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The Use of Discriminant
Analysis to Separate a Study Population by Treatment Subgroups in
a Clinical Trial with a New Pentapeptide Antidepressant* John P. Feighner, MD Lev Sverdlov, PhD Innapharma, Inc. 1 Maynard Drive, Suite 205 Park Ridge, NJ 07656 *This study was sponsored by Innapharma,
Inc.
KEY WORDS:
clinical trial, new pentapeptide antidepressant, nemifitide, discriminant
analysis, treatment subgroups
ABSTRACT This article
examines the use of multivariate discriminant analysis to separate
the drugtreated from placebo populations by treatment subgroups in
a phase 2 clinical trial with a new pentapeptide antidepressant and
shows a preference to quantify the difference in the psychometric
scores between treatment groups as a function of full observation
period instead of single timepoint at the end of treatment. Data were
evaluated from a singlecenter, randomized, placebocontrolled, doubleblind
clinical trial where the investigatory drug was administered subcutaneously
daily in 55 subjects diagnosed with major depression for either one
or two 5day treatment cycles (total 5 or 10 doses). The evaluable
efficacy data set included 51 subjects: 19 from the 10day treatment
group, 11 from the 5day treatment group, and 21 from the placebo
group. A retrospective pharmacokinetic analysis permitted the definition
of the minimum projected therapeutic concentration (MPTC) with maximum
observed plasma drug concentration (C_{max}) for 13 subjects above MPTC and 17 subjects below MPTC.
The key variable for discriminant analysis was percent change from
baseline for 21item Hamilton Depression Rating Scale scores for 11
major time points from the first evaluation during treatment (Day 3)
to the last followup evaluation (Day 40). Because of the relatively
small sample size, all subjects available for analysis were used to
derive the discriminant criteria. Discriminant analysis was very successful
in separating treatment subgroups: from 82.4% to 86.7% of subjects
with the correct classification of any two of the three subgroups
combined and 80.0% of subjects with correct classification of all
three subgroups combined. In contrast, the traditional statistical
approach did not confirm the effect of separation between treatment
subgroups using a single endpoint at the end of observation. INTRODUCTION The separation of drugtreated
from placebo populations in the development of new antidepressants
is usually determined at a single timepoint (for the majority of trials,
the end of 4 or 6 weeks of treatment). However, this is particularly
problematic in analyzing results of clinical trials with an atypical
dose regimen (e.g., cycles of drug treatment followed by notreatment
periods). We have previously reported1 the use of four different approaches
to separate a drugtreated from a placebo population after treatment
with a new synthetic pentapeptide antidepressant, nemifitide (former
INN 00835).2 The
first approach3,4 was based on pharmacokinetic evaluation to define
the Minimum Projected Therapeutic Concentration (MPTC) and then to
separate the drugtreated population into two subgroups: subgroup
1 with maximum observed plasma drug concentrations (C_{max}) in the therapeutic range (above MPTC) and subgroup
2 with C_{max} below the therapeutic range (below MPTC). Application
of standard statistical analysis to these grouped data showed a significant
difference in efficacy between subgroup 1 versus placebo and versus
subgroup 2. The
second approach5 was based on the platelet serotonin uptake rate,
a research surrogate biochemical marker for the treatment of depression.
The platelet serotonin uptake rate for the drugtreated population
after treatment increased to a level close to that of a normal population,
while the placebo group had little change. This difference was statistically
significant. The
third approach6,7 used multivariate cluster analysis with seven independent
efficacy variables from psychometric scores and four optimal clusters.
Cluster analysis effectively separated a heterogeneous study population
into relatively homogeneous clusters with an equal number of placebo
subjects per cluster and a significantly different number of subjects
per cluster in the drugtreated group in accordance with plasma drug
concentration. Cluster differentiation was then interpreted clinically.
