976 896	U_D = 0.008 442 447
E1 = 0.219 742 944	H1 = 0.359 860 715	U1 = 0.019 632 99
E2 = 3.910 8e-05	H2 = 5.433 19e-05	U2 = 2.317 65e-10
E3c = -0.163 644 789	H3c = -0.111 514 028	U3c = 0.002 717 616
E4c = -8.308 95e-05	H4c = -6.304 05e-05	U4c = 4.019 6e-10
E_q = 0.057 257 267		U_q = 0.030 793 054	H_η = 0.232 736 764

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 106	H_D = 0.113 976 896	U_D = 0.008 442 447
E1 = 0.219 742 944	H1 = 0.359 860 715	U1 = 0.019 632 99
E2 = 3.910 8e-05	H2 = 5.433 19e-05	U2 = 2.317 65e-10
E3c = -0.163 644 789	H3c = -0.111 514 028	U3c = 0.002 717 616
E4c = -8.308 95e-05	H4c = -6.304 05e-05	U4c = 4.019 6e-10
E_q = 0.057 257 267		U_q = 0.030 793 054	H_η = 0.232 736 764

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 106	H_D = 0.113 976 896	U_D = 0.008 442 447
E1 = 0.219 742 944	H1 = 0.359 860 715	U1 = 0.019 632 99
E2 = 3.910 8e-05	H2 = 5.433 19e-05	U2 = 2.317 65e-10
E3s = -0.505 515 326	H3s = -0.344 478 125	U3s = 0.025 932 98
E4s = -0.000 256 672	H4s = -0.000 194 739	U4s = 3.835 72e-09
E_q = -0.263 895 84		U_q = 0.054 008 421	H_η = -0.031 498 721

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 106	H_D = 0.113 976 896	U_D = 0.008 442 447
E1 = 0.219 742 944	H1 = 0.359 860 715	U1 = 0.019 632 99
E2 = 3.910 8e-05	H2 = 5.433 19e-05	U2 = 2.317 65e-10
E3s = -0.505 515 326	H3s = -0.344 478 125	U3s = 0.025 932 98
E4s = -0.000 256 672	H4s = -0.000 194 739	U4s = 3.835 72e-09
E_q = -0.263 895 84		U_q = 0.054 008 421	H_η = -0.031 498 721

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 1	H_D = 0.113 976 9	U_D = 0.008 442 445
E1 = 0.219 742 9	H1 = 0.359 860 7	U1 = 0.019 632 99
E2 = 3.910 825e-05	H2 = 5.433 216e-05	U2 = 2.317 674e-10
E3c = -0.163 644 8	H3c = -0.111 514	U3c = 0.002 717 616
E4c = -8.308 86e-05	H4c = -6.303 988e-05	U4c = 4.019 514e-10
E_q = 0.057 258 26		U_q = 0.030 793 05	H_η = 0.232 737 7

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 1	H_D = 0.113 976 9	U_D = 0.008 442 445
E1 = 0.219 742 9	H1 = 0.359 860 7	U1 = 0.019 632 99
E2 = 3.910 825e-05	H2 = 5.433 216e-05	U2 = 2.317 674e-10
E3c = -0.163 644 8	H3c = -0.111 514	U3c = 0.002 717 616
E4c = -8.308 86e-05	H4c = -6.303 988e-05	U4c = 4.019 514e-10
E_q = 0.057 258 26		U_q = 0.030 793 05	H_η = 0.232 737 7

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 1	H_D = 0.113 976 9	U_D = 0.008 442 445
E1 = 0.219 742 9	H1 = 0.359 860 7	U1 = 0.019 632 99
E2 = 3.910 825e-05	H2 = 5.433 216e-05	U2 = 2.317 674e-10
E3s = -0.505 498 7	H3s = -0.344 466 8	U3s = 0.025 931 28
E4s = -0.000 256 660 7	H4s = -0.000 194 730 2	U4s = 3.835 388e-09
E_q = -0.263 879 3		U_q = 0.054 006 71	H_η = -0.031 485 82

E_q related intermediate parameter	H_q related intermediate parameter	U_q related intermediate parameter	H_η = E_q + (U_q)^1/2
E_D = 0.022 094 1	H_D = 0.113 976 9	U_D = 0.008 442 445
E1 = 0.219 742 9	H1 = 0.359 860 7	U1 = 0.019 632 99
E2 = 3.910 825e-05	H2 = 5.433 216e-05	U2 = 2.317 674e-10
E3s = -0.505 498 7	H3s = -0.344 466 8	U3s = 0.025 931 28
E4s = -0.000 256 660 7	H4s = -0.000 194 730 2	U4s = 3.835 388e-09
E_q = -0.263 879 3		U_q = 0.054 006 71	H_η = -0.031 485 82

经口吸入和鼻用药物制剂体外生物等效性统计学评价方法

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耿颖 ¹ , 杨泉 ² , 张军 ³ , 王蕊 ¹ , 周颖 ¹ , 郑静 ¹ , 宁保明 ¹^,^* , 魏宁漪 ¹^,^*

药学学报 | 专题报道：吸入给药系统 2021,56(10): 2630-2641

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药学学报 | 专题报道：吸入给药系统 2021, 56(10): 2630-2641

经口吸入和鼻用药物制剂体外生物等效性统计学评价方法

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耿颖¹, 杨泉², 张军³, 王蕊¹, 周颖¹, 郑静¹, 宁保明¹^,^*, 魏宁漪¹^,^*

作者信息

1.中国食品药品检定研究院, 北京 102629

2.默克雪兰诺 (北京) 医药研发有限公司, 北京 100000

3.国家药典委员会, 北京 100061

通讯作者:

*宁保明, Tel/Fax: 86-10-53851575, E-mail: ningbm@nifdc.org.cn;

魏宁漪, Tel: 86-10-53851604, E-mail: weiny@nifdc.org.cn

Statistical evaluation methods of in vitro studies for bioequivalence for orally inhaled and nasal drug products

Ying GENG¹, Quan YANG², Jun ZHANG³, Rui WANG¹, Ying ZHOU¹, Jing ZHENG¹, Bao-ming NING¹^,^*, Ning-yi WEI¹^,^*

