The importance of statistics in ophthalmology
Edgar Lozano-Cruz
Submitted Dec 27, 2023. Accepted for publication Feb 02, 2024. Published online Mar 12, 2024.
doi: 10.21037/qims-23-1843
I recently read the article by Wang et al. about continuous surgical treatment (CST) to improve the scarring process and probably patient outcomes in anterior segment open globe injuries (1). An interesting idea, as other researchers in different fields have demonstrated the benefits of debridement when healing a wound after trauma.
However, I would like to address some concerns regarding the statistical analysis due to the small sample size, with an n of 19 (eyes and patients) for a quasi-experimental design, where two groups were compared, one with CST and the other without it, and the multiple tests applied to the data.
Having a small sample size has its limitations. Researchers are limited mostly to descriptive analysis and analysis of independence. Statistical models, correlations, associated factors, or predictions are hindered by the lack of power that small numbers give. Interceptions between variables with small numbers and multiple categories are likely to produce tables with zeros in some cells, which is often a challenge to reach reliable conclusions from the data.
To analyze any variable, test selection is vital. One needs to study first if the assumptions of the test are fulfilled. Two tests are used to analyze independence between two categorical variables: the chi-squared test and the Fisher’s exact test. Selection of the proper test is based on the expected value for each cell in the table n × n, which are calculated as follows:
Using the data from Tab. 1 to 3 in the Wang et al. study, one can find that there are expected values that are lower than 5. Running tests, both the chi-squared and Fisher’s exact tests using Stata18®, it seems that the authors used chi-squared where it should not be used, generating inaccurate P values and, therefore, results and conclusions (2). Most of the P values in Tab. 3 change when a Fisher’s test is applied, and the significance is lost in most of the variables as described in Table 1 of this letter.
Table 1
| Complication | Group 1, n [E(x)] | Group 2, n [E(x)] | P value (Chi2) | P value (Fisher’s exact test) | Wang et al., P value |
|---|---|---|---|---|---|
| Adhesive corneal leucoma | 0.005 | 0.011 | 0.011 | ||
| Yes | 0 [2.8] | 6 [3.2] | |||
| No | 9 [6.2] | 4 [6.8] | |||
| Uneven anterior chamber by slit lamp/AS OCT/UBM | 0.027 | 0.057* | 0.022 | ||
| Yes | 1 [3.3] | 6 [3.7] | |||
| No | 8 [5.7] | 4 [6.3] | |||
| Blocking the light passing through the pupil | 0.073 | 0.211* | 0.037 | ||
| Yes | 0 [1.4] | 3 [1.6] | |||
| No | 9 [7.6] | 7 [8.4] | |||
| Fibrosis or scarring in the AS | 0.040 | 0.070* | 0.040 | ||
| Yes | 3 [5.2] | 8 [5.8] | |||
| No | 6 [3.8] | 2 [4.2] | |||
| Secondary glaucoma | 0.073 | 0.211* | 0.037 | ||
| Yes | 0 [1.4] | 3 [1.6] | |||
| No | 9 [7.6] | 7 [8.4] | |||
| Severe destruction of the AS | 0.156 | 0.474 | 0.474 | ||
| Yes | 0 [0.9] | 2 [1.1] | |||
| No | 9 [8.1] | 8 [8.9] | |||
n, sample size. E(x): expected value. *, P values that compared with Wang et al.’s (1) P values changed from significant to non-significant. Group 1: patients with AS open globe injuries who received CST; group 2: patients without CST after the initial wound repair. CST, continuous surgical treatment; AS, anterior segment; OCT, optical coherence tomography; UBM, ultrasound biomicroscope.
Amendments to this manuscript are worthy as the analysis has serious limitations due to the small sample size, but mostly because the analysis was not carried out with the proper test. Another pending discussion might be the effect of multiple tests on the study’s outcomes.
I encourage the authors to consider these points in a revised analysis or future research. Such improvements could greatly enhance the reliability and applicability of the study’s findings, further benefiting the field of ophthalmology.
Appendix 1: Response to “The importance of statistics in ophthalmology”.
Acknowledgments
Funding: None.
Footnote
Conflicts of Interest: The author has completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-23-1843/coif). The author has no conflicts of interest to declare.
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References
- Wang X, Feng K, He S, Xie X, Ma Z. The continuous treatment of anterior segment open globe injury: an eye injury vitrectomy study. Quant Imaging Med Surg 2023;13:6257-67. [Crossref] [PubMed]
- McDonald JH. Handbook of biolological statistics: 3rd ed. Baltimore, MD: Sparky House Publishing, 2014.
