Literature selection results

This initial literature search yielded 4854 papers. After duplicates were excluded, 3322 studies remained. Of these, 127 studies matched the inclusion criteria, and 7 additional single papers were added from other reference sources listed above. Five of the 134 papers were excluded as they were reviews or letters rather than comparative studies, or they did not include any primary or secondary outcome data. Ultimately, 129 studies met our criteria and were included in our network meta-analysis (Fig. 1).

Fig. 1Study characteristics and network geometry

A summary of all eligible studies published until 2020 is shown in the Additional file 1: Appendix I Table S1. A total of 17,181 eyes were measured by one of 12 optical biometry and ultrasound biometry (with both contact and immersion techniques), with a total of five different techniques (Fig. 2). Almost all trials involved only two devices (92.2%). Among the included 129 trials, 43 (33.3%) recruited healthy or ametropia subjects, 85 (65.9%) recruited participants with cataract, 3 (2.3%) recruited participants who underwent cataract surgery, 1 (0.78%) recruited participants with glaucoma, 1 (0.78%) recruited participants with keratoconus, 1 (0.78%) recruited participants with silicone-filled eyes, and 5 (3.9%) recruited mixed participants.

Fig. 2

Network of direct comparison for the ophthalmological biometric measurement instruments. Each node represents one instrument. The size of the node is proportional to the number of eyes included in the instrument. The edges represent direct comparisons and the width of the edge is proportional to the number of trials

Risk of bias assessment results

The risk of bias from the trials included in our study is shown in Additional file 1: Appendix I Table S2. The evaluation of some trials in items 1–5 were “No” or “Not clear”, but all trials gained the full “Yes” for items 6–11. In general, all trials were regarded as high-quality.

Results of meta-analysisDirect comparisons

Figures 3, 4, 5 and 6 (upper right) and Additional file 1: Appendix I Tables S3–S14 show the direct comparisons between each pair of instruments. In total, 112 studies involving 14 instruments were available for the comparison of the AL. Direct comparisons found that contact ultrasound measured shorter AL when compared with the IOLMaster (WMD =  − 0.159 mm). With regards to measurements of Kf, Ks and astigmatism, there were no statistically significant differences among the various instruments. With respect to the Km, statistically significant differences existed when the Pentacam AXL was compared with the IOLMaster 500 (WMD =  − 0.235 D) and the Lenstar (WMD =  − 0.233 D). When considering the ACD, statistically significant differences existed when contact ultrasound was compared with the IOLMaster (WMD =  − 0.133 mm), the IOLMaster 700 (WMD =  − 0.13 mm), and the OA-1000 (WMD =  − 0.47 mm). Besides, there were statistically significant differences between the IOLMaster 700 and the following devices (WMD from large to small): Argos (WMD =  − 0.113 mm), ANTERION (WMD =  − 0.07 mm), and Lenstar (WMD =  − 0.019 mm). We also found that the Lenstar obtained higher CCT measurements when compared to the OA-2000 (WMD = 13.683 μm) and the Pentacam AXL (WMD = 9.071 μm). There was also a statistical difference between the OA-2000 and the Pentacam AXL (WMD =  − 8.42 μm). As for the measurement of the CD, there were no significant differences among the devices except the Lenstar and the IOLMaster 700, the IOLMaster and the Lenstar, the IOLMaster 500 and the OA-2000, the Galilei G6 and the IOLMaster 700, the IOLMaster 500 and the Pentacam AXL, the IOLMaster 500 and the IOLMaster 700, the IOLMaster 700 and the ANTERION.

Fig. 3

Meta-analysis results comparing all instruments with respect to axial length (AL), corneal diameter (CD), and lens thickness (LT). The upper right shows the direct comparisons meta-analysis between each pair of formulas and the bottom left shows the network meta-analysis between each pair of formulas. Weighted mean differences (95% confidence intervals) are calculated by column. NA, not available. The underline data indicate the statistical significant effect

Fig. 4

Meta-analysis results comparing all instruments with respect to keratometry. The upper right shows the direct comparisons meta-analysis between each pair of formulas and the bottom left shows the network meta-analysis between each pair of formulas. Weighted mean differences (95% confidence intervals) are calculated by column. Ks, keratometry in the steepest meridian; Kf, keratometry in the flattest meridian; Km, mean keratometry; NA, not available. The underline data indicate the statistical significant effect

Fig. 5

Meta-analysis results comparing all instruments with respect to astigmatism and astigmatism vectors. The upper right shows the direct comparisons meta-analysis between each pair of formulas and the bottom left shows the network meta-analysis between each pair of formulas. Weighted mean differences (95% confidence intervals) are calculated by column. J0, anterior corneal power vectors for the cardinal (axes at 90° and 180°) meridians; J45, anterior corneal power vectors for the oblique (axes at 45° and 135°) meridians; AST, astigmatism; NA, not available. The underline data indicate the statistical significant effect