Affiliations

1. National Institutes for Food and Drug Control, Beijing 102629, China

2. Merck Serono (Beijing) Pharmaceutical R&D Co., Ltd., Beijing 100000, China

3. Chinese Pharmacopoeia Commission, Beijing 100061, China

出版时间: 2021-10-12 doi: 10.16438/j.0513-4870.2021-0640

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摘要

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本文系统阐述了经口吸入和鼻用药物制剂（orally inhaled and nasal drug products，OINDPs）生物等效性（bioequivalence，BE）研究评估背景，综述了中国及国际上对该类制剂生物等效性的要求及体外等效性评价指导原则，详细阐述了美国食品药品管理局（FDA）体外生物等效性（in vitro bioequivalence，IVBE）评估的统计学方法和计算公式。采用FDA颁布的布地奈德吸入混悬液指导原则拟定稿中的实例，通过R语言编程途径计算群体生物等效性（population bioequivalence，PBE）统计学参数，并将结果与指导原则中的结果进行对比，提供计算程序的伪代码。本文为OINDPs的研发、质量控制及仿制制剂的开发提供了有益的思路与参考。

关键词

经口吸入和鼻用药物 / 生物等效性 / 体外生物等效性 / 群体生物等效性 / 计算程序伪代码 / 布地奈德吸入混悬液

Abstract

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This article systematically reviews the background and regulatory requirements of bioequivalence of orally inhaled and nasal drug products (OINDPs), as well as the basic regulatory requirements for the assessment by the guidelines and guidance issued in China, the United States, and the European Union. Detailed statistical evaluation method considerations and calculations of the US FDA population bioequivalence (PBE) method were presented for the evaluation of in vitro bioequivalence (IVBE) for OINDPs. Using the example described in the FDA Draft Guidance for budesonide inhalation suspension, the PBE analysis statistical parameters were calculated via the R programming, and the results were compared with that in the guidelines. Moreover, pseudo-code for the PBE calculation program was provided. This paper aims to provide guidance and references for the research and development of new drug, as well as pharmaceutical quality control, and development of generic medicinal products for OINDPs.

Key words

orally inhaled and nasal drug product / bioequivalence / in vitro bioequivalence / population bioequivalence / pseudo-code of calculation program / budesonide inhalation suspension

引用本文

耿颖, 杨泉, 张军, 王蕊, 周颖, 郑静, 宁保明, 魏宁漪. 经口吸入和鼻用药物制剂体外生物等效性统计学评价方法. 药学学报, 2021 , 56 (10) : 2630 -2641 . DOI: 10.16438/j.0513-4870.2021-0640

Ying GENG, Quan YANG, Jun ZHANG, Rui WANG, Ying ZHOU, Jing ZHENG, Bao-ming NING, Ning-yi WEI. Statistical evaluation methods of in vitro studies for bioequivalence for orally inhaled and nasal drug products[J]. Acta Pharmaceutica Sinica, 2021 , 56 (10) : 2630 -2641 . DOI: 10.16438/j.0513-4870.2021-0640

正文

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在2020年版《中国药典》制剂通则中, 吸入制剂系指原料药物溶解或分散于适宜介质中, 以气溶胶或蒸汽形式递送至肺部发挥局部或全身作用的液体或固体制剂。吸入制剂包括吸入气雾剂、吸入粉雾剂、吸入喷雾剂、吸入液体制剂和可转变成蒸汽的制剂。鼻用制剂系指直接用于鼻腔, 发挥局部或全身治疗作用的制剂, 包括滴鼻剂、洗鼻剂、鼻用气雾剂、鼻用喷雾剂、鼻用粉雾剂、鼻用软膏剂、鼻用乳膏剂、鼻用凝胶剂、鼻用散剂和鼻用棒剂。在美国药典中将吸入和鼻用制剂(inhalation and nasal products) 归为一大类, 包括了经口吸入和鼻用药物制剂(orally inhaled and nasal drug products, OINDPs), 欧洲药典对吸入制剂及鼻用制剂也有分别的通则进行描述, 但与中国药典的分类略有区别。

1 生物等效性(bioequivalence, BE) 及体内(in vivo)、体外(in vitro) 研究

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生物等效性研究在新药的变更研究和仿制药物的开发和审批中起重要作用, 是比较受试制剂(T) 与参比制剂(R) 的吸收速度和吸收程度的差异是否在可接受范围内的研究。美国相关药品法规中, BE强调在其作用部位的药物的等效性, 通常包括直接指示药物作用部位的药效动力学(pharmacodynamics, PD), 反映药物在其作用部位的可用性的药代动力学(pharmacokinetics, PK) 和临床终点研究(clinical endpoint, CE)^[1]; 在欧洲药品管理局(European Medicines Agency, EMA) 指导原则中, 生物等效性主要强调全身暴露, 即PK研究。对于局部作用的口服吸入药物产品, 其中PK、PD和/或体外等效性研究均是可能进行的评估, 对于该类药物的等效使用术语为“治疗效果等效(therapeutic equivalence, TE)”^[2]。我国指导原则中对于BE的定义是基于药动学终点^[3], 国家药品监督管理局药品审评中心(CDE) 发布的《经口吸入制剂仿制药生物等效性研究指导原则》中认为经口吸入制剂首先被递送到作用部位, 而后进入体循环, 同时还通过其他部位如口、咽和胃肠道等进入体循环, PK和局部递药等效性之间关系复杂, 通常仅采用PK方法评价其与参比制剂等效依据尚不充分^[4]。

美国、欧盟和中国的指南/指导原则均指出, 可通过体内和体外方法建立特定药物产品的生物等效性。适用于经口吸入药物制剂(orally inhaled drug products, OIDPs) 的体内BE研究有3种类型^[1]: PK、PD和CE。对于局部作用的OIDPs, 人体PK研究的主要目的是测定吸入活性物质的全身暴露, 或者与参比制剂相比, 监测吸入药物的全身安全性。如果活性物质的血液浓度太低而无法在PK研究中可靠地量化, 也可进行临床PD研究。此外, 适当的PK研究(如活性炭阻断条件下) 也被认为提供了间接证据, 支持局部递送到适当的作用部位的一致性。PD和临床终点研究通常用作评估局部作用OIDPs临床效果等效性的方法。

