Download PDF
CC BY-NC-ND 4.0 · Indian J Radiol Imaging 2025; 35(S 01): S74-S92
DOI: 10.1055/s-0044-1800971
Research and Publications: The Process
Review Article

Statistics Primer for Radiologists: Part 2—Advanced statistics for Enhancing Diagnostic Precision and Research Validity

Adarsh Anil Kumar
1   Department of Imaging Sciences and Interventional Radiology, Sree Chitra Institute of Medical Sciences, Trivandrum, Kerala, India
,
Santhosh Kannath
1   Department of Imaging Sciences and Interventional Radiology, Sree Chitra Institute of Medical Sciences, Trivandrum, Kerala, India
,
Jineesh Valakkada 
1   Department of Imaging Sciences and Interventional Radiology, Sree Chitra Institute of Medical Sciences, Trivandrum, Kerala, India
› Author Affiliations Funding None.
› Further Information
Also available at
   Permissions and Reprints

Abstract

Second part of this statistics primer focuses on advanced statistical concepts continuing on the foundation of basic statistics built from the first part of this primer. This advanced primer aims to delve deeper into essential statistical concepts beyond the basics, equipping the reader with the knowledge to effectively analyze complex data sets, explore correlations and causality, employ regression analysis techniques, interpret survival curves, and evaluate diagnostic tests rigorously. It primarily focuses on the statistical tests used to analyze the relationship between groups of variables (the statistical tests to analyze the difference between groups of variables was discussed in the part 1 of this series). Toward the end of the article concepts of survival curves and methods for assessing the diagnostic accuracy of tests are stressed upon.

Keywords

primer - radiologists - statistics

Note

Work done in: Department of Imaging Sciences and Interventional Radiology, Sree Chitra Institute of Medical Sciences, Trivandrum


Authors' Contributions

All the authors were involved in the procedure, data collection, and manuscript revision.




Publication History

Article published online:
09 January 2025

© 2025. Indian Radiological Association. This is an open access article published by Thieme under the terms of the Creative Commons Attribution-NonDerivative-NonCommercial License, permitting copying and reproduction so long as the original work is given appropriate credit. Contents may not be used for commercial purposes, or adapted, remixed, transformed or built upon. (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Thieme Medical and Scientific Publishers Pvt. Ltd.
A-12, 2nd Floor, Sector 2, Noida-201301 UP, India

 