Fig. 6

Meta-analysis results comparing all instruments with respect to anterior chamber depth (ACD), aqueous depth (AQD), and central corneal thickness (CCT). The upper right shows the direct comparisons meta-analysis between each pair of formulas and the bottom left shows the network meta-analysis between each pair of formulas. Weighted mean differences (95% confidence intervals) are calculated by column. NA, not available. The underline data indicate the statistical significant effect

Combination of direct and indirect comparisons

Figure 3 shows the results of the AL based on network meta-analyses that combine direct and indirect comparisons. As shown, statistically significant differences existed when the contact ultrasound biometry was compared with the following devices (WMD from large to small): Lenstar (WMD =  − 0.26 mm), Pentacam AXL (WMD =  − 0.22 mm), Argos (WMD =  − 0.22 mm), Aladdin (WMD =  − 0.22 mm), OA-2000 (WMD =  − 0.21 mm), IOLMaster 700 (WMD =  − 0.21 mm), AL-Scan (WMD =  − 0.20 mm), IOLMaster 500 (WMD =  − 0.20 mm) and IOLMaster (WMD =  − 0.18 mm). There were no statistically significant difference among the other instruments. As for the ranking results, the instruments were arranged based on the measured value of AL from the maximum to the minimum on the SUCRA values: Lenstar (80.1%), immersion ultrasound (63.3%), Pentacam AXL (60.8%), Argos (60.5%), Aladdin (60.3%), OA-2000 (55.4%), IOLMaster 700 (55.4%), IOLMaster 500 (50.7%), ANTERION (50.2%), AL-Scan (49.9%), Galilei G6 (47.8%), IOLMaster (39.8%), OA-1000 (22.3%), and contact ultrasound (3.5%) (Additional file 2: Fig. S1 and Additional file 1: Appendix I Table S15).

The results of the keratometry findings from the network meta-analyses are shown in Fig. 4. With respect to Kf, there was no statistically significant difference among the optical biometers (P > 0.05). The instruments were ranked consulting the maximum to minimum Kf values depending on the SUCRA values: AL-Scan (76.2%), IOLMaster (75.5%), IOLMaster 500 (63%), IOLMaster 700 (52.1%), Galilei G6 (48.8%), OA-2000 (41.9%), Lenstar (41.3%), Aladdin (38.5%), Pentacam AXL (12.8%). As for Ks, only when the Pentacam AXL was compared with the IOLMaster 500 (WMD =  − 0.26 D) and the IOLMaster (WMD =  − 0.29 D), a statistically significant difference existed. The rank results were as follows: IOLMaster (80.1%), IOLMaster 500 (75.3%), AL-Scan (62.8%), Lenstar (53.5%), IOLMaster 700 (46.3%), Galilei G6 (45.5%), Aladdin (40.1%), OA-2000 (37.5%), Pentacam AXL (9%). For Km, statistically significant differences existed when the Pentacam AXL was compared with the following devices (WMD from large to small): AL-Scan (WMD =  − 0.24 D), IOLMaster (WMD =  − 0.24 D), Argos (WMD =  − 0.22 D), IOLMaster 500 (WMD =  − 0.21 D), Lenstar (WMD =  − 0.18 D), OA-2000 (WMD =  − 0.15 D) and IOLMaster 700 (WMD =  − 0.13 D). As for the ranking results, the instruments were ranked as follows: IOLMaster (82.8%), AL-Scan (79.1%), Argos (71.4%), IOLMaster 500 (66.6%), Galilei G6 (52%), Lenstar (49.2%), OA-2000 (40.2%), IOLMaster 700 (28.5%), Aladdin (27.3%), Pentacam AXL (2.9%) (Additional file 2: Fig. S2 and Additional file 1: Appendix I Tables S16–S18).

Figure 5 shows the results for astigmatism. We found that there were no statistically significant differences between any of the studied instruments (P > 0.05) considering the AST, J0 and J45. As for the ranking results, the Lenstar obtained the maximum measured value of AST and J0 (70.9%, 65.4%, respectively), and got the minimum measured value of J45 (25%) (Additional file 2: Figure S3 and Additional file 1: Appendix I Tables S19–S21).