与传统剂型不同, 大多数吸入产品被设计为局部作用于肺部^{[5, 6]}, 其药物递送并不完全或并不直接依赖于体循环。此外, 大多数吸入产品是复杂的剂型, 整合了处方和设备, 增加了其BE建立的复杂性。体外测试的科学性和实用性挑战来源于以下两个方面: ①基础科学研究的发展加强了对药物递送系统和递送后吸入肺部药物行为的了解; ②当前和新兴的体外测试方法和应用。体外数据的分析和解释对于决策起到越来越重要的作用; 应用体外测试方法准确测量和表征经OIDPs的有效吸入能力为建立仿制药和创新产品的开发和监管质量标准提供了工具^[7-9]。

2 中国及国际上对经口吸入制剂及鼻用制剂的生物等效性要求

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2.1 经口吸入制剂的生物等效性要求

目前, FDA对于经口吸入制剂的BE建立是基于证据权重(weight-of-evidence approach) 的方法^[8], 要求同时满足以下三者的一致性: ①体外研究确定受试和参比制剂的体外一致; ② PK研究以确定全身暴露的等效性; ③ PD或CE研究以证明局部作用的等效性, 同时还要考虑处方和设备的相似性。针对OINDPs中的各类剂型FDA发布了多个具有代表性的各论指导原则^[10-18]。FDA在国际各类OIDPs指导原则中要求较为谨慎, 但在新颁布的异丙托溴铵吸入气雾剂指导原则^[19]中提出了支持新的BE途径开发, 为体外实验部分替代临床试验提供了可能性, 并且接受计算机模拟研究, 这将成为体外雾化特性研究的新热点。

EMA颁布的经口吸入产品指导原则中采用循序渐进法(step-wise)^{[2, 7-9]}, 以建立治疗效果等效: 申请人首先可研究受试制剂与参比制剂的体外一致性, 如果满足所有体外一致要求(包含设备的一致性), 则可以批准; 如果无法证明体外一致, 则需进行肺部沉积和全身暴露的比较研究; 如果可证明等效, 则可以批准; 否则, 需要继续进行药效学等效性评估。理论上如果所有体外一致性测试均成功, 则可不进行其他的安全性及有效性临床试验; 当吸入溶液(solutions for nebulization) 与参比制剂具有相同的定性和定量组成时, 可豁免临床研究的要求。对于吸入混悬液(suspensions for nebulization), 应通过体内研究来证明治疗等效性, 除非提供了使用其他类型研究证明等效性的理由^{[2, 20]}。EMA发布的上述要求在国际同类指导原则中要求较为宽泛。

目前我国已颁布的吸入制剂相关指导原则有: 《吸入制剂质量控制研究技术指导原则》^[21]和《经口吸入制剂仿制药生物等效性研究指导原则》^[4], 其中对于口服吸入制剂评价的总体要求与FDA较为相似, 包括体外药学等效性研究及人体生物等效性试验, 后者包括PK-BE、PD-BE和CE。其中对于吸入溶液制剂, 如证明与参比制剂药学质量一致, 通常不再要求进行人体生物等效性研究。但指导原则中未对具体的实验项目内容及参数、结果计算和统计方法等内容进行详细规定, 鉴于不同的统计方法会造成体内外等效性判断结果的不同, 建议我国的相关指导原则进行进一步细化或发布配套文件。

2.2 鼻用制剂的生物等效性要求

对于局部给药机制的鼻用制剂, 用传统的药代动力学方法进行仿制制剂生物等效性分析缺乏准确性; 通过对鼻用制剂体外特性进行分析, 可以预测药物在体内的沉积情况, 从而评价仿制制剂和参比制剂之间的生物等效性。各国监管机构对于鼻用制剂体外特性的控制和监管要求不尽相同, 对于溶液型和混悬型的鼻喷剂, 质量标准控制的关键质量属性及其检测方法具有差异。此外, 对于仿制制剂, 其获批的豁免原则, 各国的指导原则也具有较大差异。对于鼻用药物制剂, 美国FDA指南^[22]中指出: 企业需按照规定提供生物利用度(bioavailability, BA) 和BE数据, 可以使用体内、药代动力学、药效学或临床和体外研究, 在某些情况下, 可单独使用体外研究来建立BA和BE。对于溶液型鼻喷剂, FDA对其仿制制剂的生物等效性研究包括以下几点: 仿制制剂应与参比制剂在质(Q1) 和量(Q2) 两方面一致; 仿制制剂与参比制剂的密闭系统及装置与参比制剂具有可比性; 通过体外实验来验证仿制制剂与参比制剂的等效性。对混悬型鼻喷剂仿制制剂的要求除了满足上述条件外, 还需进行体内生物等效性试验及安全性实验。

EMA尚未颁布对于鼻用制剂的生物等效指导原则, 在其吸入制剂和鼻用制剂药学质量指导原则^[23]中规定: 对于声称与原研制剂基本相似的仿制药鼻用制剂, 证明治疗等效性所需的研究可能取决于药物活性组分对于预期部位的作用(局部或全身)。对于局部应用、局部作用产品, 应满足EMA生物等效性指导原则^[24]的相应要求, 即: 如果仿制药是相同类型的溶液(水性或油性), 并且含有与当前批准的参比制剂有相同浓度的相同活性物质, 例如滴眼液、鼻喷雾剂或皮肤用溶液, 豁免提供临床等效性数据可能是可以接受的。如果仿制药和参比制剂的相关药学特性相同或基本相似, 辅料组成的微小差异也可能是可以接受的。辅料中的任何定性或定量差异在影响治疗等效性方面必须得到充分的论证。除非另有说明, 给药方式和方法也应与当前批准的药品相同。当局部应用、局部作用的药物产生的全身暴露存在全身不良反应的风险时, 应测量全身暴露。应证明受试制剂的全身暴露量不高于参比制剂, 即90%置信区间的上限不应超过生物等效性可接受限度的上限125.00%。在药学方面, 对于鼻用喷雾剂, 须使用经过验证的方法(如激光衍射) 提供仿制剂与原研制剂的完整液滴尺寸分布的比较数据。对于鼻用喷雾剂和鼻用粉雾剂, 需比较仿制制剂与原研制剂的递送剂量。

