Download Group 3: Bladder Cancer - University of Colorado Denver

BIOS 6648 Final Project
Group 3: Anna Ivashchenko, Jesse Krisher, Kristen Weishaar
Adjuvant Sequential Intravesical BCG and Electromotive Mitomycin-C (EMDA/MMC)
after Transuretheral Resection in Patients with Primary High Risk Non-Muscle Invasive
Transitional Cell Carcinoma of the Bladder.
A one-group phase II study.
Background and Setting
Disease Background
Bladder cancer, accounting for 5-10% of all malignancies in males in Europe and the USA, with
a growing incidence in females, has an annual estimate of 357,000 newly diagnosed cases and
145,000 deaths worldwide [1]. Transitional cell carcinoma (TCC) is the most common type of
cancer found in the urinary system, including the kidneys, urinary bladder, ureters, and urethra.
Known risk factors for this type of cancer include cigarette smoking, chemical exposures, and
increasing age (> 55 years).
Diagnosis
The most common clinical sign with bladder cancer is blood in the urine, which is present in
about 80-90% of patients at the time of diagnosis. Other common symptoms include painful
urination, increased frequency of urination, or feeling the urge to urinate without being able. As
these signs can be associated with a number of conditions other than bladder cancer, additional
tests are needed to diagnose this disease. The simplest way to obtain a diagnosis is by taking a
small piece of the tumor (biopsy) in a procedure known as cystoscopy, which involves
introducing a tube equipped with a camera (cystoscope) into the bladder through the urethra.
This allows visualization of the lining of the bladder, and instruments can also be introduced to
obtain a biopsy.
Staging
One of the most important aspects of cancer diagnosis and treatment is a process known as tumor
staging, which provides information about the characteristics of the tumor as well as if there has
been any spread to other organs (metastasis). While the biopsies obtained with cystoscopy can
confirm a diagnosis of TCC, these samples are not sufficient for tumor staging. Classification of
bladder cancer is done using the TNM staging system, which stands for “Tumor” (describes the
size of the primary tumor and its invasiveness into surrounding tissues), “Node” (describes
involvement of nearly lymph nodes), and “Metastasis” (spread of cancer to other organs. For
bladder cancer, the “T” classification ranges from least invasive to most invasive. Tis, which
signifies a non-invasive or “flat” tumor, is the lowest stage, and then tumor invasion into the
bladder wall increases with stages T1-4, with T4 representing a tumor that invades through the
bladder wall and into other organs, such as the prostate, uterus, or vagina.
Treatment
The recommended treatment protocol for bladder cancer will depend on the results of the staging
tests, particularly the level of invasiveness of the primary tumor. For tumors that do not invade
the muscle layer of the bladder (non-muscle invasive bladder cancer, or NMIBC), a procedure
known as transurethral resection (TUR) can be used, which involves using a cautery device
attached to a cystoscope to “shave off” the portion of the tumor that is visible in the bladder.
While this procedure can be successful in the treatment of superficial tumors, it is not a sufficient
treatment for tumors that invade into the muscle layer or deeper, as these tumors have a high
likelihood of recurrence following TUR, and can also progress to involve surrounding organs.
The major challenge with this disease is preventing tumor recurrence and disease progression,
and currently there is no 100% effective way to do this. After TUR alone, 5-year-recurrence rates
vary from 31% in low-risk to 78% in high-risk patients, while progression rates range from 0.8%
to 45% [2].
In an effort to prevent tumor regrowth after TUR, standard treatment involves infusion of
chemotherapy or immune-stimulating agents directly into the bladder (known as intravesical
instillation). The most common chemotherapy agents used are mitomycin-C (MMC),
doxorubicin, and epirubicin, which have been tested in numerous randomized clinical trials [3,4].
A single instillation of MMC or epirubicin immediately after TUR was shown to reduce the
recurrence risk by 39%, which led to standardization of this procedure [5]. Immunotherapy for
bladder cancer involves the use of BCG (Bacillus Calmette-Guerin), which is a vaccine against
tuberculosis. This is the standard treatment for more aggressive, high-risk bladder cancers. While
this treatment is associated with more side effects, recurrence rates are lower than after
intravesical chemotherapy [6]. In patients whose tumors recur after BCG treatment, the final
treatment option is surgery to remove the bladder (cystectomy).