  • References

  • 1 Bewick V, Cheek L, Ball J. Statistics review 7: correlation and regression. Crit Care 2003; 7 (06) 451-459
    CrossrefPubMedSearch in Google Scholar
  • 2 Zaniletti I, Larson DR, Lewallen DG, Berry DJ, Maradit Kremers H. How to distinguish correlation from causation in orthopaedic research. J Arthroplasty 2023; 38 (04) 634-637
    CrossrefPubMedSearch in Google Scholar
  • 3 Mukaka MM. Statistics corner: a guide to appropriate use of correlation coefficient in medical research. Malawi Med J 2012; 24 (03) 69-71
    PubMedSearch in Google Scholar
  • 4 Schober P, Boer C, Schwarte LA. Correlation coefficients: appropriate use and interpretation. Anesth Analg 2018; 126 (05) 1763-1768
    CrossrefPubMedSearch in Google Scholar
  • 5 de Winter JC, Gosling SD, Potter J. Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: a tutorial using simulations and empirical data. Psychol Methods 2016; 21 (03) 273-290
    CrossrefPubMedSearch in Google Scholar
  • 6 Rovetta A. Raiders of the lost correlation: a guide on using Pearson and Spearman coefficients to detect hidden correlations in medical sciences. Cureus 2020; 12 (11) e11794
    PubMedSearch in Google Scholar
  • 7 Chen S, Ghadami A, Epureanu BI. Practical guide to using Kendall's τ in the context of forecasting critical transitions. R Soc Open Sci 2022; 9 (07) 211346
    CrossrefPubMedSearch in Google Scholar
  • 8 Bonett DG. Point-biserial correlation: interval estimation, hypothesis testing, meta-analysis, and sample size determination. Br J Math Stat Psychol 2020; 73 (Suppl. 01) 113-144
    CrossrefPubMedSearch in Google Scholar
  • 9 Shimonovich M, Pearce A, Thomson H, Keyes K, Katikireddi SV. Assessing causality in epidemiology: revisiting Bradford Hill to incorporate developments in causal thinking. Eur J Epidemiol 2021; 36 (09) 873-887
    CrossrefPubMedSearch in Google Scholar
  • 10 Provost LP. Commentary: establishing causality in quality improvement studies. Pediatr Qual Saf 2023; 8 (03) e653
    CrossrefPubMedSearch in Google Scholar
  • 11 Ali P, Younas A. Understanding and interpreting regression analysis. Evid Based Nurs 2021; 24 (04) 116-118
    CrossrefPubMedSearch in Google Scholar
  • 12 Streiner DL. Control or overcontrol for covariates?. Evid Based Ment Health 2016; 19 (01) 4-5
    CrossrefPubMedSearch in Google Scholar
  • 13 Hazra A, Gogtay N. Biostatistics series module 10: brief overview of multivariate methods. Indian J Dermatol 2017; 62 (04) 358-366
    CrossrefPubMedSearch in Google Scholar
  • 14 Kim HY. Statistical notes for clinical researchers: simple linear regression 1 - basic concepts. Restor Dent Endod 2018; 43 (02) e21
    CrossrefPubMedSearch in Google Scholar
  • 15 Casson RJ, Farmer LDM. Understanding and checking the assumptions of linear regression: a primer for medical researchers. Clin Exp Ophthalmol 2014; 42 (06) 590-596
    CrossrefPubMedSearch in Google Scholar
  • 16 Riley RD, Snell KI, Ensor J. et al. Minimum sample size for developing a multivariable prediction model: part II - binary and time-to-event outcomes. Stat Med 2019; 38 (07) 1276-1296
    CrossrefPubMedSearch in Google Scholar
  • 17 Marill KA. Advanced statistics: linear regression, part II: multiple linear regression. Acad Emerg Med 2004; 11 (01) 94-102
    CrossrefPubMedSearch in Google Scholar
  • 18 Alexopoulos EC. Introduction to multivariate regression analysis. Hippokratia 2010; 14 (Suppl. 01) 23-28
    PubMedSearch in Google Scholar
  • 19 Sperandei S. Understanding logistic regression analysis. Biochem Med (Zagreb) 2014; 24 (01) 12-18
    CrossrefPubMedSearch in Google Scholar
  • 20 Stoltzfus JC. Logistic regression: a brief primer. Acad Emerg Med 2011; 18 (10) 1099-1104
    CrossrefPubMedSearch in Google Scholar
  • 21 Schober P, Vetter TR. Logistic regression in medical research. Anesth Analg 2021; 132 (02) 365-366
    CrossrefPubMedSearch in Google Scholar
  • 22 van Ginkel JR. Standardized regression coefficients and newly proposed estimators for [formula: see text] in multiply imputed data. Psychometrika 2020; 85 (01) 185-205
    PubMedSearch in Google Scholar
  • 23 Yang K, Tu J, Chen T. Homoscedasticity: an overlooked critical assumption for linear regression. Gen Psychiatr 2019; 32 (05) e100148
    CrossrefPubMedSearch in Google Scholar
  • 24 Vatcheva KP, Lee M, McCormick JB, Rahbar MH. Multicollinearity in regression analyses conducted in epidemiologic studies. Epidemiology (Sunnyvale) 2016; 6 (02) 227
    CrossrefPubMedSearch in Google Scholar
  • 25 Abd ElHafeez S, D'Arrigo G, Leonardis D, Fusaro M, Tripepi G, Roumeliotis S. Methods to analyze time-to-event data: the Cox regression analysis. Oxid Med Cell Longev 2021; 2021: 1302811
    CrossrefPubMedSearch in Google Scholar
  • 26 Andrade C. Survival analysis, Kaplan-Meier curves, and Cox regression: basic concepts. Indian J Psychol Med 2023; 45 (04) 434-435
    CrossrefPubMedSearch in Google Scholar
  • 27 Deo SV, Deo V, Sundaram V. Survival analysis-part 2: Cox proportional hazards model. Indian J Thorac Cardiovasc Surg 2021; 37 (02) 229-233
    CrossrefPubMedSearch in Google Scholar
  • 28 Zeng Z, Gao Y, Li J. et al. Violations of proportional hazard assumption in Cox regression model of transcriptomic data in TCGA pan-cancer cohorts. Comput Struct Biotechnol J 2022; 20: 496-507