The
fourth approach used the dynamic of change in psychometric scores
by time point for a population with a very high level of response
($70% change from baseline at peak effect). The percent of responders in
the drugtreated population in this category of responders increased
rapidly (exponential effect) versus a linear proportional increase
according to a number of doses for the placebo population (linear
effect). All these approaches were
developed to provide additional methodology for dealing with common
statistical analysis of clinical data810 and were very effective
in separating the drug‑treated population from placebo in two
pilot clinical trials. We now report the use of
an additional approach to separate drugtreated from placebo populations:
multivariate discriminant analysis, which uses data from all study
assessment points rather than a single endpoint. The effect of separation
using discriminant analysis was very strong for any combination of
two of three treatment subgroups combined and for all three treatment
subgroups combined. In contrast, the traditional currently used single
endpoint statistical analysis (ANOVA at the end of observation) did
not show the effect of separation between treatment subgroups. METHOD Study Design and Materials The study design is shown in Figure 1. Fiftyfive
physically healthy subjects (male and female), 18 years or older,
diagnosed with nonpsychotic major depression in accordance with DSM IV
criteria were enrolled in this phase 2 study (outpatient, doubleblind,
randomized, placebocontrolled, paralleldesign, singlecenter at
Feighner Research Institute of San Diego, California, USA). The study
investigated the efficacy and safety of 18 mg of drug (nemifitide)
administered subcutaneously for 10 days (two 5day treatment cycles
[Monday to Friday] separated by two nontreatment days [Saturday and
Sunday]). Subjects were screened for enrollment and then returned
to the facility between 3 to 7 days before the initial treatment to
be randomized. At the end of the second cycle of 5‑day treatment,
the subjects returned to the facility once weekly for the next 4 weeks
for followup evaluations. The placebo group included 22 subjects
(40%) who received a lactose injection, and the drug group included
33 subjects (60%). Twentytwo of 33 subjects (66.7%) treated with
new drug received drug for both cycles and 11 subjects of 33 (33.3%)
treated with new drug received drug only in the first cycle and placebo
(lactose injection) in the second cycle. The main objective of the
onecycle group was to compare safety profiles with those subjects
receiving two cycles. Standard inclusion and exclusion criteria
were utilized with the following values for the psychometric tests
at screening for enrollment: 21item Hamilton Depression Rating Scale
(HAMD21) score of $20, Carroll SelfRating Scale score of $18, and Clinical Global Impression score of $4. The study population available for analysis
of safety data included all the subjects who received at least one
dose of medication (intenttotreat data set). The leading efficacy
variable was the HAMD21 (change and percentage change from baseline).
The study population for the primary analysis of the efficacy data
included all subjects from the intenttotreat data set. The study
population for the secondary analysis of the efficacy data included
only subjects who received both cycles of the 5‑day treatment
(evaluable data set). The lastobservationcarriedforward approach
was used for missing data for both data sets. A retrospective pharmacokinetic analysis
in the study4 permitted the definition of the MPTC and the subsequent
division of the study population into three treatment subgroups: placebo
subgroup (all subjects from the placebo group), drugtreated subgroup
1 with C_{max} in the therapeutic
range (above MPTC), and drugtreated subgroup 2 with C_{max} below the therapeutic
range (below MPTC). Statistical Evaluation
(Discriminant Analysis) Discriminant analysis11,12 is a multivariate statistical
procedure that mathematically defines a special discriminant function
to separate a study population by one classification variable (treatment
subgroups). The numeric value of the discriminant function is different
for each subject, and the treatment subgroup determined from discriminant
analysis may or may not be the same as the actual treatment subgroup.
The more subjects with the same classified and actual treatment subgroup,
the better the effect of separation. The discriminant function can use several
quantitative variables, each of which makes an independent contribution
to the overall discrimination. Taking into consideration the effect
of all quantitative variables, this discriminant function produces
the statistical decision for guessing to which subgroup of classification
variable each subject belongs. Assuming a multivariate normal distribution
of quantitative variables within each level of classification variable,
a parametric method generates either a linear discriminant function
(equal withinclass covariance) or a quadratic discriminant function
(unequal withinclass covariance). In either case, the discriminant
function is a weighted combination of all quantitative variables.
The performance of
discriminant analysis can be evaluated by estimating the error rate
(probability of misclassification). Discriminant analysis has a proven track
record in the field of neurometrics,13 in which groups of psychiatric
subjects are discriminated based on quantitative analysis of electroencephalogram
and eventrelated potentials.14 SAS/STAT^{ฎ} is a powerful
tool for discriminant analysis with some options allowing selection
of: parametric or non The primary efficacy variable (percent
change from baseline for HAMD21) was used to create a discriminant
function. Because Day 1 cannot produce any percent change from baseline,
only 11 out of 12 time points were used: pd3 (percent change from
baseline for Day 3the first day of evaluation after two injections),
pd5 (Day 5), pd6 (Day 6), pd8 (Day 8), pd10 (Day 10), pd12 (Day 12),
pd13 (Day 13), pd19 (Day 19), pd26 (Day 26), pd33 (Day 33), and pd40
(Day 40the last day of evaluation after 4 weeks of the followup
period). As mentioned above, three treatment subgroups (placebo subgroup,
drugtreated subgroup 1 with plasma drug concentrations in the therapeutic
range and drugtreated subgroup 2 with plasma drug concentrations
below the therapeutic range were included in the levels of the classification
variable. The DISCRIM procedure in SAS/STAT^{ฎ} calculates
the posterior probability of each individual subject belonging to
each of three subgroups and assigns the subject to a corresponding
subgroup according to the higher probability. In addition, the DISCRIM
procedure summarizes the squared distance between subgroups, univariate
and multivariate statistics, canonical coefficients to derive canonical
variables (a dimensionreduction technique*), the list of misclassified
observations, classification errorrate, the result of classification
for each subject, and total frequency of separation. Some additional
procedures can be used to plot the results of classification in two
dimensions. The classified function from the training (calibration)
group of subjects can be saved and used for another (replication)
group of subjects to estimate the replication effect of separation.