While MMC does seem to reduce the risk of tumor recurrence and possibly progression, failure
rates are still high. Treatment failure may be due to invasion of tumor into the bladder wall
deeper than MMC can be absorbed through the bladder lining, or due to higher resistance to
chemotherapy in more aggressive tumors.
Electromotive Drug Administration
Electromotive drug administration (EMDA) is a novel treatment mechanism that can allow for
greater MMC accumulation in bladder tissues, which could potentially overcome some of the
problems with standard MMC intravesical treatment. Intravesical EMDA is administered by a
battery powered generator (Physionizer® 30, manufactured by Physion®, Medolla, Italy) that
delivers a controlled electric current. The current passes between two electrodes: the active
electrode, which is placed inside the bladder using a specifically designed catheter, and the
ground electrodes, which are placed on the skin of the lower abdomen. The electrical current
draws the MMC into the cells of the bladder lining, allowing for greater penetration and
accumulation of MMC in the bladder tissues.
Rationale
Largely, there is excellent survival using the standard of care; however, there is no known
method for recurrence prevention. As specified above, the patient’s risk status is a key
component in the 5-year-recurrence rates and progression rates [2]. MMC appears to reduce the
risk of tumor recurrence and possible progression of NMIBC but failures do exist and may be
due to either a stage T1 tumor at a depth where MMC cannot reach through passive transport or
high-grade cancer cells with reduced sensitivity to chemotherapy. By ensuring increased MMC
accumulation in the bladder tissues through MMC-EMDA delivery, the risk of local recurrence
may be decreased.
Previous in vitro studies have demonstrated that MMC-EMDA delivery rates had a 4- to 7-fold
increase over passive diffusion (PD), implying it may improve clinical delivery rates. Few in
vivo data exist, however those data appear confirmatory.
In a small phase II study [7], marker lesion disappeared at about the same rates between MMC
(n=13) and EMDA/MMC (n=15) instillations while recurrence rates were 27% lower in patients
treated with EMDA/MMC compared to standard of care. Low recurrence rates of high-risk
NMIBC were also reported in an observational study [8]. It was shown that within high-risk
NMIBC patients, 56% of patients were recurrent-free after 14 months. Response rates among
PD/MMC, EMDA/MMC and BCG were compared in a prospective randomized study [9]. In
follow-ups at both 3 and 6 months, EMDA/MMC response rates were significantly better than
PD/MMC, however equivalent to BCG after a median follow-up of 82 months. EMDA increased
toxic side effects in the bladder but was substantially less than with BCG, a relatively dramatic
treatment option [10]. A larger prospective randomized study showed reduced recurrence rate
and longer disease-free period in patients receiving EMDA/MMC [11].
Overall, in vivo studies suggest an improved response in patients treated with EMDA/MMC. In
our trial, we want to show that EMDA/MMC exceeds the standard of care and show marked
improvement in recurrence rates. For this reason, we have chosen a superiority study design.
Because sufficient evidence from previous randomized control trials exists, use of a single-arm
design will be able to discriminate between superiority and inferiority of EMDA/MMC treatment
by comparison with the results of these prior studies. Additionally, single-arm trial design was
chosen since the epidemiology is already established, an implicit comparison can be made
between treatment and controls in previous trials, and will be sufficient for Investigational New
Drug (IND) approval from the U.S. Food and Drug Administration.
In summary, although EMDA/MMC may be a milestone for future therapeutic concepts,
confirmation by other investigators is needed.