我国尚未颁布对鼻用制剂体外特性评价方法的相关指导原则, 然而经口吸入和鼻用制剂给药同属于局部给药, 具有一定的借鉴意义, 也说明我国正在对局部给药制剂研发与质量控制进行完善。FDA和EMA关于鼻用药物制剂BE研究的相关指南也具有参考和指导意义。

中国、美国和欧盟相关药典通则、指南和指导原则见表 1^{[2-4, 21-37]}。

3 FDA指南和EMA指导原则提出的体外生物等效性评价

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3.1 吸入制剂体外评价项目和要求

在吸入制剂的研发过程中, 体外研究与体内效能的相关性尚未完全了解, 尽管如此, 由于与体内研究相比, 体外测定通常更简便、更敏感和变异更小, 因而科学系统的体外研究在BE评估中极其重要^[8]。在吸入制剂评价中, 体外等效评估的关键项目包括递送剂量和空气动力学粒径分布。由于不同剂型具有其特殊性, 以及局部用药部位(肺部、鼻腔) 对有效粒径分布要求不同, 对于不同的剂型, 经口吸入制剂和鼻用制剂考虑的体外评价项目和接受限度也有所差异。

3.1.1 经口吸入制剂

对于经口吸入制剂, FDA指南和EMA指导原则中对于雾化吸入制剂、定量吸入气雾剂、吸入粉雾剂的体外评价项目和要求见表 2。FDA、EMA和中国要求通常使用受试制剂和参比制剂至少各3批, FDA另要求体外测试每批不少于10个剂量单位。由于经口吸入制剂多为药械组合产品, 其受试制剂与参比制剂的吸入装置的使用方式应相似。欧盟要求如产品有建议同时使用的储雾罐, 其对比研究也应提供。

3.1.2 鼻用气雾剂和喷雾剂

对于鼻用气雾剂和喷雾剂, FDA指南^[22]中确定了完整的体外等效评价法和测试项目(表 3) 来表征递送的局部作用药物的体外生物利用度和体外生物等效性。通常将对受试制剂和参比制剂至少各3批进行体外BE研究, 其中显微药物粒径分布项目仅适用于混悬型鼻用喷雾剂和鼻用气雾剂, 其他项目均适用于溶液型和混悬型鼻用喷雾剂和鼻用气雾剂。FDA上述指南中描述的体外测试项目也被欧盟所接受, 不同之处在于, 欧盟的所有体外比较方法都应基于平均生物等效性而不是群体生物等效性统计方法, 默认情况下, ±15%被认为是可接受的限度^[8]。

由上述内容可见, 对于不同的剂型, FDA指南和EMA指导原则所要求进行体外生物等效性评价的项目与评价方法也不同, 体现出经口吸入和鼻用药物局部递送的复杂性和审评审批面临的挑战。目前我国尚无对于经口吸入和鼻用药物体外生物等效测试项目和接受标准的详细指导原则, 仅规定受试制剂与参比制剂体外药学质量一致作为药代动力学研究和药效动力学研究或随机对照临床试验的前提; 对于质量特性对比研究, 原则上应选用至少3批仿制制剂和3批参比制剂用于研究, 推荐使用统计学方法进行质量特性相似性比较^[4]。

3.2 BE研究的统计学方法与考虑

FDA指南中评估经口和鼻用药物的体外生物等效性测试的统计方法分类为比较(comparative) 型和非比较(non-comparative) 型; 在比较型方法中, 又分为非轮廓(non-profile analysis) 分析和轮廓(profile analysis) 分析^[38]。

3.2.1 非比较分析

对于每个体外测试, FDA都要求进行非比较分析。非比较分析是指通过描述性统计数据对生物利用度数据进行统计汇总。应记录体外实验结果的平均值(标示量百分含量)、标准偏差和变异系数(coefficient of variation, CV)。更具体而言, 处方量的总体样品均值应在所有样本(如瓶/罐) 使用阶段(预喷和再预喷评估除外), 以及批次或批次中取平均值。除了总体方法外, 还应提供在所有使用阶段中所有瓶/罐平均的总体均值, 以及在所有使用阶段中所有批次(或批次平均值) 的总体均值。对于每个单独的测试样品, 应当报告每个阶段的数据、均值、标准差和CV百分比、批间、批内, 以及批内-样品(如瓶/罐) 的使用周期变异性, 并通过适当的统计模型进行评估^[38]。

3.2.2 比较分析—非轮廓分析

非轮廓分析为主要的比较分析方法, 适用于①容器寿命内剂量或喷雾剂量均匀性; ②级联撞击法微细粒子剂量; ③喷雾模式; ④预喷和再预喷。假设随机选择分别来自测试和参比制剂的m_T和m_R罐进行体外生物等效性测试, 并从每个罐中获得一个观察结果。数据可以通过公式(1) 模型描述^[38]:

(1)$ {y}_{ik}={\mu }_{k}+{\epsilon }_{jk}, \;\;\;\;\;\; j=1, ..., {m}_{k} $

其中, k = T为受试制剂; k = R为参比制剂; $ {\mu }_{\mathrm{T}} $和$ {\mu }_{R} $为产品固定效应; $ {\epsilon }_{jk}\mathrm{\text{'}}\mathrm{s} $为独立的随机测量误差, 分布服从$ N\left(0, {\sigma }_{k}^{2}\right) $, m_k为来自受试和参比制剂的实验检测值数量。

3.2.3 比较分析-轮廓分析

轮廓分析为级联撞击器检测粒径/雾滴分布的分析方法^{[38, 39]}, 适用于鼻用制剂粒径/雾滴分布项目, 可以根据比较其卡方差异来评估受试制剂和参比制剂粒子轮廓的等效性, 轮廓分析法仍在广泛讨论中^[39-42]。方法的基础: 比较测试制剂和参比制剂级联撞击器在各个层级检测值的卡方差异。