    CrossrefPubMedSearch in Google Scholar
  • 29 Bellera CA, MacGrogan G, Debled M, de Lara CT, Brouste V, Mathoulin-Pélissier S. Variables with time-varying effects and the Cox model: some statistical concepts illustrated with a prognostic factor study in breast cancer. BMC Med Res Methodol 2010; 10: 20
    CrossrefPubMedSearch in Google Scholar
  • 30 Stolberg HO, Norman G, Trop I. Survival analysis. AJR Am J Roentgenol 2005; 185 (01) 19-22
    CrossrefPubMedSearch in Google Scholar
  • 31 Clark TG, Bradburn MJ, Love SB, Altman DG. Survival analysis part I: basic concepts and first analyses. Br J Cancer 2003; 89 (02) 232-238
    CrossrefPubMedSearch in Google Scholar
  • 32 Park SH, Han K, Park SY. Mistakes to avoid for accurate and transparent reporting of survival analysis in imaging research. Korean J Radiol 2021; 22 (10) 1587-1593
    CrossrefPubMedSearch in Google Scholar
  • 33 Rai S, Mishra P, Ghoshal UC. Survival analysis: a primer for the clinician scientists. Indian J Gastroenterol 2021; 40 (05) 541-549
    CrossrefPubMedSearch in Google Scholar
  • 34 Leung KM, Elashoff RM, Afifi AA. Censoring issues in survival analysis. Annu Rev Public Health 1997; 18: 83-104
    CrossrefPubMedSearch in Google Scholar
  • 35 Rich JT, Neely JG, Paniello RC, Voelker CCJ, Nussenbaum B, Wang EW. A practical guide to understanding Kaplan-Meier curves. Otolaryngol Head Neck Surg 2010; 143 (03) 331-336
    CrossrefPubMedSearch in Google Scholar
  • 36 Dudley WN, Wickham R, Coombs N. An introduction to survival statistics: Kaplan-Meier analysis. J Adv Pract Oncol 2016; 7 (01) 91-100
    PubMedSearch in Google Scholar
  • 37 Bland JM, Altman DG. The logrank test. BMJ 2004; 328 (7447) 1073
    CrossrefPubMedSearch in Google Scholar
  • 38 Dormuth I, Liu T, Xu J, Yu M, Pauly M, Ditzhaus M. Which test for crossing survival curves? A user's guideline. BMC Med Res Methodol 2022; 22 (01) 34
    CrossrefPubMedSearch in Google Scholar
  • 39 Hajian-Tilaki K. Receiver operating characteristic (ROC) curve analysis for medical diagnostic test evaluation. Caspian J Intern Med 2013; 4 (02) 627-635
    PubMedSearch in Google Scholar
  • 40 Nahm FS. Receiver operating characteristic curve: overview and practical use for clinicians. Korean J Anesthesiol 2022; 75 (01) 25-36
    CrossrefPubMedSearch in Google Scholar
  • 41 Florkowski CM. Sensitivity, specificity, receiver-operating characteristic (ROC) curves and likelihood ratios: communicating the performance of diagnostic tests. Clin Biochem Rev 2008; 29 (Suppl 1, Suppl 1) S83-S87
    PubMedSearch in Google Scholar
  • 42 Safari S, Baratloo A, Elfil M, Negida A. Evidence based emergency medicine; part 4: pre-test and post-test probabilities and Fagan's nomogram. Emergency (Tehran) 2016; 4 (01) 48-51
    Search in Google Scholar
  • 43 Monaghan TF, Rahman SN, Agudelo CW. et al. Foundational statistical principles in medical research: sensitivity, specificity, positive predictive value, and negative predictive value. Medicina (Kaunas) 2021; 57 (05) 503
    CrossrefPubMedSearch in Google Scholar
  • 44 Parikh R, Mathai A, Parikh S, Chandra Sekhar G, Thomas R. Understanding and using sensitivity, specificity and predictive values. Indian J Ophthalmol 2008; 56 (01) 45-50
    CrossrefPubMedSearch in Google Scholar
  • 45 Tang W, Hu J, Zhang H, Wu P, He H. Kappa coefficient: a popular measure of rater agreement. Shanghai Jingshen Yixue 2015; 27 (01) 62-67
    Search in Google Scholar
  • 46 Li M, Gao Q, Yu T. Kappa statistic considerations in evaluating inter-rater reliability between two raters: which, when and context matters. BMC Cancer 2023; 23 (01) 799
    CrossrefPubMedSearch in Google Scholar
  • 47 Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics 1977; 33 (01) 159-174
    Search in Google Scholar
  • 48 Warrens MJ. Cohen's linearly weighted kappa is a weighted average. Adv Data Anal Classif 2012; 6: 67-79
    CrossrefSearch in Google Scholar
  • 49 Ranganathan P, Pramesh CS, Aggarwal R. Common pitfalls in statistical analysis: measures of agreement. Perspect Clin Res 2017; 8 (04) 187-191
    CrossrefPubMedSearch in Google Scholar
  • 50 Gwet KL. Large-sample variance of Fleiss generalized kappa. Educ Psychol Meas 2021; 81 (04) 781-790
    CrossrefPubMedSearch in Google Scholar
  • 51 Ma Y. On inference for Kendall's τ within a longitudinal data setting. J Appl Stat 2012; 39 (01) 2441-2452
    CrossrefPubMedSearch in Google Scholar
  • 52 Koo TK, Li MY. A guideline of selecting and reporting intraclass correlation coefficients for reliability research. J Chiropr Med 2016; 15 (02) 155-163
    CrossrefPubMedSearch in Google Scholar
  • 53 Liu J, Tang W, Chen G, Lu Y, Feng C, Tu XM. Correlation and agreement: overview and clarification of competing concepts and measures. Shanghai Jingshen Yixue 2016; 28 (02) 115-120
    Search in Google Scholar
  • 54 Liljequist D, Elfving B, Skavberg Roaldsen K. Intraclass correlation - a discussion and demonstration of basic features. PLoS One 2019; 14 (07) e0219854
    CrossrefPubMedSearch in Google Scholar
  • 55 Riffenburgh RH, Gillen DL. Techniques to aid analysis. In Statistics in Medicine 4th Ed. 2020; 631-649
    Search in Google Scholar