Synopsis of Proposed Study
Study Population
This study is designed for patients that have been diagnosed with transitional cell carcinoma of
the bladder. Specific eligibility criteria are as follows:
 After a restaging TURBT patients with histologically proven primary high grade (grade3)
and/or pT1 transitional cell carcinoma of the bladder, with or without pTis and pTis alone
are regarded as being at high risk for tumour recurrence and progression
 Patients may enroll in this study if they are thought to have no residual disease after
TURBT
 Age 18 years or over
 Adequate bone-marrow reserve (ie, white-blood-cell count 4000 x 106 cells/L and
platelet count 120 x 109/L)


ECOG performance status between 0 and 2
Patients who are known PPD positive will be screened for active tuberculosis prior to
starting treatment with BCG.
Specific exclusion criteria are as follows:
 Known allergy to BCG or MMC
 Prior systemic infection with BCG
 Prior or concomitant urothelial tumours of the upper urinary tract or urethra
 Previous muscle-invasive (ie, stage T2 or higher) transitional-cell carcinoma of the
bladder
 Bladder capacity of less than 200 ml
 Untreated urinary-tract infection
 Severe systemic infection (ie, sepsis)
 Known HIV-positivity; therapy with immunosuppressive agents
 Urethral strictures that would prevent endoscopic procedures and repeated catheterisation
 Upper urinary tract disease (eg, vesicoureteral reflux or urinary-tract stones) that would
make multiple transurethral procedures a risk
 Previous radiotherapy to the pelvis
 Other concurrent chemotherapy
 Treatment with radiotherapy-response or biological-response modifiers
 History of tuberculosis
 Other malignant diseases within 5 years of trial registration (except for adequately treated
basal-cell or squamous cell skin cancer, in situ cervical cancer and any other cancer from
which patients has been disease-free for 3 years)
 Pregnancy or nursing
 Psychological, familial, sociological, or geographical factors that would preclude study
participation
 Patients with implantable or wearable electrical devices will be excluded from this study.
 Patients with active tuberculosis
Study Treatment
Patients can begin treatment with the study intervention about 2-8 weeks after their TURBT
resection.
Prior to enrollment, all patients must sign a consent form and will have a Complete Blood Count,
Basic Metabolic Panel and a Urinalysis performed.
BCG instillation will occur at weeks 1, 2, 4, 5, 7, and 8 of the study. In this procedure, BCG are
suspended in 50 ml bacteriostatic-free 0.9% NaCl solution. After the bladder is emptied, the
suspension is infused intravesically through a 14 Fr Foley catheter and retained in the bladder for
60-90 minutes. The bladder is then emptied and the catheter removed. MMC instillation will
occur at weeks 3, 6 and 9. Prior to drug administration, a Foley catheter is inserted and the
bladder is carefully drained. 40 mg of MMC is dissolved in 100 ml NaCl 0.9% solution are
instilled intravesically through the electrode catheter by gravity and retained in the bladder for 30
minutes. Concurrent with MMC treatment, a pulsed electric current of 23 mA is given externally
for 30 minutes. Intravesical EMDA is administered by a battery powered generator
(Physionizer® 30, manufactured by Physion®, Medolla, Italy) that delivers a controlled electric
current of 0-30mA / 0-55V DC. The current passes between two electrodes: the active
intravesical electrode, which is integrated into a specifically designed transurethral catheter, and
the dispersive ground electrodes, which are placed on the skin of the lower abdomen (Figure 1).
Once treatment is complete, the bladder is emptied and the catheter removed. Patients are
assigned one course of treatment per week for 6 weeks with sequential BCG and EMDA/MMC.
Two BCG instillations and one EMDA/MMC instillation constitute one cycle for a total of two
cycles.
Figure 1. Illustrated depiction of
administration of intravesical
EDMA using the Physionizer®
Maintenance treatment of eMMC will be given at month 3, 4, 6, 7, 9 and 10 (after last dose of
BCG of the initial treatment). Maintenance of BCG will be given around month 5, 8, and 11.
CBC, BMP, urinalysis, and a history/physical will be performed before each EMDA/MMC
procedure. Urinalysis and a history/physical will be performed before each BCG.