P_Tj和P_Rj分别表示受试制剂罐和参比制剂罐在级联撞击器第j个层级的药量沉积百分比; 卡方统计量定义见公式(2)。卡方比值见公式(3)。

(2)$\mathrm{D}_{\mathrm{TR}}=\sum\limits_{j=1}^{J} \frac{\left(P_{T j}-P_{R j}\right)^{2}}{\left(P_{T j}+P_{R j}\right) / 2}$

(3)$\mathrm{RD}_{\text {TR }}=\mathrm{D}_{\text {TR }} / \mathrm{D}_{\mathrm{RR}}$

对于给定的3组样品(受试制剂T, 参比制剂R, 参比制剂R'), R与R'所观察到的PSD轮廓并非完全相同。在该条件下, 卡方比值见公式(4)。

(4)$\mathrm{RD}_{\mathrm{TR}}=\mathrm{D}_{\mathrm{TR}^{*}} / \mathrm{D}_{\mathrm{RR}}, $

其中,

$\begin{aligned}&\mathrm{D}_{\mathrm{TR}^{*}}=\sum\limits_{j=1}^{J} \frac{\left(P_{T j}-\bar{P}_{R j}\right)^{2}}{\left(P_{T j}+\bar{P}_{R j}\right) / 2} \\ &\mathrm{D}_{\mathrm{RR}^{\prime}}=\sum\limits_{j=1}^{J} \frac{\left(P_{R j}-P_{R j}\right)^{2}}{\left(P_{R j}+P_{R^{\prime}}\right) / 2} \end{aligned}$

$ {\stackrel{-}{P}}_{Rj} $为参比制剂R和参比制剂R'级在联撞击器第j个层级的沉积百分比的均值。

FDA推荐采用bootstrap法对于选定的样本进行计算^{[38, 39]}: 数学期望E(RD_TR) = E(D_TR*/D_RR’) 的95%置信上限作为等效性的度量, 即如果E(RD_TR) 的95%的置信上限小于等效性限度, 则认为这两种产品是等效的。测试步骤如下: 假设从每种样品(测受试或参比) 中, 随机抽取3批。每批抽取10个样品(如瓶或罐) 进行测试, 获得测试结果。然后将每批受试制剂与2批参比制剂进行组合, 采用bootstrap法进行数据模拟, 计算不少于500个, 共计6种配对方式的受试-参比R-参比R'组合的RD_TR值的均值。重复上述步骤不少于300次, 得出RD_TR均值的分布, 从该平均比值的分布中, 报告其度量标准(第95分位数) 与临界值进行比较, 从而评估受试制剂与参比制剂是否等效^[39]。

3.3 BE分析方法

目前, 用于评估经口吸入和鼻用药物体外生物等效的统计学方法包括平均生物等效(average bioequivalence, ABE) 和群体生物等效(population bioequivalence, PBE)。FDA指南^[31]中指出: ABE方法仅关注比较受试(T) 和参比(R) 的总体平均值, 并假设两者方差相等, 不考虑T和R产品的方差非齐性可能。ABE方法不评估T和R制剂的个体之间的变异。相反, PBE方法对平均值和总变异都进行了比较研究, 等效性的计算方法主要为T和R之间变异的比较。我国发布的《生物等效性研究的统计学指导原则》^[27]中指出: “目前生物等效性研究通常推荐使用平均生物等效性方法。平均生物等效性方法只比较药代动力学参数的平均水平, 未考虑个体内变异及个体与制剂的交互作用引起的变异。在某些情况下, 可能需要考虑其他分析方法。例如气雾剂的体外BE研究可采用群体生物等效性方法, 以评价制剂间药代动力学参数的平均水平及个体内变异是否等效”。

3.3.1 平均生物等效

由于体外测定的变异较小, FDA指南^[31]中建议限度为几何平均值之比应在0.90~1.11之间, 建议将0.90用作体外数据的ABE限度。方差项偏移的目的是允许总方差中可能出现的某些不重要的差异。由于体外测量的变异较小, FDA建议在个体生物等效性的指导下, 取值为0。但是在实际情况中, FDA可以接受0.01的值来补偿差异项, 具体取决于所研究药品的性质。缩放比例的目的是根据参比制剂差异来调整BE标准。当参比制剂的方差大于缩放方差时, 限度会增大; 当参比制剂方差小于缩放方差时, 限度变窄。FDA指出缩放比例应至少为0.1。因此, ABE限制为0.90; 方差偏移, 即受试制剂的总方差与参比制剂总方差的差值$ \left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right) $为0.0; 方差缩放比例为0.10。带入公式(5) 可得出BE限度, 并用于计算PBE限度。

(5)$ {\theta _{{\rm{BE}}}} = \frac{{{{\left( {{\rm{自然对数均值的差值}}} \right)\;\;\;\;\;\;\;}^2} + {\rm{方差偏移}}}}{{{\rm{\;\;\;\;\;\;\;\;\;方差缩放比例\;\;\;\;\;\;\;\;\;}}}}=\\ \frac{{\left(\mathrm{l}\mathrm{n}0.9\right)}^{2}+0}{0.{1}^{2}}=1.11 $

3.3.2 群体生物等效

PBE在吸入制剂及鼻喷剂的仿制研究中具有重要的应用^{[8, 43]}, PBE的基本原理是将T制剂和R制剂之间的变异与R制剂的自身变异进行比较, 接受的标准是T制剂和R制剂之间的变异不得大于R制剂自身的变异。PBE比ABE更具允许性, 因为在R制剂内的变异性大于测试产品内的变异性的情况下, PBE增加了T制剂和R制剂之间的均值差异的接受范围。

$ \frac{{\left({\mu }_{\mathrm{T}}-{\mu }_{\mathrm{R}}\right)}^{2}+\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}({{\sigma }_{\mathrm{R}}}^{2}, {{\sigma }_{\mathrm{T}0}}^{2})}\le {\theta }_{\mathrm{\rho }} $

