Biostatistics practical exercise Using the t test to determine how long
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Biostatistics practical exercise Using the t test to determine how long to conduct clinical trials of novel drug Dr. Ashley Carter Department of Biological Sciences California State University, Long Beach Bio 260, FDA t test calculations example
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Bio 260, FDA t test calculations example. Biostatistics practical exercise Using the t test to determine how long to conduct clinical trials of novel drug Dr. Ashley Carter Department of Biological Sciences California State University, Long Beach. Bio 260, FDA t test calculations example. - PowerPoint PPT Presentation
Transcript of Biostatistics practical exercise Using the t test to determine how long
Biostatistics practical exercise
Using the t test to determine how longto conduct clinical trials of novel drug
Dr. Ashley CarterDepartment of Biological Sciences
California State University, Long Beach
Bio 260, FDA t testcalculations example
As an example of the practical use of statistics you will take the role of drug company project managers.
Scenario:A new drug, ABT007, has been designed by R&D that they think will help treat Lurgi, a deadly fictional disease that causes skin lesions, intestinal distress and permanent nerve damage.
About Lurgi:The primary cause of the deleterious effects is an increase in the number
of -killer cells in infected individuals. The disease is transmitted via close bodily contact.
About ABT007:The drug is administered orally.The drug acts like a long-term vaccine, it is predicted to reduce the
increase in the number of -killer cells during infection, thereby reducing, but not eliminating, the deleterious effects.
Bio 260, FDA t testcalculations example
Bio 260, FDA t testcalculations example
About marketing ABT007:
The # of -killer cells in an infected person = 30 per lThe # of -killer cells in an un-infected person = 15 per l
If the drug can be shown to lower the # of -killer cells in an infected person it can be sold. I.E., if the p value of a One-tailed, one-sample t test comparing the value in ABT007 infected individuals to the normal level for infected indicates significance.
The marketing research department predicts that the net income from manufacturing the drug will be $2,000,000 per year if the drug is significant at the p<0.05 level.
The marketing research department predicts that the net income from manufacturing the drug will be $4,000,000 per year if the drug is significant at the p<0.01 level.
Drug patents last for 20 years, after that time the drug will no longer be profitable.
Clinical trial of ABT007:
1,000 individuals at high risk of contracting Lurgi have been recruited and administered ABT007.
They will be monitored at the end of each year to determine:How many are infected?Of those who are infected, what are their # of -killer cells?
At the end of each year we will do a one-tailed one-sample t test comparing the values for those infected to the value for normal infected individuals.
The initial cost to recruit the subjects, pay the subjects and administerthe ABT007 is $5,000,000.
The cost of each year's monitoring and testing is $1,000,000.
Infected person = 30 per l, un-infected person = 15 per l$2M per year if p<0.05, $4M per year if p<0.01, Sells for 20 years.
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
The total expected profit from ABT007 will be?
Infected person = 30 per l, un-infected person = 15 per l$2M per year if p<0.05, $4M per year if p<0.01, Sells for 20 years.Initial cost = $5M, cost each year of trial = $1M.
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
The total expected profit from ABT007 will be?
Net income = 20 x $2M, if p<0.05or20 x $4M, if p<0.01
Total study cost = initial cost + cost of the years of study= $5M + (# years of study)($1M)
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 1 begins:
Executives hold a party and wish you all luck since your work is the future of the company and you are the hope of all people with Lurgi (and may make profit for the company's shareholders).
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 2 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 1 ends:
Executives ask if the study is done yet - they thought you guys would give quick results.
Un-infected person = 30 per l, infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 2 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,9 = 1.833tcrit = t0.01,df = t0.01,9 = 2.821
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,9 = 1.833tcrit = t0.01,df = t0.01,9 = 2.821
Stop study now: profit = -$6M
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 2 ends:
Executives ask why the study is still continuing when the year 1 predicted profit numbers were negative.
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,18 = 1.734tcrit = t0.01,df = t0.01,18 = 2.552
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,18 = 1.734tcrit = t0.01,df = t0.01,18 = 2.552
Stop study now: profit = -$7M
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 3 ends:
Executives ask why the study is still continuing when the year 2 predicted profit numbers were lower than year 1 previous ones
NEWS: Rates of Lurgi infection are down due to public health efforts. - Marketing department predicts that the market is now 50% smaller.