Study Measurements
A completed blood count (CBC) and basic metabolic panel (BMP) will be performed weekly and
at the beginning of each cycle. Prior to dosing with mitomycin Cat week 3, a CBC will be
performed and also at weeks 4 and 5 if the CBC has changed. A urinalysis will be performed
prior to each intravesicular instillation.
Disease response to treatment is assessed by cystoscopy and urinary cytology at approximately 6
weeks after the last cycle of treatment. Additional assessments are then done approximately
every 3 months during the first year. Patients with carcinoma in situ undergo cystoscopy and
urinary cytology in a similar fashion. If findings on cystoscopy or cytology suggest the presence
of recurrent/progressive disease, a surgical biopsy will be performed for further evaluation.
Table 1 illustrates the complete visit schedule.
Statistical Design
This trial is designed as a phase II, superiority, single treatment arm, longitudinal (5 year) study.
The primary objective of this study is to assess the bladder cancer recurrence-free rate after treatment
with intravesical instillation of sequential BCG and EMDA/MMC following TUR. Secondary
objectives include: to compare complete response rates at 3 and 6 months in patients with
carcinoma in situ; to determine progression-free survival, overall and disease-specific survival in
the study group, to be compared with literature data of the current standard of care of BCG alone
(Lamm’s protocol); to compare the qualitative and quantitative toxicities of experimental
regimens in these patients; and to assess long-term morbidity in the study group, as defined by
requirement for fewer TURBTs, courses of traditional intravesical therapies, and surveillance
cystoscopies over 5 years (cost-effectiveness), compared with literature data of current standard
long-term morbidity of BCG alone.
Power Analysis
For the sample size calculation, a population parameter estimate of recurrence-free rate θ1=0.6
and a desired clinically significant reduction of 0.2 with the EMDA/MMC treatment were
assumed.
Controlling for both Type I error, alpha=0.05 and Type II error, beta=0.20 (90% Power), a single
sample size of 50 subjects would be necessary.
Where
•
Population parameter pi = 0.60 (standard regimen)
•
Expected proportion p=0.80 (experimental treatment)
•
u=one-sided percentage point of the normal distribution for power=0.90, u=1.28
•
v=percentage point of the normal distribution for alpha=0.05, v=1.96
Alternative methods of sample size calculation are presented in Appendix I. Power and Precision
Table is provided in Appendix II.
Statistical Analyses
Data will be analyzed when data for the visits that occur 12, 24, 36, 48, and 60 months after the
last cycle of the study from all patients are complete and accurate. Data analysis will be tailored
to the needs of a one-sample phase II activity study, with recurrence rate (rather than time to
failure) as the outcome variable. Thus, the analysis will evaluate the difference in risk of
recurrence (θ = θ1 – θ0) between the two populations (study treatment [θ1] and standard of care
[θ0]).
Data for the secondary objectives will be analyzed by the method that is most appropriate for
each individual objective. Time to first recurrence in patients with carcinoma in situ will be
estimated by the Kaplan-Meier method. Time to progression and overall and disease-specific
mortality will also be estimated by the Kaplan-Meier method, with the results to be compared
with literature data of the current standard of care treatment (BCG alone). Toxicities of the study
treatment will be expressed as incident events, and will be analyzed with standard statistical
methods for comparing proportions. Long term morbidity in the study group will be assessed in
terms of cumulative incidence. Cost-effectiveness will be calculated in terms of NNT (number
needed to treat) and NNH (number needed to harm) figures.
Median survival time estimates the time beyond which 50% of the patients are expected to
survive in the study population. In diseases with favorable prognosis such as bladder cancer, the
survival probability may not reach the value 0.5 across the study period, thus preventing estimate
of the median survival time.
Patients with carcinoma in situ who do not achieve a complete response will be excluded from
the analysis of time to first recurrence, as disease-free status is the condition for being at risk of
recurrence. However, all of these patients will be included in time to progression and survival
analyses.
Study Implementation and Protocol
Recruitment and Retention Plans
Study participants will be recruited from patient populations at the University of Colorado
Denver (Aurora, CO) and Rutgers-Cancer Institute of New Jersey (New Brunswick, NJ).
