Attachment 13 Sampling & Power

Attachment 13
Sample Size & Power Calculations

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P.C. Prorok et al.
A full discussion of the biorepository appears in a companion paper in this
supplement [122].

from: Control Clin Trials 2000;21:273S-309S
Sample-Size Calculations
Sample size was calculated using the method suggested by Taylor and
Fontana [125], modified to allow for arbitrary magnitude of screening impact,
arbitrary sample-size ratio between screened and control arms, and arbitrary
levels of compliance in the screened and control arms. Let Nc be the number
of individuals randomized to the control arm and Ns be the number randomized
to the screened arm, with Ns = f N o w h e r e f is a proportionality constant. For
0 < r < 1, assume the trial is designed to detect a (1 - r) × 100% reduction
in the cumulative disease-specific death rate over the duration of the trial. Also
let Pc be the proportion of individuals in the control arm who comply with
the usual-care protocol and Ps be the proportion of individuals in the screened
group who comply with the screening protocol. The total number of diseasespecific deaths needed for a one-sided s-level significance test with power I is then:
D = [(Qc + f Qs) Zl-~
XlQcQs (1 + f) Z,] 2
f (Qc - Qs)2
-

-

where Qc = r + (1 - r)Pc and Qs = 1 - (1 - r)Ps. The number of participants
required in the control arm is:

No=

D

(Qc + f Qs) RcY

where Y is the duration of the trial from entry to end of follow-up in years
and Rc is the average annual disease-specific death rate in the control arm
expressed in deaths per person per year.
A one-sided hypothesis testing approach to sample-size calculation was
employed based on the nature of the question being addressed. The PLCO
trial is intended to provide definitive evidence of the effect of screening on
cause-specific mortality compared to usual medical care, analogous to phase
III placebo-controlled trials in the therapeutic setting. The focal question for each
of the four cancers is whether screening reduces mortality. This is inherently a
one-sided research question, implying a one-sided design and analysis approach. The question is not whether screening reduces or increases mortality.
Determining whether screening increases mortality is not an objective of this
trial. Furthermore, if the screening intervention has no effect or if it is harmful,
the consequences in terms of a public health decision are the same screening
is not recommended. This further dictates a one-sided approach [126].
The estimation procedure is illustrated for prostate cancer for white males.
Prostate cancer screening was the impetus for the trial and is the primary focus
for sample-size calculations. Similar calculations can be done for the other sites
using the data in Table 3. This illustration is based on calculations done for
the original design prior to the pilot phase, when the eligible age range was
60-74 years and the trial duration was 10 years from randomization for each participant.

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Design of the PLCO Trial
Table 3

Cancer Mortality Rates per Person per Year (x10-5), Estimated Using
1983-1987 Data
Prostate

Ovarian

Age (years)

White

Black

Males
50-54
55-59
60--64
65--69
70-74
75-79
80--84
85+

3.5
11.5
30.4
71.1
137.8
244.8
402.8
606.3

11.1
31.9
80.4
174.1
332.3
515.7
838.7
937.1

Females
50-54
55-59
60--64
65-69
70-74
75-79
80-84
85+

m

u

m

White

Black

Colorectal

Lung

White a

White b

--------

--------

20.8
39.6
64.6
104.4
156.1
216.0
296.0
378.6

88.4
165.4
252.6
367.6
470.2
543.9
555.0
441.3

14.2
20.3
27.5
35.3
41.5
45.2
49.8
44.7

10.4
15.3
23.3
27.4
33.8
34.5
41.1
35.0

16.5
28.1
43.9
67.9
100.1
141.9
200.5
289.2

46.5
75.3
104.9
138.0
152.9
143.8
127.2
103.5

-

-

-

-

Rates for black males are very similar. Rates for black females in age group 65-79 years are about
15% higher.
bAverage rate for black males in age group 65-79 years is about 13% higher. Average rate for
black females in age group 65--79years is about 20% lower.

