Sains Malaysiana 45(3)(2016): 499–506

Comparison of Outlier Detection Methods in Standard 2 × 2 Crossover Design

(Perbandingan Kaedah Pengesanan Titik Terpencil dalam Piawai 2 × 2 Reka Bentuk Pindah Silang)

FONG PENG LIM¹, IBRAHIM MOHAMED¹*, NOORIZAM DAUD² & SIEW LI GOH³

¹Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Federal Territory

Malaysia

²Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor Darul Ehsan, Malaysia

³Sport Medicine Clinic, University of Malaya Hospital, 50603 Kuala Lumpur, Federal Territory

Malaysia

Received: 19 January 2015/Accepted: 21 September 2015

ABSTRACT

This paper discussed methods for outlier detection in standard 2 × 2 crossover studies. Two outlier detection procedures were carried out based on residuals. Under a simplified model of 2 × 2 crossover design, we present the classical calculation of studentized residual (SR1) and propose a new studentized residual using median absolute deviation (SR2) to identify possible outlying subjects. The performances of both procedures in detecting subject outliers were compared. We show via simulation that a proposed procedure using SR2 is more powerful than that using SR1 for outlier detection. As an illustration, these procedures were applied to two real data sets from studies of bioavailability and kinesiology, respectively.

Keywords: Crossover design; median absolute deviation; outlier; residual

ABSTRAK

Kertas kerja ini membincangkan kaedah untuk mengesan titik terpencil dalam piawai 2 × 2 kajian pindah silang. Dua prosedur mengesan titik terpencil telah dijalankan berdasarkan sisa. Berdasarkan satu model 2 × 2 kajian pindah silang yang diringkaskan, kami menunjukkan pengiraan studentized sisa klasik (SR1) dan mencadangkan satu studentized sisa baharu yang menggunakan sisihan mutlak median (SR2) untuk mengesan subjek terpencil yang mungkin wujud. Prestasi kedua-dua prosedur dalam pengesanan subjek terpencil dibandingkan. Melalui simulasi, kami mendapati prosedur menggunakan SR2 yang dicadangkan memberikan prestasi yang lebih baik daripada prosedur menggunakan SR1 untuk pengesanan titik terpencil. Sebagai ilustrasi, prosedur tersebut digunakan untuk dua set data kajian sebenar dalam bidang bioketersediaan dan kinesiologi.

Kata kunci: Reka bentuk pindah silang; sisa; sisihan mutlak median; titik terpencil

REFERENCES

Chow, S.C. & Liu, J.P. 2009. Design and Analysis of Bioavailability and Bioequivalence Studies. London: Chapman and Hall.

Chow, S.C. & Tse, S.K. 1990. Outliers detection in bioavailability/ bioequivalence studies. Statistics in Medicine 9: 549-558.

Clayton, D. & Leslie, A. 1981. The bioavailability of erythromycin stearate versus enteric-coated erythromycin based when taken immediately before and after food. Journal of International Medical Research 9: 470-477.

Enachescu, D. & Enachescu, C. 2009. A new approach for outlying records in bioequivalence trials. Paper presented at The XIII International Conference on Applied Stochastic Models and Data Analysis.

Jones, B. & Kenward, M.G. 1989. Design and Analysis of Cross-over Trials. London: Chapman and Hall.

Karasoy, D. & Daghan, G. 2012. Examination of outliers in bioequivalence studies. Bulletin of Clinical Psychopharmacology 22(4): 307-312.

Liu, J.P. & Weng, C.S. 1991. Detection of outlying data in bioavailability/bioequivalence studies. Statistics in Medicine 10: 1375-1389.

Lund, R.E. 1975. Tables for an approximate test for outliers in linear models. Technometrics 17(4): 473-476.

Luzar-Stiffler, V. & Stiffler, C. 2005. Higher-order crossover design outlier detection. In Proceedings of the 27th International Conference on Information Technology Interfaces. Zagreb: University of Zagreb. pp. 650-655.

Ramsay, T. & Elkum, N. 2005. A comparison of four different methods for outlier detection in bioequivalence studies. Journal of Biopharmaceutical Statistics 15(1): 43-52.

Singh, R., Namdev, K.K. & Chilkoti, D. 2014. An assessment on handling of outlier subjects in bioequivalence study - A review. Journal of Pharmaceutical and Bioanalytical Science 3(1): 14-20.

Wang, W. & Chow, S.C. 2003. Examining outlying subjects and outlying records in bioequivalence trials. Journal of Biopharmaceutical Statistics 13(1): 43-56.

Weiner, D. 1989. Bioavailability. Notes on the training course for new clinical statisticians sponsored by the Biostatistics Subsections of Pharmaceutical Manufacture Association, March, 1989, Washington, DC.

*Corresponding author; email: imohamed@um.edu.my