即: $ \frac{{\left({\mu }_{\mathrm{T}}-{\mu }_{\mathrm{R}}\right)}^{2}+\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)}{{{\sigma }_{\mathrm{R}}}^{2}}\le {\theta }_{p} $

或$ \frac{{\left({\mu }_{\mathrm{T}}-{\mu }_{\mathrm{R}}\right)}^{2}+\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)}{{{\sigma }_{\mathrm{T}0}}^{2}}\le {\theta }_{p} $

线性限度为:

$ \begin{array}{l}{\eta }_{1}={\left({\mu }_{\mathrm{T}}-{\mu }_{\mathrm{R}}\right)}^{2}+\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)-{\theta }_{p}\cdot {{\sigma }_{\mathrm{R}}}^{2}<0\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\\ \mathrm{当}{\sigma }_{\mathrm{R}}>{\sigma }_{\mathrm{T}0}\mathrm{时}\end{array} $

$ \begin{array}{l}{\eta }_{2}={\left({\mu }_{\mathrm{T}}-{\mu }_{\mathrm{R}}\right)}^{2}+\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)-{\theta }_{p}\cdot {{\sigma }_{\mathrm{T}0}}^{2}<0\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\\ \mathrm{当}{\sigma }_{\mathrm{R}}\le {\sigma }_{\mathrm{T}0}\mathrm{时}\end{array} $

其中, $ \left({\mu }_{\mathrm{T}}-{\mu }_{R}\right) $为T制剂和R制剂自然对数平均值之差; $ {\sigma }_{\mathrm{T}}^{2} $为T制剂的总方差; $ {\sigma }_{\mathrm{R}}^{2} $为R制剂的总方差; $ {\sigma }_{\mathrm{T}0} $为限度常数(0.1), 即当R制剂的标准差$ {\sigma }_{\mathrm{R}}^{} $小于0.1时, 选择0.1进行计算; $ {\theta }_{p} $为PBE限度常数(2.089), 是将ABE的上限(ln1.11, 与$ {\theta }_{\mathrm{B}\mathrm{E}} $不同)的平方加上T制剂的总方差和R制剂的总方差之差除以$ {{\sigma }_{\mathrm{R}}}^{2} $或常数$ {{\sigma }_{\mathrm{T}0}}^{2} $ (0.01), 即当R制剂的标准差小于0.1时, 选择0.1进行计算, 得到PBE上限, 如公式(6):

(6)$ \frac{{{{\left( {{\rm{自然对数均值的差值}}} \right)}\;^2} + {\rm{方差项}}}}{{{\rm{\;\;\;\;\;\;\;\;\;\;\;\;方差比较\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}}}}= \\\frac{{{{\left( {{\rm{ABE限度的自然对数}}} \right)}\;^2} + {\rm{方差偏移量}}}}{{{\rm{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;方差缩放比例\;\;\;\;\;\;\;\;\;\;\;\;}}}}= \\\frac{{\left(\mathrm{l}\mathrm{n}1.11\right)}^{2}+0.01}{0.{1}^{2}}=2.089 $

将T制剂和R制剂相应的数据进行计算, 见公式(7)~(15)。

(7)$ {\stackrel{-}{X}}_{ijk\cdot }=\frac{\sum\limits_{s=1}^{m}{X}_{ijks}}{m} $

(8)$ {\stackrel{-}{X}}_{\cdot \cdot k\cdot }=\frac{\sum\limits_{i=1}^{{l}_{k}}\sum\limits_{j=1}^{{n}_{k}}{\stackrel{-}{X}}_{ijk\cdot }}{{n}_{k}\cdot {l}_{k}} $

(9)$ \mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{k}}=\frac{m\cdot \sum\limits_{i=1}^{{l}_{k}}\sum\limits_{j=1}^{{n}_{k}}{\left({{\stackrel{-}{X}}_{i}}_{jk\cdot }-{\stackrel{-}{X}}_{\cdot \cdot k\cdot }\right)}^{2}}{{n}_{k}\cdot {l}_{k}-1} $

(10)$ \mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{k}}=\frac{\sum\limits_{i=1}^{{l}_{k}}\sum\limits_{j=1}^{{n}_{k}}\sum\limits_{s=1}^{m}{\left({X}_{ijks}-{\stackrel{-}{X}}_{ijk\cdot }\right)}^{2}}{{n}_{k}\cdot {l}_{k}\cdot \left(m-1\right)} $

(11)$ {\sigma }_{\mathrm{R}}=\sqrt{\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m}+\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m}} $

(12)$ {\sigma }_{\mathrm{T}}=\sqrt{\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m}+\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m}} $

(13)$ \widehat{\mathrm{\Delta }}={\stackrel{-}{X}}_{\cdot \cdot T\cdot }-{\stackrel{-}{X}}_{\cdot \cdot R\cdot } $

(14)$ {\widehat{\eta }}_{1}={\widehat{\mathrm{\Delta }}}^{2}+\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m}+\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m}-(1+{\theta }_{p})\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m}-\\ (1+{\theta }_{p})\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m} \mathrm{当}{\sigma }_{\mathrm{R}}>{\sigma }_{\mathrm{T}0}\mathrm{时} $

(15)$ {\widehat{\eta }}_{2}={\widehat{\mathrm{\Delta }}}^{2}+\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m}+\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m}-\\ \frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m}-\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m}-{\theta }_{p}{{\sigma }_{\mathrm{T}0}}^{2} \mathrm{当}{\sigma }_{\mathrm{R}}\le {\sigma }_{\mathrm{T}0}\mathrm{时}\;\;\;\; $