Calculation of Nc requires an estimate of Ro It was a s s u m e d that the trial
w o u l d enroll an equal n u m b e r of participants in each of three age strata: 60-64,
65-69, and 70-74 years. Because individuals recruited for screening trials are
expected to be healthier than the general population, the usual cancer mortality
rate obtained from national or registry data will overestimate the mortality
rate of the participants, at least for the early part of the trial. Therefore, for a
10-year prostate cancer screening trial with m e n entered between the ages of
60-74, it was a s s u m e d that for the first 2 years the mortality rate in the control
a r m is 25% of the usual rate, for the next 3 years it is 50% of the usual rate,
a n d for the last 5 years it equals the usual rate. The usual mortality rate was
estimated b y the u n w e i g h t e d average prostate cancer mortality rate for m e n
ages 65-79 years. This age range was used to adjust for aging over the 10 years
of the trial. The usual mortality rates from national data are s h o w n in Table 3
[127]. The estimated rate for this example is Rc = 103.763 × 10 -s.
Results of sample-size calculations for the trial are given in Table 4. These
calculations assume a 10-year trial using a one-sided, 0.05-level test, Pc = Ps =
1, and possible mortality reductions as s h o w n in a screened g r o u p c o m p a r e d
to an equal-sized, usual care g r o u p (f = 1). The sample sizes are based on
mortality rates for whites. Including blacks in the trial does not substantially
alter sample size. A sample size of 37,000 ( r o u n d e d u p from 36,221 in Table
4) screened a n d 37,000 controls of each gender was chosen on the following
basis. A high p o w e r of at least 90% is m a n d a t o r y to yield a meaningful negative
result, should that happen, a n d to achieve a high level of scientific validity

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P.C. Prorok et al.

Table 4

N u m b e r of Participants Ages 60-74 Years at Entry N e e d e d in Each
A r m of the Trial
Mortality Reduction (%)

Site
Prostate
(males)
Lung
(males and females)
Colorectum
(males and females)
Ovary
(females)

Power

10

20

30

0.9
0.8
0.9
0.8
0.9
0.8
0.9
0.8

153,577
110,906
76,721
55,404
177,208
127,971

36,221
26,182
18,095
13,080
41,794
30,211
134,697
97,365

15,078
10,920

35

17,397
12,600
56,069
40,606

39,733
28,817

because a trial of this m a g n i t u d e addressing these questions is not likely to be
repeated. In addition, it was felt that for an effect of prostate cancer or colorectal
cancer screening to be of public health importance, it must be at least 20% or
greater. Given the m a g n i t u d e of the lung cancer problem, it was felt that a
screening effect of 10% or greater w o u l d be very important. To estimate w h e t h e r
a 20% effect for prostate cancer screening was realistic, two calculations were
performed. The first used plausible stage shifts d u e to screening and survival
b y stage to project possible i m p r o v e d o u t c o m e for screen-detected cancers. The
second used projections from a c o m p u t e r model [128]. Both gave mortality
reduction estimates in the range of 25% with perfect compliance.
P o w e r calculations are displayed in Table 5. With 37,000 m e n and w o m e n
in each arm, the trial has 91% p o w e r to detect a 20% mortality reduction in
prostate cancer mortality and 89% p o w e r to detect a 10% lung cancer mortality
reduction. The p o w e r is nearly 90% to detect a 15% colorectal cancer mortality
reduction and 99% for a 20% effect. For ovarian cancer, the p o w e r is nearly
90% to detect a 35% mortality reduction.
It was recognized that compliance will not be perfect in either r a n d o m i z e d
group. Contamination or drop-in will occur in the control arm (Pc < 1) and
noncompliance or d r o p o u t is to be anticipated in the screened arm (Ps < 1).
The target mortality reductions of 20% for prostate and colorectal cancers and
10% for lung cancer therefore are to be interpreted as effects that the trial seeks

Table 5

P o w e r b y Percent Reduction in Mortality with 37,000 Men and 37,000
W o m e n in Each A r m
Mortality Reduction (%)

