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 1 Forty-two discriminant formulae proposed in the literature

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

No.	Study	Discriminating formula	Cut-off	Remarks & sample size
1	S & B	$\frac{MCH}{RBC}$	<3.8	For thalassemia minor 9 times out of 10, the cut-off value is below, but not applicable in hemodilution and decreased RBC production(SS: 500)
2	E & F	$MCV-RBC-5 Hb$	<0	Discriminant function identifies 99% of the cases studied but not applicable in pregnancy (SS: 72)
3	Mentzer	$\frac{MCV}{RBC}$	<13	Mentzer classified the highest number of patients correctly (SS: 103)
4	RBC	RBC	>5	The measurement of serum iron concentration and iron-binding capacity are needed for the reliable diagnosis of IDA (SS: 122)
5	S & L	$\frac{MCV^2 \times MCH}{100}$	<1530	The false-positives rate was 4.4% (SS:25,302)
6	RDW	RDW	<14	Determination of variation of red cell size by erythrography is a rapid and reliable way to distinguish thalassemia minor (SS:85)
7	Ricerca	$\frac{RDW}{RBC}$	<4.4	The sensitivity for the formula is 98% (SS:398)
8	G & K	$\frac{MCV^2 \times RDW}{100Hb}$	<65	Use of red cell volume dispersion results in enhanced accuracy for distinguishing IDA from $\beta$-TM (SS:102)
9	Das Gupta	1.89RBC - 0.33RDW - 3.28	$>0$	Along with the formula and the condition RDW>17.1 recommended for screening (SS:111)
10	MCHD	$\frac{MCH}{MCV}$	<0.34	MDHL provided powerful screening for discriminating
11	MDHL	$\frac{MCH\times RBC}{ MCV}$	>1.75	between IDA and thalassemia (SS: 96)
12	Jayabose	$\frac{MCV\times RDW}{RBC}$	<220	RDW index ensures highest Sens. and Spec. (SS: 102)
13	Huber-Herklotz	$\frac{MCH\times RDW}{10 RBC}+ RDW$	$<20$	Huber-Herklotz can be used to predict TT with high accuracy (SS:114)
14	Sirdah	$MCV-RBC-3 Hb$	<27	Sirdah, G &K or RDWI might be useful in early mass-screening programs (SS: 2196)
15	Kerman- II	$\frac{MCV\times MCH}{ RBC}$	<300	Kerman-I formula presented best outcome
16	Kerman- II	$\frac{MCV\times MCH \times 10}{ RBC\times MCHC}$	$<85$	in screening $\beta$-TM (SS:82)
17	Ehsani	$MCV-10 \times RBC$	<15	Mentzer and Ehsani formulae presents highest YI (SS:284)
18	Keikhaei	$\frac{Hb \times RDW \times 100}{RBC^{2} \times MCHC}$	$>1.27$	Keikhaei, G &K, RDW and E &F formulae demonstrates most reliable discrimination in BTT and IDA (SS:823)
19	Wongprachum	$\frac{MCV\times RDW}{RBC} - 10 Hb$	<104	The formulae can be used as proxy indicators if none sophisticated laboratory are available (SS:234)
20	Nishad	$0.615 MCV+0.518 MCH +0.446 RDW$	<59	Higher Sens is achieved for Ehsani formula, but Spec.is higher for Nishad (SS:326)
21	Sehgal	$\frac{MCV^{2}}{RBC}$	<972	Sehgal and Mentzer formulae showed the best combination in predicting $\beta$TT (SS: 543)
22	Sargolzaie	$\begin{array}{c} 125.6 + (44.3 \times RBC)\\ -(20.9 \times Hb)-(2.5 \times MCV)\\ +(20.3 \times MCH)\\ -(12.18 \times MCHC) \end{array}$	$<0.5$	Evaluation of specific information of each region is necessary for discriminating between BTT and IDA (SS:177)
23	Pornprasert	MCHC	<31	Sirdah and Srivastava proved reliable results for discrimination between BTT and IDA (SS: 77)
24	Sirachainan	$1.5Hb-0.05 MCV$	>14	Sirachainan demonstrates best AUC score from identifying IDA and thalassemia traits (SS: 345)
25	Bordbar	$\|80-MCV\|\times \|27-MCH\|$	>44.76	Higher Sens is achieved for Bordbar and S &L, and higher Spec. is achieved for Bordbar and Sirdah (SS: 504)
26	Hameed & Hisham	$MCH \times HCT \times \frac{RDW}{(RBC \times Hb)^2}$	<220	Hameed & Hisham was the highest and most reliable in
27		$MCH \times \frac{RDW}{RBC}$	<67	differentiating BTT from IDA (SS: 600)
