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• W4210851312 abstract "While visualization of fetal anatomy is one of the primary purposes of diagnostic ultrasound, the application of statistical analysis to biological measurements of fetal structures, such as the head, abdomen, long bones and heart, requires equations that compute changes in these measurements over time1-3. Historically, early investigators used simple linear regression models and reported the equation for the mean and SD but did not model the SD for gestational age or other biometric measurements. In 1993, Altman and Chitty published seminal papers detailing the statistical analysis for creating reference intervals to analyze the size of fetal structures as a function of gestational age1, 2. They stated that failure to allow for increasing variation with gestation has major consequences because it leads to centiles that are too far apart early in pregnancy and too close later on2. Figure 1a illustrates a reference interval graph in which SD is fixed, while Figure 1b illustrates a reference interval graph with a progressive increase of the SD as a function of fetal age (Figure 1b)3, 4. The reference interval graph represents the normal distribution of a measurement at a given point in time or a specific fetal size (e.g. estimated fetal weight). One of the challenges for an investigator who wishes to compute a reference interval for a fetal measurement is selecting the best equation for the measurement of interest. In 1998, Royston and Wright introduced the concept of fractional polynomial regression equations to describe changes in fetal measurements as a function of gestational age5. There are 44 possible fractional polynomial regression equations (Table 1). Since it would be laborious to analyze each equation manually to identify the best fit to the data, software programs have been developed for such analysis. However, depending on the software program, potential errors can occur when translating the coefficients of a complex equation to a format that can be used by a clinician to incorporate the results of a study into clinical practice. While there are a number of statistical programs available, I have identified a statistical program (NCSS 2021; NCSS, LLC, Kaysville, UT, USA) that addresses the abovementioned concerns when translating the coefficient results from one of the 44 fractional polynomial regression equations to a format that can be used in Excel. For example, when analyzing left ventricular end-diastolic area of the fetal heart, the program does the following: (1) selects the best-fit equation for the dataset among the 44 fractional polynomial regression equations (Table 1); (2) reports the equation and coefficients in tabular form for the mean and SD (Table 2); (3) creates an Excel formula for the mean and SD equations, allowing the user to copy and paste the equations directly into an Excel spreadsheet (Table 3); (4) creates an Excel formula for the Z-score equation using the mean and SD equations from the statistical analysis of the data as follows: Z-score = (measured valuestudy group − mean valuecontrol group)/SDcontrol group (Table 3). Investigators create reference tables for various centiles (1st, 5th, 10th, 50th, 90th, 95th, 99th). It is important to understand that each of the reference intervals has an equivalent K-value which is the corresponding centile of the standard Gaussian distribution. This is multiplied by SD to compute the value for a specific centile (Table 4). The equations for the 1st, 5th, 10th, 50th, 90th, 95th and 99th centiles are provided in Table 4. Table S1 presents centiles for left ventricular end-diastolic area, computed using the K-values from Table 4. Table S2 illustrates the Excel equation format for computing the 5th and 95th centiles for left ventricular end-diastolic area between 20 and 40 weeks of gestation12. Once the tables have been created for the selected centiles (Table S2), the results can be used to create centile graphs using Excel or other programs. Videoclip S1 explains how centile tables and graphs can be created in Excel using mean and SD equations in Table 3. The abovementioned approach using NCSS 2021 provides results for the data analysis and equations in Excel format. However, most investigators receive the equation and coefficients from their statistician in a non-Excel format and report the results accordingly (Table 1). This requires the reader to create Excel equations for graphical display and a Z-score calculator. The problems that I have identified in the literature usually result from equation errors or not clearly explaining the computational analysis6-11. To avoid this problem, I would suggest the following: (1) assume to be the reader of your study wishing to use the equations to create graphs or a Z-score calculator; (2) translate the equations for the mean and SD into an Excel format; (3) once the Excel equations for the mean and SD have been created, create reference tables for the mean and 5th and 95th centiles (Table S2 and Videoclip S1); (4) compare the Excel results with the output from the statistical program that is used to analyze the dataset. If the results do not match, evaluate the Excel equations for errors (Table S2); (5) once the reference table is computed, create a graph of the results from the table to determine if it is similar to the computer output from the statistical program that was used for the data analysis (Figure 2); (6) when the paper is submitted for publication, consider providing the Excel equations either as part of the main body of the paper or as an online supplement. In addition, using the Z-score calculator format, an Excel Z-score calculator can be created and provided as an online supplement. Appendix S1 presents a template for computing mean, SD and 5th and 95th centiles in tabular form and creating the corresponding graph. To use the template, the user needs to enter values for the independent variable (e.g. gestational age), enter equations for the mean and SD, and link the independent variable in the mean and SD equations to the corresponding values of the independent variable. In 1993, I published a study titled ‘Ductus venosus index: a method for evaluating right ventricular preload in the second-trimester fetus’ in which an error occurred as a result of multiple revisions of the manuscript, and the original correct equation was replaced by an incorrect equation when submitting the final manuscript13. The authors who found the error compared the published equation with the published graph and reported that they were not the same14. Having personally experienced the chagrin of making an error in a published study, I have empathy for those colleagues in whose recently published papers I have found errors. However, when errors are found, it is important that they are corrected. It is important for both authors and publishers to make every attempt to publish correct equations. It is my opinion that if investigators follow the steps I describe in the Videoclip S1, errors in equations can be identified and corrected before submitting the final manuscript for publication. No data available Table S1 Reference interval table showing mean, SD and centiles for left ventricular end-diastolic area according to gestational age Table S2 Excel format of equations for the mean, SD and 5th and 95th centiles for left ventricular end-diastolic area computed in Table S1 Appendix S1 Template for computing mean, SD, 5th and 95th centiles in tabular form and the corresponding graph Videoclip S1 Demonstration of how centile tables and graphs can be created in Excel using the mean and SD equations from Table 3. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article." @default.
• W4210851312 created "2022-02-09" @default.
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• W4210851312 date "2022-08-01" @default.
• W4210851312 modified "2023-09-27" @default.
• W4210851312 title "How to avoid errors when computing reference interval tables and graphs using regression equations for cross‐sectional studies of fetal biometry" @default.
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• W4210851312 doi "https://doi.org/10.1002/uog.24875" @default.
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