Multi-criteria decision making to validate performance of RBC-based formulae to screen $$\beta$$ -thalassemia trait in heterogeneous haemoglobinopathies

Jain, Atul Kumar; Sharma, Prashant; Saleh, Sarkaft; Dolai, Tuphan Kanti; Saha, Subhas Chandra; Bagga, Rashmi; Khadwal, Alka Rani; Trehan, Amita; Nielsen, Izabela; Kaviraj, Anilava; Das, Reena; Saha, Subrata

doi:10.1186/s12911-023-02388-w

BMC Medical Informatics and Decision Making

Table 3 Final ranking for 35 formulae

From: Multi-criteria decision making to validate performance of RBC-based formulae to screen $\beta$-thalassemia trait in heterogeneous haemoglobinopathies

Formulae	TOPSIS				COPRAS				SECA
	$D_i^*$	$D_i^*$	$D_i^*$	Rank	$\frac{{s_{i}}_{min}}{s_{i}}$	$Q_i$	$U_i$	Rank	$W_i$	Rank
S & B	0.088	0.028	0.243	23	0.044	0.407	59.487	16	0.617	16
E & F	0.105	0.013	0.111	34	0.037	0.337	49.306	25	0.553	24
Mentzer	0.072	0.043	0.374	15	0.053	0.467	68.253	9	0.672	8
RBC	0.077	0.038	0.330	17	0.050	0.414	60.422	15	0.618	15
S & L	0.009	0.109	0.927	1	0.528	0.633	92.463	2	0.801	2
Ricerca	0.049	0.076	0.606	6	0.113	0.260	37.934	32	0.394	34
G & K	0.098	0.018	0.156	32	0.040	0.350	51.096	24	0.562	23
Das Gupta	0.068	0.046	0.402	12	0.059	0.315	46.065	27	0.498	29
MCHD	0.034	0.102	0.747	5	0.431	0.362	52.882	23	0.484	31
MDHL	0.112	0.009	0.072	35	0.036	0.292	42.673	30	0.510	26
Jayabose	0.082	0.033	0.285	18	0.047	0.404	59.066	17	0.611	19
Sirdah	0.089	0.028	0.236	24	0.044	0.417	60.906	14	0.627	13
Kerman-I	0.050	0.065	0.567	8	0.075	0.517	75.570	4	0.713	4
Kerman-II	0.069	0.046	0.402	13	0.055	0.475	69.453	7	0.679	6
Ehsani	0.071	0.045	0.387	14	0.054	0.471	68.843	8	0.675	7
Keikhaei	0.093	0.023	0.201	27	0.042	0.382	55.741	22	0.592	21
Wongp.	0.096	0.018	0.159	31	0.041	0.318	46.478	26	0.528	25
Nishad	0.058	0.057	0.495	11	0.065	0.493	72.082	5	0.692	5
Sehgal	0.057	0.056	0.495	10	0.067	0.440	64.240	11	0.643	11
Sargolzie	0.099	0.015	0.135	33	0.040	0.293	42.856	29	0.503	28
Pornprasert	0.085	0.028	0.249	21	0.047	0.288	42.099	31	0.485	30
Bordbar	0.025	0.090	0.781	4	0.159	0.481	70.335	6	0.651	10
Hisham	0.087	0.028	0.245	22	0.045	0.403	58.826	18	0.612	18
Matos	0.095	0.019	0.168	30	0.042	0.301	44.042	28	0.509	27
RF-1	0.075	0.040	0.348	16	0.052	0.418	61.014	13	0.621	14
RF-2	0.095	0.020	0.174	29	0.043	0.218	31.836	35	0.410	33
RF-3	0.083	0.032	0.280	19	0.047	0.390	56.920	20	0.596	20
RF-4	0.014	0.101	0.876	3	0.243	0.585	85.497	3	0.761	3
Kandhro-2	0.091	0.024	0.207	26	0.045	0.232	33.912	34	0.423	32
Merdin-1	0.056	0.058	0.506	9	0.067	0.467	68.200	10	0.663	9
Merdin-2	0.086	0.029	0.254	20	0.045	0.384	56.142	21	0.592	22
Cruise	0.050	0.075	0.599	7	0.111	0.252	36.877	33	0.386	35
Janel(11T)	0.096	0.022	0.184	28	0.041	0.402	58.711	19	0.614	17
Index26	0.089	0.027	0.233	25	0.043	0.425	62.081	12	0.635	12
$SCS_{BTT}$	0.010	0.112	0.922	2	1.000	0.684	100.000	1	0.845	1
Best				S & L				$SCS_{BTT}$		$SCS_{BTT}$
Worst				MDHL				RF-2		Cruise

