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Biostatistics practical exercise Using the t test to determine how long to conduct clinical trials of novel drug Bio 260, FDA t test calculations example

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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 test calculations example

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Bio 260, FDA t test calculations example About marketing ABT007: The # of -killer cells in an infected person = 30 per l The # 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.

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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 administer the 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 test calculations example

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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 test calculations example

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Clinical trial of ABT007: The total expected profit from ABT007 will be? Net income = 20 x $2M, if p<0.05 or 20 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 l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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 l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1 2 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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 l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.8 2 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,9 = 1.833 t crit = t 0.01,df = t 0.01,9 = 2.821 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,9 = 1.833 t crit = t 0.01,df = t 0.01,9 = 2.821 Stop study now: profit = -$6M Continue?

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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 l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.5 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,18 = 1.734 t crit = t 0.01,df = t 0.01,18 = 2.552 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,18 = 1.734 t crit = t 0.01,df = t 0.01,18 = 2.552 Stop study now: profit = -$7M Continue?

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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 l Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $4M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.8 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,30 = 1.697 t crit = t 0.01,df = t 0.01,30 = 2.457 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,30 = 1.697 t crit = t 0.01,df = t 0.01,30 = 2.457 Stop study now: profit = -$8M Continue?

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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 l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.4 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,40 = 1.684 t crit = t 0.01,df = t 0.01,40 = 2.423 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,40 = 1.684 t crit = t 0.01,df = t 0.01,40 = 2.423 Stop study now: profit = -$9M Continue?

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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 l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.8 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,50 = 1.676 t crit = t 0.01,df = t 0.01,50 = 2.403 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,50 = 1.676 t crit = t 0.01,df = t 0.01,50 = 2.403 Stop study now: profit = -$10M Continue?

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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 l Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $2M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.5 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,60 = 1.671 t crit = t 0.01,df = t 0.01,60 = 2.390 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,60 = 1.671 t crit = t 0.01,df = t 0.01,60 = 2.390 Stop study now: profit = -$1M Continue?

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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 l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.3 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,60 = 1.671 t crit = t 0.01,df = t 0.01,60 = 2.390 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,60 = 1.671 t crit = t 0.01,df = t 0.01,60 = 2.390 Stop study now: profit = -$2M No bonusesContinue?

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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 l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.2 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,80 = 1.664 t crit = t 0.01,df = t 0.01,80 = 2.374 Stop study now: profit = $?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,80 = 1.664 t crit = t 0.01,df = t 0.01,80 = 2.374 Stop study now: profit = $7M Bonuses $14,000 each Continue?

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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 l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9$14M$0.5M$1M9029824.620.3 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example SE of infected? t calc =? t crit = ?

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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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9$14M$0.5M$1M9029824.620.32.0506 2.6334 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,80 = 1.664 t crit = t 0.01,df = t 0.01,80 = 2.374 Stop study now: profit = $?

44
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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9$14M$0.5M$1M9029824.620.32.0506 2.6334 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example t crit = t 0.05,df = t 0.05,80 = 1.664 t crit = t 0.01,df = t 0.01,80 = 2.374 Stop study now: profit = $6M Bonuses $12,000 each

45
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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9$14M$0.5M$1M9029824.620.32.0506 2.6334 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example OBSERVE: the SE decreases as sample size increases

46
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-infInf.Inf. #Inf.SDInf.SE t calc yearspentsales sales indiv.indiv. cells cells cells stat 0$5M$2M$4M1,0000 - - - - 1$6M$2M$4M9901025.720.86.5775 0.6537 2$7M$2M$4M9811925.120.54.7030 1.0419 3$8M$1M$2M9673324.720.83.6208 1.4638 4$9M$1M$2M9554525.120.43.0411 1.6113 5$10M$1M$2M9435725.420.82.7550 1.6697 6$11M$0.5M$1M9316924.920.52.4679 2.0665 7$12M$0.5M$1M9217924.820.32.2839 2.2768 8$13M$0.5M$1M9138724.720.22.1657 2.4473 9$14M$0.5M$1M9029824.620.32.0506 2.6334 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example OBSERVE: the t calc statistic increases even though the difference in means stays the same, because SE decreases

47
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-infInf. yearspentsales sales indiv.indiv. 0$5M$2M$4M1,0000 1$6M$2M$4M99010 2$7M$2M$4M98119 3$8M$1M$2M96733 4$9M$1M$2M95545 5$10M$1M$2M94357 6$11M$0.5M$1M93169 7$12M$0.5M$1M92179 8$13M$0.5M$1M91387 9$14M$0.5M$1M90298 Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations example OBSERVE: the t crit statistic decreases as sample size increases t crit = t 0.05,df = t 0.05,9 = 1.833 t crit = t 0.01,df = t 0.01,9 = 2.821 t crit = t 0.05,df = t 0.05,18 = 1.734 t crit = t 0.01,df = t 0.01,18 = 2.552 t crit = t 0.05,df = t 0.05,30 = 1.697 t crit = t 0.01,df = t 0.01,30 = 2.457 t crit = t 0.05,df = t 0.05,40 = 1.684 t crit = t 0.01,df = t 0.01,40 = 2.423 t crit = t 0.05,df = t 0.05,80 = 1.664 t crit = t 0.01,df = t 0.01,80 = 2.374 t crit = t 0.05,df = t 0.05,60 = 1.671 t crit = t 0.01,df = t 0.01,60 = 2.390 t crit = t 0.05,df = t 0.05,50 = 1.676 t crit = t 0.01,df = t 0.01,50 = 2.403

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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 $ endedprofit 0 -0 1-$6M10 2-$7M19 3-$8M33 4-$9M45 5-$10M57 6-$1M69Competitor cure here 7-$2M79Didn't treat 10 people 8+$7M87Didn't treat 8 people 9+$6M98Didn't treat 9 people Infected person = 30 per l, un-infected person = 15 per l Profit = 20 x $0.5M - $5M - (# years of study)($1M), if p<0.05 Profit = 20 x $1M - $5M - (# years of study)($1M), if p<0.01 Bio 260, FDA t test calculations 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?

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Tuskegee experiment 1932:399 syphilis infected men start study 200 non-syphilis controls 1947:Penicillian discovered to cure syphilis Study subjects were not given penicillin Study subjects were prevented from receiving penicillin. Local clinics were instructed to deny treatment & 250 draftees were prevented from receiving cure. 1972:"Study" finally ended 28 of the 399 died from syphilis 100 of 399 died from complications related to syphilis 40 wives infected 19 children born with syphilis related birth defects Who did these evil acts?

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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 started 1997: Presidential apology 1990: Survey of 1056 African-Americans in South 34% AIDS is artificial 35% AIDS is a form of genocide 44% 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)

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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 pairs Teacher 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?

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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

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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.

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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 merely by being told to by perceived authority figures and 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.

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