其中, m为不同使用阶段的数量; $ {n}_{\mathrm{T}} $和$ {n}_{\mathrm{R}} $为每批受试制剂和参比制剂的瓶数; $ {l}_{\mathrm{T}} $和$ {l}_{\mathrm{R}} $为受试制剂和参比制剂的批数; k为受试制剂或参比制剂; $ {X}_{ijks} $为受试制剂或参比制剂第j批第i瓶的s使用阶段的测定结果; $ {\stackrel{-}{X}}_{ijk\cdot } $为受试制剂或参比制剂第j批第i瓶的m个使用阶段的测定结果的平均值; $ {\stackrel{-}{X}}_{\cdot \cdot k\cdot } $为受试制剂或参比制剂的群体均值; $ \mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}} $为受试制剂的瓶内变异; $ \mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}} $为参比制剂的瓶内变异; $ \left(\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}-\mathrm{M}\mathrm{S}{\mathrm{W}}_{T}\right)/m $为受试制剂的瓶间变异; $ \left(\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}-\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}\right)/m $为参比制剂的瓶间变异; $ {\sigma }_{\mathrm{T}}^{2} $和$ {\sigma }_{\mathrm{R}}^{2} $为受试制剂和参比制剂的总方差; $ \widehat{\mathrm{\Delta }} $为受试制剂和参比制剂总体均值之差的估计; $ {\widehat{\eta }}_{1} $为置信度为95% (α = 0.05) 的参比尺度限度估计($ {\sigma }_{\mathrm{R}}>{\sigma }_{\mathrm{T}0} $时, 采用$ {\sigma }_{\mathrm{R}} $计算); $ {\widehat{\eta }}_{2} $为置信度为95% (α = 0.05) 的常数尺度限度估计($ {\sigma }_{\mathrm{R}}\le {\sigma }_{\mathrm{T}0} $时, 采用$ {\sigma }_{\mathrm{T}0} $计算)。

当$ {\sigma }_{\mathrm{R}}>{\sigma }_{\mathrm{T}0} $时, 线性化点估计和95%置信上限的计算方法, 参比制剂尺度标准($ {\widehat{\eta }}_{1} $): 95%的置信上限($ \alpha =0.05 $) 的线性化点估计等式见公式(16), 95%置信上限(H_η1) 见公式(17)。

(16)$E_{\mathrm{q}}=E_{\mathrm{D}}+E 1+E 2+E 3 \mathrm{~s}+E 4 \mathrm{~s}$

(17)$\begin{aligned}H_{\mathrm{\eta1}}=&\left(E_{\mathrm{D}}+E 1+E 2+E 3 \mathrm{~s}+E 4 \mathrm{~s}\right)+\left(U_{\mathrm{D}}+U 1+\right.\\&U 2+U 3 \mathrm{~s}+U 4 \mathrm{~s})^{1 / 2}\end{aligned}$

式中各项具体计算方法见表 4。

当$ {\sigma }_{R}\le {\sigma }_{T0} $时, 线性化点估计和95%置信上限的计算方法, 常数制剂尺度标准($ {\widehat{\eta }}_{2} $): 95%的置信上限(α = 0.05) 的线性化点估计等式见公式(18), 95%置信上限(H_η2) 见公式(19)。

(18)$E_{\mathrm{q}}=E_{\mathrm{D}}+E 1+E 2+E 3 \mathrm{c}+E 4 \mathrm{c}-\theta_{\mathrm{p}} \sigma_{\mathrm{T} 0}{ }^{2}$

(19)$\begin{aligned}H_{\mathrm{\eta} 2}=&\left(E_{\mathrm{D}}+E 1+E 2+E 3 \mathrm{c}+E 4 \mathrm{c}-\theta_{\mathrm{p}} \sigma_{\mathrm{TO}}{ }^{2}\right)+\\&\left(U_{\mathrm{D}}+U 1+U 2+U 3 \mathrm{c}+U 4 \mathrm{c}\right)^{3 / 3}\end{aligned}$

式中各项具体计算方法见表 5。

当计算结果H_η ≤ 0时, 可判定受试制剂与参比制剂体外生物等效。

3.3.3 单侧PBE法

FDA指导原则指出^[22]: 使用修改后的单侧PBE计算鼻喷剂仿制制剂微细粒子剂量体外生物等效性, 以下为单侧PBE具体计算公式^[18]。

当$ {\mu }_{T}\ge {\mu }_{R} $时, 使用PBE公式进行计算, 具体计算同公式(7)~(20)。

(20)$ \frac{{\left({\mu }_{\mathrm{T}}-{\mu }_{\mathrm{R}}\right)}^{2}+\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)}{{{\sigma }_{\mathrm{R}}}^{2}}={\theta }_{p} $

当$ {\mu }_{T}<{\mu }_{R} $时, 则不考虑其平均值的差异, 按照公式(21) 计算。

(21)$ \frac{\left({{\sigma }_{\mathrm{T}}}^{2}-{{\sigma }_{\mathrm{R}}}^{2}\right)}{{{\sigma }_{\mathrm{R}}}^{2}}={\theta }_{p} $

线性化点估计和置信上限公式中, 去除对于均值差异的估计项按照公式(22), (23):

当$ {\sigma }_{\mathrm{R}}>{\sigma }_{\mathrm{T}0} $时,

(22)$ \begin{array}{l}{\stackrel{}{\eta }}_{1}=\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m}+\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m}-(1+{\theta }_{p})\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m}-\\ (1+{\theta }_{p})\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m}\end{array} $

当$ {\sigma }_{\mathrm{R}}\le {\sigma }_{\mathrm{T}0} $时,

(23)$ {\stackrel{⌢}{\eta }}_{2}=\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{T}}}{m}+\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{T}}}{m}-\frac{\mathrm{M}\mathrm{S}{\mathrm{B}}_{\mathrm{R}}}{m}-\frac{(m-1)\mathrm{M}\mathrm{S}{\mathrm{W}}_{\mathrm{R}}}{m}-{\theta }_{p}{{\sigma }_{\mathrm{T}0}}^{2} $

计算其点估计与置信区间的方法与PBE相同, 去除对均值差异的估计项。当计算结果H_η ≤ 0时, 可判定受试制剂与参比制剂体外生物等效。

4 PBE计算实例

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4.1 计算实例

本文使用R语言(版本4.0.0), 参照FDA发布的《布地奈德吸入混悬液指南草案》^[10]中PBE定义、公式和数据, 编写程序对统计学参数进行计算。为验证程序计算结果的准确性, 采用该指南的例示数据进行计算和比较, 程序运算结果与指导原则中的例示数据计算结果一致。微小偏差是由于软件差异导致运算偏差, 程序经验证准确有效。本文计算数据与FDA指导原则计算结果数据见表 6~9。