All of the subjects in this study were included only in the training
group because of a relatively small sample size. There was no replication
group. RESULTS AND DISCUSSION Of the 55 enrolled and randomly assigned
subjects (i.e., intenttotreat data set), 51 subjects (92.7%) completed
the initial treatment (i.e., evaluable data set). The MPTC for pharmacokinetic evaluation
was defined as 45.7 ng/mL3,4 and this value for subjects treated
with drug was used to select subgroup 1 (13 subjects) and subgroup
2 (17 subjects) with plasma drug concentrations above or below the
therapeutic range (9 subjects and 10 subjects correspondingly for
the 10‑day treatment group only). Table 1 shows the summary of discriminant
analysis and discriminant classification accuracy for the separation
of subgroup 1 from placebo. Ten of 13 subjects (76.9%) from subgroup
1 and 18 of 21 (85.7%) subjects from the placebo group were classified
correctly and confirmed the prior known actual subgroups. The error
rate of classification was 17.6%, which means 82.4% of correctly classified
subjects were from both subgroups. Table 3 shows the summary of discriminant
analysis and discriminant classification accuracy for the separation
of subgroup 2 from the placebo group. Fourteen of 17 subjects (82.4%)
from subgroup 2 and 18 of 21 (85.7%) subjects from the placebo group
were classified correctly and confirmed the prior known actual subgroups.
The error rate of classification was 15.8%, which means 84.2% of correctly
classified subjects were from both subgroups. Because the primary objective of the clinical
trial was to evaluate the effect of the 10‑day treatment group
versus the placebo group, Table 4 shows the summary of discriminant
analysis and discriminant classification accuracy for the separation
of subgroup 1 from subgroup 2 and from the placebo group using only
the placebo and 10‑day treatment groups. Seven of 9 subjects
(77.8%) from subgroup 1, 8 of 10 (80.0%) subjects from subgroup 2,
and 17 of 21 subjects (80.9%) from the placebo group were classified
correctly and confirmed the prior known actual subgroups. The error
rate of classification was 20.0%, which means 80.0% of correctly classified
subjects were from three subgroups. Figure 2 is a twodimensional plot
of two canonical variables used to illustrate the results of discriminant
analysis for the three treatment subgroups. Clear separation can be
seen. There was a significant difference for both canonical variables
by treatment subgroup (ANOVA, twotailed, 2 degrees of freedom, P
, 0.01). In contrast, the traditional currently
used analysis of longitudinal data did not confirm4^{ }the
effect of separation between treatment subgroups on the basis of the
single endpoint at end of observation.^{
}It is important to mention that after discriminant analysis
the majority of responders was classified to subgroup 1 (above MPTC)
versus the majority of nonresponders to subgroup 2 (below MPTC).4 While our findings summarize the results
from a pilot study with a limited sample and take into consideration
the pharmacokinetic evaluation, discriminant analysis successfully
created a very comprehensive picture of the separation of the drug‑treated
population from the placebo population. We are now planning to use
discriminant analysis to evaluate the results of future pivotal clinical
studies. CONCLUSIONS Discriminant
analysis was very effective in separating a heterogeneous study population
of subjects diagnosed with major depression into three treatment subgroups
using HAMD21 scores for all the available time points. Discriminant
analysis demonstrated that from 82.4% to 86.7% of subjects had the
correct classification for evaluation of any two of three subgroups
combined and 80.0% correct classification for
evaluation of all three treatment subgroups combined. The results
indicate that multivariate discriminant analysis is more reflective
of the dynamics of drug effect than assessment at a single endpoint
(particularly for atypical dose regimen) and provides a valid additional
statistical approach to support conclusions of efficacy. All of the
methodological aspects presented in this paper can be used in drug
development in some pivotal studies in the CNS therapeutic area. These techniques allow for a greater sample
size, while separating the study population into training (calibration) and replication groups. REFERENCES 1. Feighner JP, Sverdlov L,
Nicolau G, Noble JF: Four different approaches to separate drugtreated
population from the placebo population after treatment with a new
pentapeptide antidepressant. Int J Neuropsychopharm, XXIInd CINP Congress,
Brussels, July 913, 2000. 3 (Suppl 1), P.03.029, 185. 2. Hlavka JJ, Nicolau G, Noble
JF, Abajian H: INN 00835 antidepressant, in Drugs of the Future.