The results of ACD, AQD and CCT are shown in Fig. 6. When considering the ACD, statistically significant differences existed between contact ultrasound biometry and the following devices (WMD from large to small): OA-1000 (WMD =  − 0.49 mm), Argos (WMD =  − 0.18 mm), OA-2000 (WMD =  − 0.18 mm), Aladdin (WMD =  − 0.14 mm), Pentacam AXL (WMD =  − 0.12 mm), Lenstar (WMD =  − 0.12 mm), IOLMaster 700 (WMD =  − 0.10 mm), AL-Scan (WMD =  − 0.10 mm), IOLMaster 500 (WMD =  − 0.10 mm) and IOLMaster (WMD =  − 0.09 mm). We also observed significant differences between the OA-2000 and the IOLMaster 700 (WMD = 0.07 mm), the OA-2000 and the IOLMaster 500 (WMD = 0.08 mm), the OA-2000 and the IOLMaster (WMD = 0.09 mm). When the OA-1000 was compared with the following devices (WMD from large to small), statistically significant differences were found: Galilei G6 (WMD = 0.40 mm), IOLMaster 500 (WMD = 0.39 mm), IOLMaster (WMD = 0.39 mm), AL-Scan (WMD = 0.38 mm), IOLMaster 700 (WMD = 0.38 mm), Lenstar (WMD = 0.36 mm), Pentacam AXL (WMD = 0.36 mm), Aladdin (WMD = 0.35 mm), OA-2000 (WMD = 0.31 mm), ANTERION (WMD = 0.31 mm), and Argos (WMD = 0.30 mm). There were no significant differences between the other comparisons of the studied instruments.

The rank from the maximum result to the minimum are as follows: OA-1000 (99.8%), OA-2000 (78.5%), Argos (76.7%), ANTERION (64.9%), Aladdin (58.6%), Lenstar (52.1%), Pentacam AXL (51.7%), AL-Scan (37.6%), IOLMaster 700 (36.8%), IOLMaster 500 (32.7%), IOLMaster (29.7%), Galilei G6 (29.6%), contact ultrasound biometry (1.4%) (Additional file 2: Fig. S1). There were significant differences between the OA-2000 with the IOLMaster 700 (WMD = 0.16 mm) and the Lenstar (WMD = 0.15 mm) when taking the AQD into account. According to the SUCRA, the rank from the maximum result to the minimum are as follows: OA-2000 (88.8%), Argos (71.8%), ANTERION (62.9%), Aladdin (53.2%), AL-Scan (41.6%), Lenstar (40.8%), IOLMaster 700 (39.9%), contact ultrasound (39.4%), IOLMaster 500 (39.4%), Pentacam AXL (38%), Galilei G6 (34.3%).

In addition, there were statistically significant differences in measuring CCT when the OA-2000 was compared with the Pentacam AXL (WMD =  − 9.52 μm), IOLMaster 700 (WMD =  − 12.56 μm), Lenstar (WMD =  − 11.43 μm), AL-Scan (WMD =  − 13.98 μm), and Galilei G6 (WMD =  − 16.91 μm). The CCT measuring instruments were ranked depending on the SUCRA values as follows: Galilei G6 (82.1%), AL-Scan (74.6%), contact ultrasound (73.7%), IOLMaster 700 (68.8%), Lenstar (59.5%), Pentacam AXL (49%), ANTERION (38.8%), Argos (22.4%), Aladdin (20.4%), OA-2000 (10.6%) (Additional file 1: Appendix I Tables S22–S24).

Figure 3 shows the results of the CD and LT measurements based on network meta-analyses that combined direct and indirect comparisons. With respect to CD, statistically significant differences existed when the Pentacam AXL was compared with the IOLMaster 700 (WMD =  − 0.26 mm), the Lenstar (WMD =  − 0.30 mm), the IOLMaster 500 (WMD =  − 0.28 mm), and the IOLMaster (WMD =  − 0.35 mm). Statistically significant differences also existed between the OA-2000 and the Lenstar (WMD =  − 0.18 mm), the OA-2000 and the IOLMaster 500 (WMD =  − 0.15 mm), the OA-2000 and the IOLMaster (WMD =  − 0.23 mm), the Aladdin and the IOLMaster 700 (WMD =  − 0.32 mm), the Aladdin and the Lenstar (WMD =  − 0.36 mm), the Aladdin and the IOLMaster 500 (WMD =  − 0.33 mm), the Aladdin and the IOLMaster (WMD =  − 0.41 mmm), the Aladdin and the Galilei G6 (WMD =  − 0.39 mm), the Lenstar and the AL-Scan (WMD = 0.25 mm), the AL-Scan and the IOLMaster 500 (WMD =  − 0.22 mm), and the AL-Scan and the IOLMaster (WMD =  − 0.30 mm). As for the ranking results, the order of CD obtained from the maximum to the minimum based on the SUCRA values are as follows: IOLMaster (84.3%), Galilei G6 (77.4%), Lenstar (74.2%), IOLMaster 500 (66.9%), IOLMaster 700 (63.5%), Argos (60.8%), ANTERION (42.1%), OA-2000 (33.9%), AL-Scan (22.2%), Pentacam AXL (15.2%), Aladdin (9.4%). Considering LT, the ranking results from the maximum to the minimum based on the SUCRA values are as follows: contact ultrasound (94.1%), Argos (68.8%), OA-2000 (63.7%), Aladdin (61%), IOLMaster 700 (30.2%), Galilei G6 (26.3%), Lenstar (5.7%) (Additional file 2: Figures S1–S2 and Additional file 1: Appendix I Tables S25–S26).