4.2 PBE计算程序伪代码

体外PBE的评价方法在国内吸入制剂仿制药的研发和生物等效评价中具有借鉴作用, 评价工作在国内尚处于新兴阶段。由于PBE的原理和计算公式较为复杂, 本文提供了计算程序的伪代码, 可采用通用的程序语言对于PBE算法进行实现。

程序伪代码如下:

//输入数据

PBE.ref←参比制剂数据

PBE.test←供试制剂数据

//定义m.T, m.R, n.T, n.R, l.T, l.R

m.R←参比制剂的测定阶段数

m.T←受试制剂的测定阶段数

l.R←参比制剂的批数

l.T←受试制剂的批数

n.R←参比制剂的瓶数

n.T←受试制剂的瓶数

//计算参比和受试制剂的最优线性无偏估计(best linear unbiased estimator, BLUE), 批内和批间变异

mu.R←参比制剂均值

mu.T←受试制剂均值

MSB.R←参比制剂批间变异

MSB.T←受试制剂批间变异

MSW.R←参比制剂批内变异

MSW.T←受试制剂批内变异

//定义θp和σ_T0

theta.BE←2.089

sigma.T0←0.1

//计算参比制剂的变异

sigma.R←sqrt(MSB.R/m.R+MSW.R*(m.T-1)/m.R)

//计算点估计和区间估计

delta←mu.T-mu.R

E.D←$ {\left|\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{t}\mathrm{a}\right|}^{2} $

E.1←MSB.T/m.T

E.2←MSW.T*(m.T-1)/m.T

E.3s←-(1+theta.BE)*MSB.R/m.R

E.3c←-MSB.R/m.R

E.4s←-(1+theta.BE)*MSW.R*(m.R-1)/m.R

E.4c←-MSW.R*(m.R-1)/m.R

H.D←(|delta|+(t_{(0.95, (n.T*l.T+n.R*l.R-2)} *(MSB.T/(m.T*n.T*l.T) +MSB.R/(m.R*n.R*l.R)) ^1/2)²

H.1←((n.T*l.T-1)*E.1)/$ {\chi }_{}^{2} $_{(0.05, (n.T*l.T-1))}

H.2←((n.T*l.T*(m.T-1))*E.2)/$ {\chi }_{}^{2} $_{(0.05, (n.T*l.T*(m.T-1)))}

H.3s←((n.R*l.R-1)*E.3s)/$ {\chi }_{}^{2} $_{(0.95, (n.R*l.R-1))}

H.3c←((n.R*l.R-1)*E.3c)/$ {\chi }_{}^{2} $_{(0.95, (n.R*l.R-1))}

H.4s←((n.R*l.R*(m.R-1))*E.4s)/$ {\chi }_{}^{2} $_{(0.95, (n.R*l.R*(m.R-1)))}

H.4c←((n.R*l.R*(m.R-1))*E.4c)/$ {\chi }_{}^{2} $_{(0.95, (n.R*l.R*(m.R-1)))}

U.D←(H.D-E.D)²

U.1←(H.1-E.1)²

U.2←(H.2-E.2)²

U.3s←(H.3s-E.3s)²

U.3c←(H.3c-E.3c)²

U.4s←(H.4s-E.4s)²

U.4c←(H.4c-E.4c)²

//判定并计算E_q和H_η

If (sigma.R > sigma.T0) then {

Eq←E.D+E.1+E.2+E.3s+E.4s

H.eta←Eq+(U.D+U.1+U.2+U.3s+U.4s)^1/2

}

else {

Eq←E.D+E.1+E.2+E.3c+E.4c-theta.BE*(sigma.T0)²

H.eta←Eq+(U.D+U.1+U.2+U.3c+U.4c)^1/2

}

5 总结与展望

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本文系统综述了OINDPs体外生物等效的评估背景, 阐述采用体外生物等效方法的基本考虑, 介绍美国、欧盟和中国药品监管机构对于该类制剂体外生物等效评估的指导原则及指南的基本要求, 分析各国对于OINDPs体外生物等效的差异, 详细说明美国FDA体外生物等效性评估的统计学评估方法和计算公式。通过FDA布地奈德吸入混悬液指导原则拟定稿中的实例通过R语言编程的途径计算出PBE计算统计学参数, 将结果与指导原则中的结果进行对比, 并提供计算程序的伪代码。

经口吸入和鼻用药物的研发和仿制在我国正在兴起。OINDPs的监管具有挑战, 在国内尚属起步阶段。为深化OINDPs的质量控制与仿制制剂研发, 需尽快开发具有区分性的OINDPs质量评价和体内外生物等效方法, 着重分析各体外检测项目与体内特性的相关性, 以期通过体外评价方法替代部分临床研究, 节约研发时间和成本。本文为OINDPs的研发、质量控制及仿制制剂的开发提供了有益的思路与参考。

致谢: 特别感谢侯曙光博士对本文提出重要的指导和修改意见。

作者贡献: 耿颖负责综述的文献资料收集、统计学计算和主要内容撰写; 宁保明、魏宁漪负责综述的选题和内容框架; 张军、王蕊、周颖和郑静撰写部分内容并负责表格的编辑。杨泉博士对本文提出重要的指导和修改意见。

利益冲突: 本文不涉及个人与组织利益冲突。

免责声明: 本文表述观点为作者个人观点, 不代表任何公司和组织的观点。

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2021年第56卷第10期

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文章信息

doi: 10.16438/j.0513-4870.2021-0640

接收时间：2021-04-27
首发时间：2025-12-18
出版时间：2021-10-12

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收稿日期：2021-04-27
修回日期：2021-07-15

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1.中国食品药品检定研究院, 北京 102629

2.默克雪兰诺 (北京) 医药研发有限公司, 北京 100000

3.国家药典委员会, 北京 100061

通讯作者:

*宁保明, Tel/Fax: 86-10-53851575, E-mail: ningbm@nifdc.org.cn;

魏宁漪, Tel: 86-10-53851604, E-mail: weiny@nifdc.org.cn

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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