Barcelona, Prous Science Publishers, 1997, pp 13141318. 3. Sverdlov L, Noble JF, Nicolau
G: Application for pharmacokinetic evaluation and analysis of the
effect of treatment with a new antidepressant drug in a population
with major depression. PharmaSUG 2000, Conference proceedings, May
710, 2000, Seattle, WA, pp 301308. 4. Feighner JP, Ehrensing RH,
Kastin AJ, et al: Doubleblind, placebocontrolled study of pentapeptide
INN 00835 in the treatment of outpatients with major depression.
Int Clin Psychopharmacol 16:345352, 2001. 5. Kelly JP, Nicolau G, Redmond
A, et al: The effect of treatment with a new antidepressant, INN 00835,
on platelet serotonin uptake in depressed patients. J Affect Disord
55 (23): 231236, 1999. 6. Sverdlov L, Noble JF, Nicolau G: Cluster
analysis (FASTCLUS Procedure) to replicate platelet serotonin uptake
rates as a biochemical marker of treatment effect for a new antidepressant
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Orleans, LA, pp 161164. 7. Feighner JP, Sverdlov L,
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Table 1. Discriminant Analysis
for Separation Population with Plasma Drug Concentrations Above the
Therapeutic Range (Subgroup 1) Versus Placebo
Classification After Discriminant Actual Treatment Subgroup
Number of Analysis,
Number (%) of Subjects by
Subjects Treatment Subgroup
Subgroup 1
Placebo Subgroup
1 (Above MPTC) 13 10 (76.9%)
3 (23.1%) Placebo
21
3 (14.3%) 18 (85.7%) Total
34
13 (38.2%) 21 (61.8%) Total Number of Subjects
with Correct Classification:
28 (5
10 1 18) of 34 (82.4%) Error Rate of Classification:
6 (5
3 1 3) of 34 (17.6%)
Table 2. Discriminant Analysis
for Separation Population with Plasma Drug Concentrations Above the
Therapeutic Range (Subgroup 1) Versus Below the Therapeutic Range
(Subgroup 2)
Classification After Discriminant Actual Treatment Subgroup
Number of Analysis,
Number (%) of Subjects by
Subjects Treatment Subgroup
Subgroup 1
Subgroup 2 Subgroup
1 (Above MPTC) 13 10 (76.9%)
3 (23.1%) Subgroup
2 (Below MPTC)
17
1 (5.9%) 16 (94.1%) Total
30
11 (36.7%) 19 (63.3%) Total Number of Subjects
with Correct Classification:
26 (5
10 1 16) of 30 (86.7%) Error Rate of Classification:
4 (5
3 1 1) of 30 (13.3%)
Table 3. Discriminant Analysis
for Separation Population with Plasma Drug Concentrations Below the
Therapeutic Range (Subgroup 2) Versus Placebo
Classification After Discriminant Actual Treatment Subgroup
Number of Analysis,
Number (%) of Subjects by
Subjects Treatment Subgroup
Subgroup 2
Placebo Subgroup
2 (Below MPTC)
17 14 (82.4%)
3 (17.6%) Placebo
21
3 (14.3%) 18 (85.7%) Total
38
17 (44.7%) 21 (55.3%) Total Number of Subjects
with Correct Classification:
32 (5
14 1 18) of 38 (84.2%) Error Rate of Classification:
6 (5
3 1 3) of 38 (15.8%)
Table 4. Discriminant Analysis
for Separation Population with Plasma Drug Concentrations Above the
Therapeutic Range (Subgroup 1) Versus Below the Therapeutic Range
(Subgroup 2) and Versus Placebo
Classification After Discriminant Actual Treatment Subgroup
Number of Analysis,
Number (%) of Subjects by
Subjects Treatment Subgroup
Subgroup 1 Subgroup
2 Placebo Subgroup 1 (Above MPTC)
9 7 (77.8%) 0 (0.0%)
2 (22.2%) Subgroup 2 (Below MPTC)
10
0 (0.0%) 8 (80.0%) 2 (20.0%) Placebo
21
1 (4.8%) 3 (14.3%) 17 (80.9%) Total
40
8 (20.0%) 11 (27.5%) 21 (52.5%) Total Number of Subjects
with Correct Classification:
32 (5
7 1 81 17) of 40 (80.0%) Error Rate of Classification: 8 (5 2 1 2 1 4) of 40 (20.0%) 