ZZ. WNK5
Math 2271 Differential Equations for Scientists and Engineers: Test 2
Wednesday February 29, 2012
10:30am to 11:20am
Name: 60 L01 [bids Student Number:
Instructions: Complete all 5 of the following problems in the Space provided. Notes and
c
Monitoring Trial Progress
47
Amongst the 354 patients assigned to medical therapy, the cumulative 14year crossover rate from medical to surgical therapy was 55%.
In contrast, only 20 of the 332 patients assigned to surgical therapy
refused surgery. Analy
Design and Analysis of Clinical Trials
54
+4

Months
3
Months
2
Months
%I Month
B
P
P
c
04
0
4
1
2
3
4
Auassmont
Fig. 3.4. Physical functioning score by time of dropout (taken with permission from Curran et al., 1998).
the patient remained in the stud
Basic Analyses of Clinical Trials .
73
Table 4.2. Results from Applying
Twosample ttest to Mouthwash
Data in Table 4.1.
Placebo
Active
0.5348
0.2907
15
0.2367
0.3432
15
Mean
SD
n
t
= 2.567, d.f. = 28, pvalue = 0.0159,
95% confidence interval for treatm
Design and Analysis of Clinical Trials
42
0
0
0
The amount of discomfort produced by the study treatments
or procedures performed,
The amount of effort required of the patient to maintain the
treatment regime,
The number and type of side effects associate
Design and Analysis of Clinical Dials
62
Table 3.4. Values of C1, C2 and n for various combinations of P,K
and A when S / u = 1 (part of table in Pampallona and Tsiatis,
1994).
1  ,L3 = 0.80
K
5
c
2
n
c1
3.3118
1.9987
2.9760
2.7506
2.4440
4.69
1.7954
3.5
Monitoring Dial Progress
53
and the probability of dropping out depends on the values of the
fixed covariates X , but given X , it is conditionally independent of
an individuals outcome values, Y1,. . ,YT. Such a definition allows
dependence of dropout o
Monitoring Trial Progress
AS
 RANDOMIZED
ADHERERS
49
 ONLY
TREATMENT
 RECEIVED
\
5
U
0.3
MEDICAL
IN
S U O C A L IN
0.1


3501
0.0
0
2
4
I
b
YEARS ON STUDY
MEDICAL IN
sunaicAL IN
3501
10
0
2
4
I

P

OOI2
2111

3501
$
YEARS ON STUDY
1
0
0
1
MEDICAL
Basic Analyses of Clinical Trials . .
socalled sandwich estimator, H
81
(p)H ( P ) where
Commonly referred to as a robust or heteroscedastic consistent parameter covariance matrix, the use of standard errors derived from
this matrix and the related con
Monitoring Trial Progress
43
Table 3.1. Factors and Approaches that Enhance Patient
Interest and Participation.
Clinic staff who treat patients with courtesy and dignity and who
take an interest in meeting their needs,
Clinic located in pleasant physical
Basic Analyses of Clinical Trials . . .
83
To clarify the general comments made above and to illustrate
the way in which different choices of model can influence the results,
we now describe a detailed application of GLMs to a set of clinical
trial data.
Design and Analysis of Clinical Trials
66
Freedman et al. (1994) illustrate their philosophical difficulties
with the usual frequentist approaches to interim analyses with the
following (hypothetical) situation:
Suppose that a clinician Dr. C comes to sta
Design and Analysis of Clinical Trials
44
In some studies measuring compliance is relatively easy. For example, trials in which one group receives surgery and the other group
does not. Most of the time, however, assessment of compliance is not
so simple a
Monitoring Trial Progress
51
baseline
1
L
111
TREATMENT 2
time 1
time 2
nn
#
I
time
t
n
Fig. 3.3. Monotone data pattern caused by patients dropping out of trial.
of time points leading to what might be termed a balanced data
set. But although balanced lo
Basic Analyses of Clinical Trials
. .
71
Fig. 4.2. Boxplots for placebo and active treatment groups in doubleblind
trial of a n oral mouthwash.
type of plot for the data shown in Table 4.1; these data arise from
a double blind trial in which an oral mout
46
Design and Analysis of Clinical Trials
results of all patients in the treatment groups to which they were
randomly assigned. This approach is recommended since it maintains the benefits of randomisation, whereas the second and third
of the methods abov
Monitoring Trial Progress
63
approach which eliminates some of these inconsistencies. This requires, for rejecting the null hypothesis, that a succession of T tests
are significant at the current a level. The value of T is chosen so that
the global type I
Basic Analyses of Clinical T~ials. . .
77
Table 4.7. Analysis of Covariance of Pain Data in Table 4.6.
The analysis of covariance model assumes that pain on discharge and age
are linearly related and that the slope of the regression line is the same for
e
Design and Analysis of Clinical Trials
48
Control Group
Treatment Group
I
i
I
+
. .
. .' .
*
Fig. 3.1. Compliance doseresponse curves for decrease in cholesterol level
in active treatment and control groups in a trial of cholestyramine (taken
with permi
ZS HAWKS ToluQ_
Math 2271 Differential Equations for Scientists and Engineers: Test2
Wednesday, March 2nd, 2016
10:30am to 11:20am
Name: SOL0'1 IONS Student Number:
Section Number:
Instructions: Complete all 4 of the following problems in the space provi
20 Works. icing
Math 2271 Differential Equations for Scientists and Engineers: Test 3
Wednesday March 26, 2014
10:30am to 11:20am
Name: S 0 L0 '1 L 0) 3 Student Number:
Instructions: Complete all 4 of the following problems in the space provided. Notes a
20 NAME Trying.
hiath 22H Diiferential Equations for Scientists and Engineers: Testii
Friday April 11], 2015
lllam to 11:2Dsm
SOL UT [bra f: Stutlent Number:
Instructions: Complete all 4 of the following problems in the space provided. Notes and
calculat
g4 Wimks Tea.
Math 2271 Differential Equations for Scientists and Engineers: Test 3
Wednesday March 23, 21316
izam to 11:20am
Name: SD]. if"; is] [45 Student Number:
Section (Circle one]: Section M [Haslam Section W cfw_Wang
Instructions: Complete all 4
20 WWVs Todreg.
Math 2271 Differential Equations for Scientists and Engineers: Testl
Friday January 31. 2014
10:30um to 11:20mn
Name: SDLU'T lhl$ Student Number:
Instructions: Complete all  of the following problems in the space provided. Notes and
cal