Comparison of Unconditional Asymptotic, Exact Conditional and Robust Logistic Regression Methods for Binary Contaminated Data Sets: A Simulation Study

Year 2018, Volume 40, Issue 2, 53 - 59, 12.04.2018

Muzaffer Bilgin Ertugrul Colak

https://doi.org/10.20515/otd.409043

Abstract

    In clinical research outliers occurs in spite of careful study design, and implementation of error-prevention techniques. Exact conditional and Robust logistic regression techniques are alternatives to the unconditional asymptotic logistic regression analysis when the dataset is contaminated with outliers. Our specific objectives were to compare the performance of exact conditional and robust logistic regression methods by Monte-Carlo simulation study when the data is skewed with outliers. Robust logistic regression method had less biased parameter estimates even at the 1% contamination level. We proposed using robust logistic regression method rather than exact conditional method when the data set is contaminated.

Keywords

Contaminated dataset, Logistic regression, Robust logistic regression, Exact logistic regression

İkili Bozulmuş Veri Yapılarında Genel, Sağlam ve Kesin Lojistik Regresyon Yöntemlerinin Karşılaştırılması: Bir Simülasyon Çalışması

Abstract

Klinik araştırmalarda, ölçüm hatasını yok etmek için dikkatli çalışma düzen tasarımları kullanılmasına rağmen aykırı değerler ile karşılaşılabilir. Veri setlerinde aykırı değerler bulunduğu durumda, koşullu olmayan asimptotik lojistik regresyon yöntemlerine alternatif olarak kesin koşullu ve sağlam lojistik regresyon yöntemleri kullanılmaktadır. Bu çalışmanın temel amacı, veri setinde aykırı değerler ile çarpık bir yapı olduğu durumda, kesin ve sağlam lojistik regresyon yöntemlerinin performanslarını Monte-Carlo simülasyon çalışmaları ile karşılaştırmaktır. Sağlam lojistik regreson yöntemi, % 1 kontaminasyon seviyesinde bile daha az yanlı parametre tahminleri yaptığı bulundu. Veri setlerinde aykırı değerler ile bozulma durumu söz konusu olduğunda sağlam lojistik regresyon yöntemi kullanılmasını öneriyoruz.

Keywords

Bozulmuş İkili Veri, Lojistik Regresyon, Sağlam Lojistik Regresyon, Kesin Lojistik Regresyon

References

• Ryan TP. Some issues in logistic regression. Commun Stat-Theor M. 2000;29(9-10):2019-32.
• Rush S. Logistic regression: The standard method of analysis in medical research. Technical Report Mathematics; 2001.
• Czepiel SA. Maximum likelihood estimation of logistic regression models: theory and implementation.
• Dominguez-Almendros S, Benitez-Parejo N, Gonzalez-Ramirez AR. Logistic regression models. Allergol Immunopathol (Madr). 2011;39(5):295-305.
• Chen C, editor Paper 265-27 Robust Regression and Outlier Detection with the ROBUSTREG Procedure. Proceedings of the Proceedings of the Twenty-Seventh Annual SAS Users Group International Conference; 2002.
• Van den Broeck J, Cunningham SA, Eeckels R, Herbst K. Data cleaning: detecting, diagnosing, and editing data abnormalities. PLoS Med. 2005;2(10):e267.
• Derr RE, editor Performing Exact Logistic Regression with the SAS System-Revised 2009. Proceedings of the Twenty-fifth Annual SAS Users Group International Conference; Cary, NC; 2009: Citeseer.
• Gervini D. Robust adaptive estimators for binary regression models. Journal of Statistical Planning and Inference. 2005;131(2):297-311.
• Cox DR, Snell EJ. Analysis of binary data: CRC Press; 1989.
• Hirji KF, Mehta CR, Patel NR. Computing Distributions for Exact Logistic-Regression. Journal of the American Statistical Association. 1987;82(400):1110-7.
• King EN, Ryan TP. A preliminary investigation of maximum likelihood logistic regression versus exact logistic regression. Am Stat. 2002;56(3):163-70.
• Pampel FC. Logistic regression: A primer: Sage; 2000.
• Croux C, Haesbroeck G. Implementing the Bianco and Yohai estimator for logistic regression. Computational Statistics & Data Analysis. 2003;44(1-2):273-95.
• Mehta CR, Patel NR. Exact logistic regression: theory and examples. Stat Med. 1995;14(19):2143-60.
• Bianco AM, Martinez E. Robust testing in the logistic regression model. Computational Statistics & Data Analysis. 2009;53(12):4095-105.
• Hosmer Jr DW, Lemeshow S. Applied logistic regression: John Wiley & Sons; 2004.
• Hosseinian S, Morgenthaler S. Robust binary regression. Journal of Statistical Planning and Inference [Internet]. 2011 Apr; 141(4):[1497-509 pp.].
• Komarek P, Moore AW, editors. Fast Robust Logistic Regression for Large Sparse Datasets with Binary Outputs. AISTATS; 2003.
• Kordzakhia N, Mishra GD, Reiersolmoen L. Robust estimation in the logistic regression model. Journal of Statistical Planning and Inference. 2001;98(1-2):211-23.
• Mehta CR, Patel NR, Senchaudhuri P. Efficient Monte Carlo methods for conditional logistic regression. Journal of the American Statistical Association. 2000;95(449):99-108.
• Agresti A, Kateri M. Categorical data analysis: Springer; 2011.