The use of sum statistics for multiple endpoints in clinical and
preclinical trials.
Violeta Labarta
Centro de Ingeniería Genética y Biotecnología, División de Ensayos Clínicos.
Ave 31 e/ 158 y 190 Playa, Apartado postal 6162, Ciudad de la Habana CP 10600, Cuba.
Havana, Cuba
e-mail: clintr@cigbdec.cigb.edu.cu
1. Introduction
The efficacy of two or more treatments frequently are measured for more than one response
variable. Although univariate methods for individual assessing of each characteristic are useful in
this setting, there is the additional need for a single, overall, objective probability statement that
addresses the question of whether or not the experimental therapy is efficacious (Obrien, 1984). The
standard analysis for the comparison of two multivariates samples, which is based on Hotelling’s T2
statistic, addresses somewhat the wrong question and consequently has very poor power for the
alternatives of primary interest. A second approach would be to assign per-experiment error rates to
each of the univariate test by using Bonferroni’s inequality. This approach may lack power for
alternatives in which most or all measures of efficacy are improved. This will be of particular
concern when the number of endpoints studied is large relative to sample size. This problem will be
exacerbated when the measures of efficacy are highly correlated, as is often the case.
In the last 15 years have been reported tests that carry out a global analysis. O’Brien’s
Ordinary Least Squares test for testing the multivariate one-sided hypothesis when the covariance
matrix is unknown. Exact tests,
P{decision for H1  µx=µy} = α,
for any ∑, where α is the level of the test: test of stochastic order of Wei-Lachin (Wei L.J., Lachin
J.M. ,1984), test of Follman (Follmann D., 1996) and Standardized Sum and Principal Components
tests published recently (Läuter J., 1996; Läuter J., Glimm E., Kropf S., 1996).
Standardized Sum and Principal Components tests can be applied in differences between two
or more populations have to be tested and a factorial structure of the means and covariances can be
supposed. He proposed statistics which permit exact t and F tests keeping the error of first kind at
the prescribed level.
We did a MatLab program v.5.2. to calculate the Standardized Sum and Principal
Components tests. These tests were applied in four preclinical and clinical studies with the objective
of comparing their results with standard analyses. We proposed that methods for studies of scaring
and the studies of lesions of the acne.
2. Materials and Methods
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Study Treatments Disease Subjects
n
1
8
ulcer
rats
58
2
5
burn
picks
74
3
4
acne
humans
226
4
2
acne
humans
75
Response variables in the studies of scaring (1 y 2): wound area, not wound area, perimeter, middle
radio, circularity, eccentricity and lineal growth. We select for multivariate analyses: wound area,
perimeter and middle radio.
Response variables in the studies of lesions of the acne (3 y 4): comedones, papule, pustule, cyst,
nodules and abscess. We select for multivariate analyses all of then.
3. Results and Discussion
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Study Standard analysis Standardized Sum Principal Components
1
RRao=0.95
FSS= 0.97
FPC= 0.99
(d.f.=21 y 138)
(d.f.=3 y 54)
(d.f.=3 y 54)
PR=.5224
PSS=0.416
PPC=0.403
2
RRao=0.95
FSS= 1.06
FPC= 1.08
(d.f.=12 y 185)
(d.f.=3 y 70)
(d.f.=3 y 70)
PR=.4910
PSS=0.372
PPC=0.365
3
RRao=0.39
FSS= 0.44
FPC= 0.45
(d.f.=15 y 602)
(d.f.=6 y 219)
(d.f.=6 y 219)
PR=0.9807
PSS=0.851
PPC=0.843
4
FT2=0.77
tSS=0.75
tPC=0.76
(d.f.=6 y 68)
(d.f.=73)
(d.f.=73)
PT2=0.5929
PSS=0.457
PPC=0.448
The p values in Standardized Sum and Principal Components tests were lower than in the
standard analyses and the power were better too. A definitive response to the clinical variable
measured in those studies were possible by used Standardized Sum or Principal Components test
but not when we used classical analyses.
These tests are useful for preclinical and clinical studies particularly when the sample size is
small for standard analyses. Standardized Sum and Components Principal are methods of choise for
studies of scaring and the studies of lesions of the acne, because the power is better than in classical
analyses with the same sample size.
REFERENCES
Follmann, D. (1996). A simple multivariate test for one-sided alternatives. J. Amer. Statist. Assoc.
91, 854-861
Läuter J. (1996). Exact t and F Tests for Analyzing Studies with Multiple Endpoints. Biometrics 52,
964-970.
Läuter J., Glimm, E. Kropf, S. (1996). New multivariate test for data with an inherent structure.
Biom. Journ. 38, 5-23.
O’Brien, P.C. (1984). Procedures for comparing samples with multiple endpoints. Biometrics 40,
1079-1087.
Wei, L.J., Lachin, J.M. (1984). Two-sample asymptotically distribution-free tests for incomplete
multivariate observations. J. Amer. Statist. Assoc. 79, 653-661.
FRENCH RÉSUMÉ
Nous avons fait un MatLab programme v.5.2. pour calculer la Somme Standardisée et les
épreuves des Composants Principaux. Ces épreuves ont été appliquées dans quatre études
preclinique et clinique avec l'objectif de comparer leurs résultats avec les analyses standardes.
Nous avons proposé ces méthodes pour les études d'effrayer et les études de lésions de l'acné. Une
réponse définitive au variable clinique mesuré dans ces études était possible par l’usage de la
Somme Standardisée ou des Composants Principaux mais pas quand nous avons utilisé des
analyses classiques. La Somme Standardisée et les Composants Principaux sont méthodes de
choisir pour les études d'effrayer et les études de lésions de l'acné, parce que le pouvoir est meilleur
que dans les analyses classiques avec la même dimension de l'échantillon.