Potential participants will be identified by evaluation of all patients undergoing the TURBT
procedure at participating hospitals. Eligibility will be further assessed using the defined
inclusion/exclusion criteria. If patients are deemed eligible for the study, enrollment will occur
after obtaining the patient’s informed consent. This trial is also listed on clinicaltrials.gov
(NCT02202044).
Retention of enrolled patients is likely to be the most difficult once patients enter the
maintenance treatment phase (after study week 9). Study personnel will reach out to each
participant at least monthly during this time period, either by phone and/or email. This will allow
for continued follow up with the patients as well as updating of contact information if this has
changed. Participants will also be encouraged to contact study personnel if any questions or
concerns arise. A more individualized form of contact with patients will be achieved by sending
annual birthday and holiday cards.
Randomization and Blinding Procedures
As this is a single treatment arm study, no randomization or blinding is needed. If this study was
being conducted as a prospective, two-arm study comparing the study treatment to the standard
of care, both randomization and blinding would be important to ensure reliability of the results.
If the study patients were to be randomized, a randomization tool, such as that at
https://www.randomizer.org/), could be used to create an unbiased randomization schedule (see
attached). All investigators participating in patient care would be blinded to the schedule.
Unfortunately, it would be nearly impossible to blind patients and treating physicians to the
treatment assignment, as the experimental arm would require additional treatments with the
EDMA/MMC that the patients receiving standard of care would not have. However, those
involved in response assessment (such as the doctors performing cystoscopy and interpretation of
cytology/histopathology samples) could be blinded to the treatment assignment, thus making the
outcome data more reliable.
Procedures for Minimizing Missing Data
Data will be entered and managed through REDCap (Research Electronic Data Capture), which
is a secure, we-based application designed to support data capture for research studies. The
secondary site will be given access to REDCap for data entry. Any entry fields that are not
completed will be flagged to notify both the data enterer and the data monitors. Data entry will
also be monitored for accuracy by checking realistic limits of entries and comparing at least 20%
of the entries with the original documentation. These procedures will be conducted throughout
the course of the study.
References
1. Parkin DM (2008) The global burden of urinary bladder cancer. Scand J Urol Nephrol 26:1-9.
2. Babjuk M, Oosterlinck W, Sylvester R, Kaasinen E, Böhle A, Palou-Redorta J (2008) EAU
Guidelines on Non-Muscle-Invasive Urothelial Carcinoma of the Bladder. Eur Urol 54:303-314.
3. Pawinski A, Sylvester R, Kurth KH, Bouffioux C, van der Meijden A, Parmar MK, Bijnens L
(1996) A combined analysis of European Organization for Research and Treatment of Cancer,
and Medical Research Council randomized clinical trials for the prophylactic treatment of stage
TaT1 bladder cancer. European Organization for Research and Treatment of Cancer
Genitourinary Tract Cancer Cooperative Group and the Medical Research Council Working
Party on Superficial Bladder Cancer. J Urol 156:1934-1940.
4. Lamm DL, Riggs DR, Traynelis CL, Nseyo UO (1995) Apparent failure of current intravesical
chemotherapy prophylaxis to influence the long-term course of superficial transitional cell
carcinoma of the bladder. J Urol 153:1444-1450.
5. Sylvester RJ, Oosterlinck W, van der Meijden AP (2004) A single immediate postoperative
instillation of chemotherapy decreases the risk of recurrence in patients with stage Ta T1 bladder
cancer: a meta-analysis of published results of randomized clinical trials. J Urol 171:2186-2190.
6. Böhle A, Jocham D, Bock PR (2003) Intravesical bacillus Calmette-Guerin versus mitomycin
C for superficial bladder cancer: a formal meta-analysis of comparative studies on recurrence
and toxicity. J Urol 169:90-95.
7. Brausi M, Campo B, Pizzocaro G, Rigatti P, Parma A, Mazza G, Vicini A, Stephen RL (1998)
Intravesical electromotive administration of drugs for treatment of superficial bladder cancer: a
comparative Phase II study. Urology 5: 506-509.
