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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
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
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
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.
68
Design and Analysis of Clinical Trials
a clinical trial which has a substantial proportion of missing values,
whilst possible with particular statistical techniques, does present
considerably more problems than when the data is complete. The
proportion
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
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
41
oesteoporosis studies, these requiring the measure of fractures for
bisphophonates but accepting BMD for hormone replacement.
3.3.
COMPLIANCE, DROPOUTS AND
INTENTIONTOTREAT
There could be no worse experimental animals on ear
90
Design and Analysis of Clinical Trials
The proportionalodds model can be considered as an extension
of the binary logistic model in which, instead of a single threshold
partitioning scores on a continuous dimension into two categories,
multiple thresh
Monitoring Trial Progress
Zvolua 6

57
BetaBlocker Heart Attack Trial
5 
4 
3 I
1
196
0l Junb
1978
1979
May
Ocl.
1979 'Much
1980
% %:
1991
Oct.
June
la2
i
Data
Fig. 3.5. Results from a trial comparing mortality in clofibrate and placebo
treated pati
Design and Analysis of Clinical Trials
76
Wisdom tooth extraction data
v
l
l 1
0
L
n

2
.E
a

52
2
2
1
1
I
2
1
1
2 ' 1
 7 0
2
1
2
2
2
N
0

7
,
I
I
I
I
I
I
20
25
30
35
40
45
Fig. 4.3. Scatterplot of age of patient vs. pain score after wisdom tooth
extr
58
Design and Analysis of Clinical D i a l s
0
0
number of events are small,
randomisation may not yet have achieved balance.
The basic strategy involved in the group sequential approach is to
k = 1, . . . , K )
define a critical value at each interim ana
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
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
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
Math 2271 Di'erential Equations for Scientists and Engineers: Test'z
F ridey March 7, 2014
10:30am to 11:20am
Name: SOLOT 10 I 5 Student Number:
Instructions: Complete all 4 of the following problems in the space provided. Notes and
calculators are not pe
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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
1
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Department of Mathematics and Statistics
Math 2271 Differential Equations for Scientists and Engineers
FINAL EXAM
_ 7:009:31 to 16:00pm Fday April 11, 2914
Name:
3 CLQT lg vEb
Student Number:
Instructions: Complete all 10 of
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
SCIMATH 2271 3.1]
Differential Equations for Scientists and Engineers
Winter Ell
Practice problems in linear algebra
1. Consider the following set of WEtOIS in R3:
em (1595.) (9
La] Are the teeters linearly independent, or linearly dependent? Jua
tit.r y