Design and Analysis of Clinical Trials
216
.
Placebo
20
0
40
El
Time in months
Fig. 8.3. Kaplan-Meier estimated survivor functions for the two treatment
groups in t.he prostate cancer trial.
For the prostate trial data we have:
~
Group
~
7l
Observed
Expec

Design and Analysis of Clinical Trials
238
o perf1
A perf2
0 perf0
6
500
time
1000
Cumulative hazard by performance stratum against time
Fig. 8.8. Cumulative hazard functions for strata defined by the Karnofsky
Performance Index from the lung cancer trial

Design and Analysis of Clinical Trials
236
0
Schoenfeld or Eficient Score Residuals
Schoenfeld (1982) suggested the use of residuals derived directly
from the score function of the partial likelihood. A set of partial
scores for each event can be obtained

Design and Analysis of Clinical Trzals
156
with
representing the missing values for this subject. The terms
and 2 1 1 are appropriate submatrices of X(6). The estimated missing values depend on the covariance structure assumed
for the repeated observation

160
Design and Analysis of Clinical Trials
Chi- squared plot of Mohalanobis distances of
residuais from compound symetry model
0
0
0
0
8ooo
I
I
I
5
tO
15
Chi-square quonliies
(b)
Chi-squored plot of Moholanobis distances of
residuals from unstructured mod

142
5.5.
Design and Analysis of Clinical Trials
SUMMARY
The methods described in this chapter provide for the exploration
and simple analysis of longitudinal data collected in the course of
a clinical trial. The graphical methods can provide insights into

244
Design and Analysis of Clinical Trials
inclusion runs the risk of biasing the treatment effect as a result of
their being internal, i.e., they reflect the development of the disease
process and may themselves be partly influenced by treatment. Biochem

246
Design and Analysis of Clinical Trials
be proportional, but the baseline hazard is now quite separately estimated for each stratum. The contribution to the partial likelihood
from each failure event is modified such that the risk set over which
the de

166
Design and Analysis of Clinical Traals
We assume that the recovery scores for the kth subject at the j t h
time point and the ith drug dose, y i j k , are given by:
where a i k and bik are random intercept and slope for subject k having
dose i, and ~

202
Design and Analysis of Clinical Trials
illustrate this point, consider a typical random effects model in which
the lagged response is used as a covariate. The random effect in a
typical random intercept model is included to account for betweensubjects

Design and Analysis of Clinical Dials
180
visits. Two treatment groups were involved and in addition two further covariates, sex and age, were available together with a binary
indicator for centre. One possible logistic marginal model is given
by:
0
Corr(

176
D e s i g n a n d A n a l y s i s of Clinical Trials
1
improved
Fig. 6.6. Individual profiles for all patients and for mixture modellingderived 'types'.
routinely] using software such as PROC MIXED in SAS and
BMDP5V. When the data are unbalanced but t

206
Design and Analysis of Clinical Trials
treatment is consistent with treatment leading to a slightly quicker
recovery, but the effect is not significant and the confidence intervals
are wide. Thus the substantial differences in the point estimates
aris

Design and Analysis of Clinical Trials
182
It is important to keep in mind that what is being estimated by
the fitted model is the cross-sectional relationship between variables.
Table 7.2 shows the sample frequencies over the joint distribution
of the ba

Design and Analysis of Clinical Trials
138
Table 5.9 (Continued)
Patient
Treat.
Sex
Age
BL
V1
V2
V3
V4
32
A
A
P
A
P
A
A
P
P
P
A
P
P
P
P
P
A
P
A
A
P
A
A
P
A
M
M
M
M
F
M
M
M
M
M
M
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1

198
Design and Analysis of Clinical Trials
conditional on past responses y Z j - ] ~ ,for k 2 1. The assumptions
of a cross-sectional GLM would now be replaced by:
yij
are the expectation and variance of y i j conwhere now pfj and
ditional on all x j - k

Design and Analysis of Clinical Trials
232
Table 8.7. Estimated Baseline Survivor Function at Selected Intervals for Lung Cancer Trial Data.
~
~
~
Survival time
Survival Prob.
Standard Treatment
Survival Prob.
Standard and Chemotherapy
1
125
249
373
497
6

Design and Analysis of Clinical Dials
248
8.8.
CENSORING AND COMPETING
RISKS
The discussion so far has given rather little consideration as to how
censored observations may have come about. Indeed, because they
seem to pose no practical difficulty for ana

D.R.I.P. HISTORY
xi
oered a very readable and lucid treatment that might have had an influence if the
curricula of the time had been less inflexible. At about this time, according to reliable reports, Henstock announced at an international meeting that th

CHAPTER 2
Covering Relations
The full definition of the integral will require the following notions:
Covering relations.
Full covers.
Partitions of a compact interval [a, b].
Riemann sums.
Cousin covering lemma.
We motivate these concepts in this cha

CHAPTER 1
Newtons Original Integral
Integration as it was originally conceived of by Newton is the process inverse
to dierentiation. Such a process, he saw, would have numerous applications in
geometry and physics.
In modern language we can describe the s

2.3. RIEMANN SUMS CONSTRUCTED FROM THE DERIVATIVE
11
2.3.1. A full cover. The idea is a good one if we approach it dierently. Let
us assume that
F 0 (x) = f (x) (a x b)
(which is a somewhat stronger assumption than we need for Newtons integral).
Let > 0 a

28
5. THE INTEGRAL
.
This allows our earlier convention to be broadly generalized: change the value
of any integrated function freely on a negligible set. No integration statement or
integration formula will change.
SOLUTION IN SECTION 7.7.8
5.7. Order
Th

10
2. COVERING RELATIONS
that we have just seen might be improved by subdividing the interval [a, b] by
intermediate points:
a = a1 < b1 = a2 < b2 = a3 < < an < bn = b.
This expresses the interval [a, b] as the union of a collection of n nonoverlapping,
c

iv
PREFACE
function is adequate justification in the correct theory of integration, but not at all
for the Riemann integral.
More distressingly would be their solution to this problem: Verify that
Z 1
1
xp dx =
( 1 < p < 0).
1
+
p
0
My students would use

THE INTEGRAL CALCULUS
Alan Smithee
For information about this publication consult the web site
classicalrealanalysis.com
Direct all correspondence to Alan Smithee
calculusprogram at gmail.com

222
Design and Analysis of Clinical Trials
Within each of these two types of model, either the baseline
hazard in the proportional hazards model, or the baseline survivor
function in the acccelerated failure time model, can be assumed t o
be either fully

Design and Analysis of Clinical Dials
200
Table 7.11. Results from Fitting Transition Model
Logistic Regression to Respiratory Status Data.
~
~
Covariate
~
Estimate
Classical SE
Robust SE
0.321
0.314
0.461
0.380
0.384
0.568
~
Treatment
yt-1
Interact ion
0

240
Design and Analysis of Clinical Trials
g ( t ) = t , g ( t ) = ln(t) and a step function such that g ( t ) = 0 if
t <T
and 1 if t 2 T . We describe and illustrate how such time-varying
variables can be included in Section 8.6. A likelihood ratio test

154
Design and Analysis of Clinical Trials
Table 6.3. Results from Likelihood Analysis of Oestrogen Patch
Data (assuming compound symmetry for the covariance structure
of the repeated observations).
Parameter
constant
group
linear time
quadratic time
base