Statistics Seminar Series 2009-10
Title:
Statistical test procedures for
unreplicated Bland-Altman method
comparison plots
Speaker:
Kevin Hayes, Statistics Department, University of
Limerick
Venue and time:
Western Gateway (IT) Building, G09
Mon 29th March 3-4pm
Abstract:
Altman and Bland (1983) criticise the use of correlation, regression and differences
between means when analysing data which arises from the experimental comparison of
two techniques or methods of measurement. They propose a simple graphical technique
based on a plot of case-wise differences between methods against case-wise means of the
methods, hereafter referred to as the Bland-Altman method comparison plot. All casewise differences between two methods showing good agreement are expected to fall
within the limits of agreement set at plus or minus 2 standard deviations of the average
difference. Ryan and Woodall (2005) report that the subsequent Lancet paper by Bland
and Altman (1986) is the sixth most highly cited statistical paper ever. The Bland-Altman
method has become the expected (often obligatory) approach for presenting
determinations of method reliability in many scientific journals (Hollis, 1996, for
example). The successful impact of this paper is perhaps, in part, due to the fact that only
an informal inspection of the graphical method is required supplemented by the
correlation coefficient of the plotted quantities. Surprisingly, the Bland-Altman
methodology does not recommend any statistical protocol based on statistical testing for
the purpose of distinguishing between the issues of bias and lack of precision.
This talk considers the problem of testing 12  22 and  12   22 using a random sample
from a bivariate normal distribution with parameters  1 , 2 , 1, 2 ,   . The new
contribution is a decomposition of the Bradley-Blackwood test statistic (Bradley and
Blackwood, 1989) for the simultaneous test of 12  22 and  12   22 as a sum of two
statistics. One is equivalent to the Pitman-Morgan (Pitman, 1939; Morgan, 1939) test
statistic for  12   22 and the other one is a new alternative to the standard paired-t test of
D  1  2  0 : Surprisingly, the classic Student paired-t test makes no assumptions
about the equality (or otherwise) of the variance parameters. The power functions for
these tests are quite easy to derive, and show that when  12   22 ; the paired t-test has a
slight advantage over the new alternative in terms of power, but when  12   22 ; the new
test has substantially higher power than the paired-t test.
While Bradley and Blackwood provide a test on the joint hypothesis of equal means and
equal variances their regression based approach does not separate these two issues. The
rejection of the joint hypothesis may be due to two groups with unequal means and
unequal variances; unequal means and equal variances, or equal means and unequal
variances. We propose an approach for resolving this (model selection) problem in a
manner controlling the magnitudes of the relevant type I error probabilities.
References
Altman, D. G. and J. M. Bland (1983), Measurement in Medicine: The Analysis of
Method Comparison Studies," The Statistician: Journal of the Institute of Statisticians,
32, 307-317.
Ryan, T. and W. Woodall (2005), The Most-Cited Statistical Papers," Journal of Applied
Statistics, 32, 461-474.
Bland, J. M. and D. G. Altman (1986), Statistical Methods for Assessing Agreement
Between Two Methods of Clinical Measurement," The Lancet, i.
Hollis, S. (1996), Analysis of Method Comparison Studies," Annals of Clinical
Biochemistry, 33, 1-4.
Bland, J. M. and D. G. Altman (1999), Measuring Agreement in Method Comparison
Studies, Statistical Methods in Medical Research, 8, 135-160.
Bradley, E. L. and Blackwood, L. G. (1989) Comparing Paired Data: a Simultaneous
Test for Means and Variances, The American Statistician, 43, 234{235.
Morgan, W. A. (1939) A Test for the Significance of the Difference Between Two
Variances in a Sample from a Normal Bivariate Population. Biometrika, 31, 13-19.
Pitman, E. J. G. (1939) A Note on Normal Correlation. Biometrika, 31, 9-12.
[“Student”] Gosset, W. S. (1908) The Probable Error of the Mean. Biometrika, 6, 1-25.