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,30 = 1.697tcrit = t0.01,df = t0.01,30 = 2.457
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,30 = 1.697tcrit = t0.01,df = t0.01,30 = 2.457
Stop study now: profit = -$8M
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 4 ends:
Executives ask why the study is still continuing when the year 3 predicted profit numbers were lower than year 2 previous ones
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,40 = 1.684tcrit = t0.01,df = t0.01,40 = 2.423
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,40 = 1.684tcrit = t0.01,df = t0.01,40 = 2.423
Stop study now: profit = -$9M
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 5 ends:
Executives ask why the study is still continuing when the year 4 predicted profit numbers were lower than year 3 previous ones
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,50 = 1.676tcrit = t0.01,df = t0.01,50 = 2.403
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,50 = 1.676tcrit = t0.01,df = t0.01,50 = 2.403
Stop study now: profit = -$10M
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 6 ends:
Executives ask why the study is still continuing when the drug has not been shown to be effective.
NEWS: a competitor has just received FDA approval for a drug that "cures" Lurgi. - If administered quickly the drug reverses all deleterious effects.- Marketing department predicts that by using appropriate advertising
ABT007 can still be marketed, although fully informed doctors will not prescribe it so the market is 50% smaller.
- Administering to study subjects invalidates their data.
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,60 = 1.671tcrit = t0.01,df = t0.01,60 = 2.390
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,60 = 1.671tcrit = t0.01,df = t0.01,60 = 2.390
Stop study now: profit = -$1M
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 7 ends:
Executives send congratulations that the year 6 predicted profit numbers were better than the year 5 previous ones, but would prefer positive values.
NEWS: a new internal bonus system will allow each employee to collect a share of their division's profits.
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,60 = 1.671tcrit = t0.01,df = t0.01,60 = 2.390
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,60 = 1.671tcrit = t0.01,df = t0.01,60 = 2.390
Stop study now: profit = -$2M
No bonuses Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 8 ends:
Executives ask why the study is still continuing when the drug has been show to work and the year 7 predicted profit numbers were lower than year 6 previous ones
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,80 = 1.664tcrit = t0.01,df = t0.01,80 = 2.374
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,80 = 1.664tcrit = t0.01,df = t0.01,80 = 2.374
Stop study now: profit = $7M
Bonuses$14,000 each
Continue?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year 9 ends:
Executives ask why the study continued, the drug could not have been more profitable than after year 8.
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9 $14M $0.5M $1M 902 98 24.6 20.3
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
SE of infected?tcalc =?tcrit = ?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9 $14M $0.5M $1M 902 98 24.6 20.3 2.0506 2.6334
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,80 = 1.664tcrit = t0.01,df = t0.01,80 = 2.374
Stop study now: profit = $?
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9 $14M $0.5M $1M 902 98 24.6 20.3 2.0506 2.6334
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
tcrit = t0.05,df = t0.05,80 = 1.664tcrit = t0.01,df = t0.01,80 = 2.374
Stop study now: profit = $6M
Bonuses$12,000 each
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9 $14M $0.5M $1M 902 98 24.6 20.3 2.0506 2.6334
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
OBSERVE: the SE decreases as sample size increases
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf. Inf. # Inf.SD Inf.SE tcalc
year spent sales sales indiv. indiv. cells cells cells stat 0 $5M $2M $4M 1,000 0 - - - - 1 $6M $2M $4M 990 10 25.7 20.8 6.5775 0.6537 2 $7M $2M $4M 981 19 25.1 20.5 4.7030 1.0419 3 $8M $1M $2M 967 33 24.7 20.8 3.6208 1.4638 4 $9M $1M $2M 955 45 25.1 20.4 3.0411 1.6113 5 $10M $1M $2M 943 57 25.4 20.8 2.7550 1.6697 6 $11M $0.5M $1M 931 69 24.9 20.5 2.4679 2.0665 7 $12M $0.5M $1M 921 79 24.8 20.3 2.2839 2.2768 8 $13M $0.5M $1M 913 87 24.7 20.2 2.1657 2.4473 9 $14M $0.5M $1M 902 98 24.6 20.3 2.0506 2.6334
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
OBSERVE: the tcalc statistic increases even though the difference in means stays the same, because SE decreases
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Study $ $/yr $/yr Non-inf Inf.year spent sales sales indiv. indiv. 0 $5M $2M $4M 1,000 0 1 $6M $2M $4M 990 10 2 $7M $2M $4M 981 19 3 $8M $1M $2M 967 33 4 $9M $1M $2M 955 45 5 $10M $1M $2M 943 57 6 $11M $0.5M $1M 931 69 7 $12M $0.5M $1M 921 79 8 $13M $0.5M $1M 913 87 9 $14M $0.5M $1M 902 98
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
OBSERVE: the tcrit statistic decreases as sample size increases
tcrit = t0.05,df = t0.05,9 = 1.833tcrit = t0.01,df = t0.01,9 = 2.821
tcrit = t0.05,df = t0.05,18 = 1.734tcrit = t0.01,df = t0.01,18 = 2.552
tcrit = t0.05,df = t0.05,30 = 1.697tcrit = t0.01,df = t0.01,30 = 2.457
tcrit = t0.05,df = t0.05,40 = 1.684tcrit = t0.01,df = t0.01,40 = 2.423
tcrit = t0.05,df = t0.05,80 = 1.664tcrit = t0.01,df = t0.01,80 = 2.374
tcrit = t0.05,df = t0.05,60 = 1.671tcrit = t0.01,df = t0.01,60 = 2.390
tcrit = t0.05,df = t0.05,50 = 1.676tcrit = t0.01,df = t0.01,50 = 2.403
Clinical trial of ABT007:
Task of your division is to monitor the trial and decide when it will end in order to maximize profit.