Site
Prostate
Lung
Colorectum
Ovary

Gender

5

10

15

male
both genders
female
male
both genders
female
male
female

-0.41
0.17
0.34
-----

-0.89
0.41
0.81
-----

0.71
0.997
0.69
0.985
0.89
0.56
0.72
--

20

25

30

0.91
0.98
-.
.
.
.
.
.
.
.
.
.
.
.
0.99 0.999 - 0.79
0.93
-0.92
0.99
-0.45
0.62
0.77

35
--

---0.88

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Design of the PLCO Trial
Table 6

Percent Mortality Reduction Required When Compliance Is 100%
in Both Groups, Based on a Mortality Reduction of 20% in the
Presence of Noncompliance, as a Function of Ps and Pc

Compliance in the
Control Group (Pc)

0.5

0.5
0.6
0.7
0.8
0.9
1.0

-90
77
59
48
40

Compliance in the Screened Group (Ps)
0.6
0.7
0.8
0.9
100
71
56
45
39
33

67
53
43
37
32
29

50
42
36
31
28
25

40
34
30
27
24
22

1.0
33
29
26
24
22
20

to detect in the presence of whatever noncompliance and contamination exist
in the populations. This implies that if there were perfect compliance, the
mortality reductions would be greater since they would not be diminished
by noncompliance.
One can assess the relationship between true effect size and level of noncompliance during the screening period by examining Table 6, which shows what
the mortality reductions with perfect compliance would have to be to realize
a 20% mortality reduction for various levels of noncompliance in the screened
and control groups. For example, if 90% of participants in the screened group
undergo a PSA test (Ps = 0.9) while 20% of controls are so screened (Pc = 0.8),
then the prostate cancer mortality reduction from such screening would have
to be 27% with perfect compliance for there to be a 20% effect in the presence
of noncompliance. The 27% figure corresponds very closely to the modeling
estimate. Thus, compliance of at least 90% and contamination of no greater
than 20% for prostate cancer screening, particularly with PSA, were chosen as
the target values for these parameters.
Inquiries into potential screening compliance and screening contamination
for the four cancer sites being studied in this trial indicated that the ranges of
reasonable target values at the time of initiation of recruitment were as shown
in Table 7. In addition to direct contact with health maintenance organizations
and existing SCs, published data from the 1987 National Health Interview
Survey were used to gauge these effects [129, 130]. These numbers were necessarily somewhat subjective. Additional estimates were obtained directly from
the trial population during the pilot phase, and further assessment will occur
as the trial progresses, possibly leading to sample-size adjustment.
In the context of these levels of contamination and compliance, the required
true levels of mortality effect (effect size) with perfect compliance are, approximately, lung 20%, colon 25%, and prostate 25%. These requirements are consistent with expected effects based on modeling efforts [74, 75, 103].
Regarding the ovarian cancer objectives of this trial, if the mortality reduction
from screening for ovarian cancer were 35%, this design would have almost a
90% power to demonstrate this effect. However, if the mortality effect were
only 25%, 84,000 screened women and an equal number of controls would be
required to achieve 90% power. Thus, the ovarian component of this trial is to
be viewed as a two-step process. Near the end of the screening phase of the
trial, sufficient cases of ovarian cancer should accrue to provide good estimates

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Table 7

Design Contamination and Compliance Ranges Projected by
Modality
Compliance (%)
>90
>90
>90
>85
>85
>85
>85

Digital rectal exam
Prostate-specific antigen
CA125
Ovarian palpation
Transvaginal ultrasound
Sigmoidoscopy
Chest X-ray