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Formulae	TOPSIS				COPRAS				SECA
	\(D_i^*\)	\(D_i^*\)	\(D_i^*\)	Rank	\(\frac{{s_{i}}_{min}}{s_{i}}\)	\(Q_i\)	\(U_i\)	Rank	\(W_i\)	Rank
S & B	0.088	0.028	0.243	23	0.044	0.407	59.487	16	0.617	16
E & F	0.105	0.013	0.111	34	0.037	0.337	49.306	25	0.553	24
Mentzer	0.072	0.043	0.374	15	0.053	0.467	68.253	9	0.672	8
RBC	0.077	0.038	0.330	17	0.050	0.414	60.422	15	0.618	15
S & L	0.009	0.109	0.927	1	0.528	0.633	92.463	2	0.801	2
Ricerca	0.049	0.076	0.606	6	0.113	0.260	37.934	32	0.394	34
G & K	0.098	0.018	0.156	32	0.040	0.350	51.096	24	0.562	23
Das Gupta	0.068	0.046	0.402	12	0.059	0.315	46.065	27	0.498	29
MCHD	0.034	0.102	0.747	5	0.431	0.362	52.882	23	0.484	31
MDHL	0.112	0.009	0.072	35	0.036	0.292	42.673	30	0.510	26
Jayabose	0.082	0.033	0.285	18	0.047	0.404	59.066	17	0.611	19
Sirdah	0.089	0.028	0.236	24	0.044	0.417	60.906	14	0.627	13
Kerman-I	0.050	0.065	0.567	8	0.075	0.517	75.570	4	0.713	4
Kerman-II	0.069	0.046	0.402	13	0.055	0.475	69.453	7	0.679	6
Ehsani	0.071	0.045	0.387	14	0.054	0.471	68.843	8	0.675	7
Keikhaei	0.093	0.023	0.201	27	0.042	0.382	55.741	22	0.592	21
Wongp.	0.096	0.018	0.159	31	0.041	0.318	46.478	26	0.528	25
Nishad	0.058	0.057	0.495	11	0.065	0.493	72.082	5	0.692	5
Sehgal	0.057	0.056	0.495	10	0.067	0.440	64.240	11	0.643	11
Sargolzie	0.099	0.015	0.135	33	0.040	0.293	42.856	29	0.503	28
Pornprasert	0.085	0.028	0.249	21	0.047	0.288	42.099	31	0.485	30
Bordbar	0.025	0.090	0.781	4	0.159	0.481	70.335	6	0.651	10
Hisham	0.087	0.028	0.245	22	0.045	0.403	58.826	18	0.612	18
Matos	0.095	0.019	0.168	30	0.042	0.301	44.042	28	0.509	27
RF-1	0.075	0.040	0.348	16	0.052	0.418	61.014	13	0.621	14
RF-2	0.095	0.020	0.174	29	0.043	0.218	31.836	35	0.410	33
RF-3	0.083	0.032	0.280	19	0.047	0.390	56.920	20	0.596	20
RF-4	0.014	0.101	0.876	3	0.243	0.585	85.497	3	0.761	3
Kandhro-2	0.091	0.024	0.207	26	0.045	0.232	33.912	34	0.423	32
Merdin-1	0.056	0.058	0.506	9	0.067	0.467	68.200	10	0.663	9
Merdin-2	0.086	0.029	0.254	20	0.045	0.384	56.142	21	0.592	22
Cruise	0.050	0.075	0.599	7	0.111	0.252	36.877	33	0.386	35
Janel(11T)	0.096	0.022	0.184	28	0.041	0.402	58.711	19	0.614	17
Index26	0.089	0.027	0.233	25	0.043	0.425	62.081	12	0.635	12
\(SCS_{BTT}\)	0.010	0.112	0.922	2	1.000	0.684	100.000	1	0.845	1
Best				S & L				\(SCS_{BTT}\)		\(SCS_{BTT}\)
Worst				MDHL				RF-2		Cruise