Year $ ended profit 0 - 0 1 -$6M 10 2 -$7M 19 3 -$8M 33 4 -$9M 45 5 -$10M 57 6 -$1M 69 Competitor cure here 7 -$2M 79 Didn't treat 10 people 8 +$7M 87 Didn't treat 8 people 9 +$6M 98 Didn't treat 9 people
Infected person = 30 per l, un-infected person = 15 per lProfit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01
Bio 260, FDA t testcalculations example
NOTE: did anyone suggest treating these people with the competitor's cure?- Does the company have an ethical responsibility to give cure to these people?- Did YOU have an ethical responsibility to give drug to these people?
Tuskegee experiment
1932: 399 syphilis infected men start study200 non-syphilis controls
1947: Penicillian discovered to cure syphilis
Study subjects were not given penicillinStudy subjects were prevented from receiving penicillin. Local clinics were instructed to deny treatment & 250 draftees
were prevented from receiving cure.
1972: "Study" finally ended28 of the 399 died from syphilis100 of 399 died from complications related to syphilis40 wives infected19 children born with syphilis related birth defects
Who did these evil acts?
Institutions involved in Tuskegee study:
Tuskegee Institute: an Alabama HBC (Historically Black College) US PHS (Public Health Service)CDC (Centers for Disease Control)NMA (national Medical Association) Mission statement: "To advance the art and science of medicine for people of African descent through education, advocacy, and health policy to promote health and wellness, eliminate health disparities, and sustain physician viability.
AMA (American medical association)
Long-term impact:
1974: regulations on true informed consent started1997: Presidential apology1990: Survey of 1056 African-Americans in South
34% AIDS is artificial35% AIDS is a form of genocide44% Government not "telling truth" about AIDS
Q: Why would people do this sort of thing?Not racism: Eunice Evers did much of the patient monitoring and contact. (Only staff person to do all 40 years)
A: because people tell them to
Milgram experiment, 1963+
E: "Experimenter" - person running the study.T: "Teacher" asks Learner questions.L: "Learner" must answer questions.
Learner must memorize word pairsTeacher then asks for partner word- Correct - next Q- Incorrect - Experimenter asks Teacher to administer electric shock
Shocks increase by 15 volts per wrong answer
What do the Teachers and Learners do?
A: because people tell them to
Milgram experiment, 1963+
E: "Experimenter" - person running the study.T: "Teacher" asks Learner questions.L: "Learner" must answer questions.
What do the Teachers and learners do?
In fact the Learner is an actor, shocks are not real, but seem real to Teacher. First the Learner screams in pain, then bangs on wall asking to stop, then complains about heart condition, then becomes silent (I.E., dead or unconscious).
If the Teacher asks to stop, the experimenter provides 4 verbal prompts to continue, after the 4th prompt the experiment stops.
This is really an experiment on the Teachers
A: because people tell them to
Milgram experiment, 1963+
E: "Experimenter" - person running the study.T: "Teacher" asks Learner questions.L: "Learner" must answer questions.
What do the Teachers and Learners do?
Results (n=40)- Some paused at 135V and expressed concern.- Only 1 person stopped before 300V.- 26/40 Teachers went all the way to 450V and silence.- Nobody who stopped early insisted overall experiment should end.- Nobody left room to check on Learner without asking permission first.
Multiple similar studies agree that ~65% of Teachers can be easily convinced to inflict what they believe to be painful (AND LETHAL!) shocks.
If there are more accomplices Teachers 92% become killers.
A: because people tell them to
Milgram experiment, 1963+
E: "Experimenter" - person running the study.T: "Teacher" asks Learner questions.L: "Learner" must answer questions.
Implications?
Normal people can be convinced to kill merelyby being told to by perceived authority figuresand that this power is enhanced in groups.
Explains (but may or may not excuse) the unethical behavior by Nazi and Abu Ghraib guards under orders from superiors.
We "scientists" must be careful in scientific situations because we are the "experts" and are authority figures, we must be careful of the power we have even if we don't realize it.