8. Riedl CR, Knoll M, Plas E, Pfluger H (1998) Intravesical electromotive drug administration
technique: preliminary results and side effects. J Urol 159:1851-1856.
9. Di Stasi SM, Giannantoni A, Stephen RL, Capelli G, Navarra P, Massoud R, Vespasiani G
(2003) Intravesical electromotive mitomycin C versus passive transport mitomycin C for high
risk superficial bladder cancer: a prospective randomized study. J Urol 170: 777–782.
10. Di Stasi SM, Storti L, Giurioli A, Zampa G, Liberati E, Sciarra M, Iorio B, Stephen RL
(2008) Carcinoma in situ of the bladder: long-term results of a randomized prospective study
comparing intravesical electromotive mitomycin-C, passive diffusion mitomycin-C and bacillus
Calmette-Guerin. Eur Urol Suppl 7 (3): 180, abs #439.
11. Di Stasi SM, Verri C, Capelli G, Brausi M, Leprini G, Zampa G, Stephen RL (2010) Single
preoperative intravesical instillation of electromotive mintomycin-C for primary non-muscle
invasive bladder cancer: a randomized trial. J Urol 183 (suppl. 4): 520, abs #1346.
Table 1. Study Timeline
Study Timeline
Informed consent
Medical history
Vital Signs
Urinalysis, CBC w/ diff, BMP
CBC, BMP
CBC
Urinalysis
AEs/SAEs
Physical Exam
Dosing* BCG
Dosing* MMC
***Maintenance Dose of eMMC
****Maintenance Dose of BCG
Study Timeline
Cystoscopy
Vital Signs/Physical Exam
Urinalysis, CBC w/diff, BMP
AEs/SAEs
Maintenance tx given after neg. cystoscopy
Screening
(2-8 weeks
post TURBT)
X
X
X
X
Precystoscopy
PreTreatment
Prior to
start of
cycle
Prior to
MMC
dosing
X
X
Week
1
Week
2
Week
4
Week
5, 7, 8
Week
3
Week
6, 9
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X**
X
X**
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
6 weeks after
last cycle
X
X
X
X
3months after
last cycle
X
X
6 months after
last cycle
X
X
9 months after last cycle
X
X
X
X
X
*. Dosing may be delayed up to 2 weeks for cystitis or hematuria.
**Only performed if the CBC at week 3 is unchanged
***Will occur at months 3, 4, 6, 7. 9 and 10
****Will occur at months 5, 8 and 11.
X
X
12, 24, 36, 48 and 60
months after last cycle
X
X
X
Appendix I: Additional Power Analysis Methodology
1. Two-Group N Calculation:
Functional: True mean improvement in risk of cancer recurrence free rates with BCG (θ0) or BCG with EMDA/MMC (θ1)
Contrast: θ = θ1 - θ0  Risk difference
θ0 = 0.60
θ1 = 0.80
Hypotheses: Superiority test
H0: θ ≤ 0
(Inferiority)
H1: θ ≥ 0.20
(Clinically important benefits)
Variance: Under H1
θ0(1−θ0)
θ1(1−θ1)
Var(θ) = Var(θ1 - θ0 ) =
+
N
N
Choose: N
1.96+1.28 2
N = ( 0.8−0.6 ) (0.8 ∗ 0.2 + 0.6 ∗ 0.4)
N = 105 per group
2. Simple One-Sample N Calculation:
θ1 = 0.80
Goal: Superiority test
If observed θ1=0.8 then need lower CI limit to be above 0.6
0.8 - 1.96se = 0.6
0.8∗0.2
0.8 – 1.96 𝑠𝑞𝑟𝑡 ( 𝑁 ) = 0.6

1.96
2
N=(
) (0.8 ∗ 0.2)
0.8−0.6
N = 15.37
16 per group too small for normal approximation
Instead, if want lower limit at 0.7