28	Matos	$1.91 \times RBC + 0.44 \times MCHC$	>23.85	Developed formula provides excellent performance and great diagnostic accuracy (SS: 291)
29	Ravanbakhsh-F1	$\frac{MCV}{HCT}$	<2	Best performing discriminating formulae:
30	Ravanbakhsh-F2	$RDW-3RBC$	$<1.5$	G &K, Keikhaei, RDWI, and E &F are best in terms of YI (SS: 227)
31	Ravanbakhsh-F3	$MCV\times RDW-100RBC$	$<600$
32	Ravanbakhsh-F4	$\frac{MCV\times Hb}{RDW\times RBC}$	$<10$
33	Zaghloul-1 & 2	$Hb \times HCT + RBC$	>52.5	E &F and Zaghloul-1 outperforms in discriminating men E &F and RDW outperform for women data set (SS: 249)
34		$Hb \times HCT + RBC - RDW$	>37.1
35	Kandhro-1 & 2	$\frac{RBC}{HCT} + 0.5 \times RDW$	<8.2	Mentzer, E &F, G &K, RDWI, Ricerca, and Huber are reliable
36		$\frac{5RDW}{RBC}$	$<16.8$	formulae for ease of use in the general population (SS: 610)
37	Merdin-1 & 2	$\frac{RDW \times RBC}{MCV}$	$>1.27$	RDWI, Alparslan and Merdin-1 demonstrated
38		$\frac{RDW \times RBC\times Hb}{MCV}$	$>14.7$	highest YI (SS: 40)
		$\frac{0.66(MCH-27.0)}{3.9} +0.98$
39	Cruise & Index26	$MCHC + 0.603RBC$	$\ge$42.63	Index26 outperforms existing discriminating formulae and can
		$+ 0.523RDW$		be useful to discriminate between IDA and BTT (SS: 907)
40		Combination 26 formulae	$\ge$ 16
41	Janel (11T)	Combination 11 formulae	$\ge$ 8	11T demonstrates best percentage of correctly identified patients between IDA and BTM (SS: 129)
42	$SCS_{BTT}$	$\begin{array}{c} 0.2815MCV+ 0.2015MCH\\ - 0.2641RBC- 0.1693RDW\\ + 0.0835Hb \end{array}$	<24.99	MLP and decision tree algorithm can jointly ensure 100% sensitivity (SS: 1076)

Formulae: S &B: [20]; E &F: [21]; Mentzer: [22]; RBC: [23]; S &L: [24]; RDW: [25]; Ricerca: [26]; G & K: [27]; Das Gupta: [28]; MCHD & MDHL: [29]; Jayabose: [30]; Huber-Herklotz: [31]; Kerman-I & II:[32]; Sirdah: [33]; Ehsani: [34]; Keikhaei: [35]; Wongprachum: [36]; Nishad: [37]; Sehgal: [38]; Sargolzie: [39]; Sirachainan: [40]; Pornprasert [41]; Bordbar: [42]; Hameed & Hisham: [43]; Matos: [44]; Ravanbakhsh-F1, F2, F3 & F4:[45]; Zaghloul-1 & 2: [6]; Kandhro-1 & 2: [46]; Merdin-1 & 2: [5]; Cruise & Index26: [4]; Janel (11T): [47]; $SCS_{BTT}$; [18]; SS: sample size

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No.	Study	Discriminating formula	Cut-off	Remarks & sample size
1	S & B	\(\frac{MCH}{RBC}\)	<3.8	For thalassemia minor 9 times out of 10, the cut-off value is below, but not applicable in hemodilution and decreased RBC production(SS: 500)
2	E & F	\(MCV-RBC-5 Hb\)	<0	Discriminant function identifies 99% of the cases studied but not applicable in pregnancy (SS: 72)
3	Mentzer	\(\frac{MCV}{RBC}\)	<13	Mentzer classified the highest number of patients correctly (SS: 103)
4	RBC	RBC	>5	The measurement of serum iron concentration and iron-binding capacity are needed for the reliable diagnosis of IDA (SS: 122)
5	S & L	\(\frac{MCV^2 \times MCH}{100}\)	<1530	The false-positives rate was 4.4% (SS:25,302)
6	RDW	RDW	<14	Determination of variation of red cell size by erythrography is a rapid and reliable way to distinguish thalassemia minor (SS:85)
7	Ricerca	\(\frac{RDW}{RBC}\)	<4.4	The sensitivity for the formula is 98% (SS:398)
8	G & K	\(\frac{MCV^2 \times RDW}{100Hb}\)	<65	Use of red cell volume dispersion results in enhanced accuracy for distinguishing IDA from \(\beta\)-TM (SS:102)
9	Das Gupta	1.89RBC - 0.33RDW - 3.28	\(>0\)	Along with the formula and the condition RDW>17.1 recommended for screening (SS:111)
10	MCHD	\(\frac{MCH}{MCV}\)	<0.34	MDHL provided powerful screening for discriminating
11	MDHL	\(\frac{MCH\times RBC}{ MCV}\)	>1.75	between IDA and thalassemia (SS: 96)
12	Jayabose	\(\frac{MCV\times RDW}{RBC}\)	<220	RDW index ensures highest Sens. and Spec. (SS: 102)