Inconsistency

Node-splitting analysis between contact ultrasound biometry and the Lenstar for closed-loop comparisons in terms of AL showed significant inconsistency (P < 0.05). Similar results included: the Lenstar and the OA-2000 for Kf, the IOLMaster and the Lenstar for Kf and AST, the IOLMaster and contact ultrasound biometry for ACD, the Lenstar and contact ultrasound biometry for ACD, the IOLMaster and the OA-2000 for ACD, the IOLMaster 500 and the OA-2000 for ACD, the AL-Scan and the Lenstar for CD, the Argos and the Lenstar for CD, the Argos and the IOLMaster 700 for CD. We also used the design-by-treatment interactions model and found that global inconsistency existed for Kf, ACD, CCT and CD (P = 0.0041, P < 0.001, P < 0.001, P < 0.001, respectively) (Additional file 1: Appendix I Tables S27–S38).

Subgroup analysis

The results of the subgroup analysis also found no global inconsistency existing for AL, Ks, Km, AST, J0, J45, AQD and LT, and did not significantly change the results of the original network meta-analysis. There were 14 trials involving 9 instruments in the subgroups for the Kf measurement in cataract subjects. This process produced no significant inconsistency in the results. Statistically significant differences existed between the OA-2000 and the Pentacam AXL (WMD = 0.4 D); the OA-2000 and the Lenstar (WMD = 0.28 D) (full process and data shown in Additional file 3: Appendix II Tables S1–S18 and Additional file 3: Appendix II Tables S22–S39). Taking ACD into consideration, the subgroup in healthy subjects prompted no significant inconsistency in the results. Statistically significant differences only existed between the OA-2000 and the IOLMaster 500 (WMD = 0.07 mm); the Lenstar and the IOLMaster (WMD = 0.08 mm); the Pentacam AXL and contact ultrasound biometry (WMD = 0.13 mm); the Argos and contact ultrasound biometry (WMD = 0.18 mm); the OA-2000 and contact ultrasound biometry (WMD = 0.10 mm); the Lenstar and contact ultrasound biometry (WMD = 0.11 mm); the IOLMaster and contact ultrasound biometry (WMD = 0.06 mm). For CCT and CD, the subgroup in healthy subjects both found no significant inconsistency in the results. When considering the measurement of the CCT, there was no statistically significant difference between the Argos and the IOLMaster 700, which differs from the network meta-analysis. As for the measurement of the CD, statistically significant differences only existed when the OA-2000 was compared to the Lenstar and the IOLMaster.

Since there were global inconsistencies noted for Kf, ACD and CCT, we further performed comparison between groups according to the principle of the measurements. With respect to Kf, there was no statistically significant difference among the different measurement principles (P > 0.05). The principle of the measurements was ranked consulting the maximum to minimum Kf values depending on the SUCRA values: automated keratometer (AL-Scan, IOLMaster, IOLMaster 500, IOLMaster 700, Lenstar), Placido (Galilei G6, OA-2000, Aladdin), Scheimpflug (Pentacam AXL). The results were consistent with the results of the original network meta-analysis. When considering the measurement of the CCT, there was also no statistically significant difference among the different principles (P > 0.05). The principle of the measurements was ranked consulting the maximum to the minimum CCT values depending on the SUCRA values: A-Scan ultrasound (contact ultrasound), Scheimpflug (Galilei G6, AL-Scan, Pentacam AXL), OLCR (Lenstar), SS-OCT (IOLMaster 700, ANTERION, Argos, OA-2000), OLCI (Aladdin). The results are essentially in agreement with the results of the original network meta-analysis. For the ACD, there were statistically significant differences between the A-Scan ultrasound and the following principle: PCI, OLCR, OLCI, SS-OCT, Scheimpflug. Statistically significant differences also existed between the SS-OCT and the PCI. These results were consistent with the results from the original network meta-analysis (Additional file 3: Appendix II Tables S19–S21 and Additional file 3: Appendix II Tables S40–S42).

Publication bias

Comparison-adjusted funnel plots for each parameter are provided in Additional file 1: Appendix I Figs. S1–S12. Most of these plots except ACD showed that the included studies lie symmetrically around the “0” line (vertical line). However, the significant publication bias in the ACD did not show up when we performed subgroup analysis for the ACD measurement in healthy subjects (Additional file 3: Appendix II Figs. S1–S18).