1.96
2
N = (0.8−0.7) (0.8 ∗ 0.2)
N = 61.47
3. Power Calculation in Current Protocol:
θ1 = 0.80
N = 50
Where
• Type I error alpha=0.05
•
Type II error beta=0.20, Power=0.90
•
Population parameter (p) = 0.60 (standard regimen)
•
Expected proportion p=0.80 (experimental treatment)
•
u=one-sided percentage point of the normal distribution for power=0.90, u=1.28
•
v=percentage point of the normal distribution for alpha=0.05, v=1.96
NOTE: Similarities to 2-group or 1-group study
a. If we use 0.8*0.2 and 0.8*0.2:
1.28+1.96 2
) (0.8 ∗
0.8−0.6
N=(
1.28 𝑠𝑞𝑟𝑡(0.8∗0.2)+1.98 𝑠𝑞𝑟𝑡(0.8∗0.2) 2
) =
0.8−0.6
42
1.28 𝑠𝑞𝑟𝑡(0.6∗0.4)+1.98 𝑠𝑞𝑟𝑡(0.6∗0.4) 2
) =
0.8−0.6
63
0.2) = (
b. If we use 0.6*0.4 and 0.6*0.4:
1.28+1.96 2
) (0.6 ∗
0.8−0.6
N=(
0.4) = (
4. Logic Behind Power Analysis in Protocol:
Goal: Power
Want 90% power to reject θ1 ≥ 0.80 if θ1 = 0.60  Type I Error
a. What does it mean to reject θ1 ≥ 0.80?
5%
α=0.05
1.96 se
0.8 – 1.96 se = 0.8 – 1.96 𝑠𝑞𝑟𝑡 (
Yields the Critical Value.
0.8
0.8∗0.2
)
𝑁
b. What is power when θ1 = 0.60?
observed 0.6
0.8∗0.2
0.6 + 1.28 se = 0.6 + 1.28 𝑠𝑞𝑟𝑡 ( 𝑁 )
Want this cut-off for power to be same as critical value.
So, want:
0.8∗0.2
0.8∗0.2
0.6 + 1.28 𝑠𝑞𝑟𝑡 (
) = 0.8 – 1.96 𝑠𝑞𝑟𝑡 (
)
𝑁
Rearranging yields:
𝑁
1.28 se
10%
Β=90
NOTE:
At N=50, CV=0.698
CONCLUSION:
The justification in the protocol implies that we primarily want to reject θ1 ≥ 0.80.
Appendix II: Power and Precision Table
N
Observed
CI 95% low
CI 95%
high
15
15
15
15
15
0.6
0.65
0.7
0.75
0.8
0.35207743 0.847923
0.40862008 0.89138
0.46808967 0.93191
0.53086534 0.969135
0.59757207 1.002428
20
20
20
20
20
0.6
0.65
0.7
0.75
0.8
0.38529276
0.44095886
0.49915976
0.56022382
0.62469227
25
25
25
25
25
0.6
0.40796 0.79204
0.65 0.46302792 0.836972
0.7 0.52036303 0.879637
0.75 0.58025902 0.919741
0.8
0.6432
0.9568
30
30
30
30
30
0.6
0.65
0.7
0.75
0.8
0.42469227
0.47931862
0.53601463
0.59504839
0.65686184
0.814707
0.859041
0.90084
0.939776
0.975308
0.775308
0.820681
0.863985
0.904952
0.943138
35
35
35
35
35
0.6
0.65
0.7
0.75
0.8
0.43769658 0.762303
0.49197975 0.80802
0.54817905 0.851821
0.60654269 0.893457
0.66747981 0.93252
40
40
40
40
40
0.6
0.65
0.7
0.75
0.8
0.44817905
0.50218559
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45
45
45
45
45
0.6
0.65
0.7
0.75
0.8
0.45686184
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50
50
50
50
0.6
0.65
0.7
0.75
0.8
0.46420722
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0.57297748
0.629975
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55
55
55
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55
55
0.75 0.63556066 0.864439
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60
60
60
60
60
0.6
0.65
0.7
0.75
0.8
100
100
100
100
100
0.47603872
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0.50398 0.69602
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0.8
0.7216
0.8784