13	Huber-Herklotz	\(\frac{MCH\times RDW}{10 RBC}+ RDW\)	\(<20\)	Huber-Herklotz can be used to predict TT with high accuracy (SS:114)
14	Sirdah	\(MCV-RBC-3 Hb\)	<27	Sirdah, G &K or RDWI might be useful in early mass-screening programs (SS: 2196)
15	Kerman- II	\(\frac{MCV\times MCH}{ RBC}\)	<300	Kerman-I formula presented best outcome
16	Kerman- II	\(\frac{MCV\times MCH \times 10}{ RBC\times MCHC}\)	\(<85\)	in screening \(\beta\)-TM (SS:82)
17	Ehsani	\(MCV-10 \times RBC\)	<15	Mentzer and Ehsani formulae presents highest YI (SS:284)
18	Keikhaei	\(\frac{Hb \times RDW \times 100}{RBC^{2} \times MCHC}\)	\(>1.27\)	Keikhaei, G &K, RDW and E &F formulae demonstrates most reliable discrimination in BTT and IDA (SS:823)
19	Wongprachum	\(\frac{MCV\times RDW}{RBC} - 10 Hb\)	<104	The formulae can be used as proxy indicators if none sophisticated laboratory are available (SS:234)
20	Nishad	\(0.615 MCV+0.518 MCH +0.446 RDW\)	<59	Higher Sens is achieved for Ehsani formula, but Spec.is higher for Nishad (SS:326)
21	Sehgal	\(\frac{MCV^{2}}{RBC}\)	<972	Sehgal and Mentzer formulae showed the best combination in predicting \(\beta\)TT (SS: 543)
22	Sargolzaie	\(\begin{array}{c} 125.6 + (44.3 \times RBC)\\ -(20.9 \times Hb)-(2.5 \times MCV)\\ +(20.3 \times MCH)\\ -(12.18 \times MCHC) \end{array}\)	\(<0.5\)	Evaluation of specific information of each region is necessary for discriminating between BTT and IDA (SS:177)
23	Pornprasert	MCHC	<31	Sirdah and Srivastava proved reliable results for discrimination between BTT and IDA (SS: 77)
24	Sirachainan	\(1.5Hb-0.05 MCV\)	>14	Sirachainan demonstrates best AUC score from identifying IDA and thalassemia traits (SS: 345)
25	Bordbar	\(\|80-MCV\|\times \|27-MCH\|\)	>44.76	Higher Sens is achieved for Bordbar and S &L, and higher Spec. is achieved for Bordbar and Sirdah (SS: 504)
26	Hameed & Hisham	\(MCH \times HCT \times \frac{RDW}{(RBC \times Hb)^2}\)	<220	Hameed & Hisham was the highest and most reliable in
27		\(MCH \times \frac{RDW}{RBC}\)	<67	differentiating BTT from IDA (SS: 600)
28	Matos	\(1.91 \times RBC + 0.44 \times MCHC\)	>23.85	Developed formula provides excellent performance and great diagnostic accuracy (SS: 291)
29	Ravanbakhsh-F1	\(\frac{MCV}{HCT}\)	<2	Best performing discriminating formulae:
30	Ravanbakhsh-F2	\(RDW-3RBC\)	\(<1.5\)	G &K, Keikhaei, RDWI, and E &F are best in terms of YI (SS: 227)
31	Ravanbakhsh-F3	\(MCV\times RDW-100RBC\)	\(<600\)
32	Ravanbakhsh-F4	\(\frac{MCV\times Hb}{RDW\times RBC}\)	\(<10\)
33	Zaghloul-1 & 2	\(Hb \times HCT + RBC\)	>52.5	E &F and Zaghloul-1 outperforms in discriminating men E &F and RDW outperform for women data set (SS: 249)
34		\(Hb \times HCT + RBC - RDW\)	>37.1
35	Kandhro-1 & 2	\(\frac{RBC}{HCT} + 0.5 \times RDW\)	<8.2	Mentzer, E &F, G &K, RDWI, Ricerca, and Huber are reliable
36		\(\frac{5RDW}{RBC}\)	\(<16.8\)	formulae for ease of use in the general population (SS: 610)
37	Merdin-1 & 2	\(\frac{RDW \times RBC}{MCV}\)	\(>1.27\)	RDWI, Alparslan and Merdin-1 demonstrated
38		\(\frac{RDW \times RBC\times Hb}{MCV}\)	\(>14.7\)	highest YI (SS: 40)
		\(\frac{0.66(MCH-27.0)}{3.9} +0.98\)
39	Cruise & Index26	\(MCHC + 0.603RBC\)	\(\ge\)42.63	Index26 outperforms existing discriminating formulae and can
		\(+ 0.523RDW\)		be useful to discriminate between IDA and BTT (SS: 907)
40		Combination 26 formulae	\(\ge\) 16
41	Janel (11T)	Combination 11 formulae	\(\ge\) 8	11T demonstrates best percentage of correctly identified patients between IDA and BTM (SS: 129)
42	\(SCS_{BTT}\)	\(\begin{array}{c} 0.2815MCV+ 0.2015MCH\\ - 0.2641RBC- 0.1693RDW\\ + 0.0835Hb \end{array}\)	<24.99	MLP and decision tree algorithm can jointly ensure 100% sensitivity (SS: 1076)