Contamination (%)
<20
<20
<10
<10
<10
< 15
<40

of sensitivity for each screening modality. Specificity and predictive value can
also be estimated. If as a result any one or combination of the tests appears
sufficiently promising to justify a full mortality study, the female population
base of this trial could be supplemented or a meta-analysis of data from this
trial and other relevant studies could be done to increase power.
As noted above, in January 1996 the lower age limit for trial participation
was reduced from 60 to 55 years. Given the lower mortality rates in the 55-59
age stratum, this would ordinarily imply the need for an increase in the sample
size. However, this protocol change took place after the April 1995 eligibility
criterion change, also noted above, to exclude men who had prior repeat PSA
screening, thereby reducing the contamination level. Sample-size estimates for
prostate cancer screening for the age range 55-74 years are shown in Table 8.
For compliance of 90% and a revised estimate of contamination of 10-15%, a
sample of 37,000 men (and therefore 37,000 women) in each trial arm is still
appropriate. A similar conclusion holds for the other cancer sites as well. As
mentioned, this estimate is monitored regularly during the enrollment phase
of the trial to determine if adjustment is required.
Based on the monitoring of design parameters, further protocol modifications
were adopted in December 1998. These were to change from a 3-year to a
5-year interval for flexible sigrnoidoscopy for individuals who had not yet had
their second exam, and at the same time to add year 4 and 5 PSA and CA125
tests. Also, the remaining third annual chest X-ray exams are offered only to
current or former smokers, and follow-up is extended 3 years, so that all
participants will be followed at least 13 years from randomization. A final
change was that the ovarian palpation exam, which had been part of the original
protocol, was eliminated.

Table 8

Number of Males Required in Each Arm to Achieve 90% Power
with Age at Entry Range 55-74 Years, as a Function of Ps and Pc

Ps
Pc
0.80
0.85
0.90

0.85

0.90

0.95

53,057
46,087
40,440

45,338
39,787
35,225

39,134
34,650
30,918

Design of the PLCO Trial

299S

The interval between flexible sigmoidoscopy was lengthened to coincide
with recommendations in the community and was based on preliminary information suggesting that sigmoidoscopy at 3 years finds polyps, but very few
are likely to be of any significance. A delay of 2 years was expected to yield
more polyps and cancers, leading to a greater potential for mortality reduction.
The addition of 2 extra years of PSA and CA125 blood tests and at least 3
additional years of follow-up were adopted to provide assurance of sufficient
screening effect and statistical power in the event that initial design assumptions
were incorrect. The final round of chest X-ray testing for individuals who never
smoked was eliminated because of the very low yield of this exam. Finally,
the ovarian palpation exam was deleted because of very low yield and the
fact that a very high proportion of women participating in the trial regularly
underwent pelvic examination, thereby diluting any possible effect of the palpation exam.

Data Reporting
The data management system for the trial has the following operational
requirements: ability for the NCI and the CC to access SCs remotely, synchronization of databases on multiple platforms, preparation of high-quality analysis
datasets, secure backup and archiving of data, and robust configuration management. Data are exchanged via a distributed data entry system and are
transmitted among collaborators via common carrier service using modems,
with transmission to the NIH mainframe on a regular basis. A detailed description of the system is provided in a companion manuscript in this supplement [131].
Various forms were developed for collection of information in this trial.
Included are eligibility and consent forms, male and female versions of the
baseline questionnaire, a dietary questionnaire, examination forms for each
screening procedure, diagnostic evaluation and treatment forms, and a questionnaire for regular follow-up of participants. Additional forms are developed
as needed as the trial progresses. Most forms are scanned into the data system.
All trial forms are catalogued in the trial's manual of operations and procedures.
Pertinent data items include but are not necessarily restricted to the following:
1. participant trial identification number;
2. participant demographic and risk factor information;
3. participant randomized group, date of birth, and date of entry into the
trial;
4. date and result of each screening test for each screened group participant;
5. sufficient information regarding diagnostic procedures performed as a
result of a positive or suspicious screening test to allow determination of
whether a cancer was or was not diagnosed as a result of screening;
6. for all screening tests, detailed physical findings and any complications
or morbid events possibly associated with the test, and description of
any diagnostic procedures subsequent to a positive test;
7. for every PLCO cancer diagnosed during the trial in both randomized
groups, date of diagnosis, histology and stage at diagnosis, and initial
therapy;