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Biostatistics practical exercise Using the t test to determine how long

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.

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Biostatistics practical exercise Using the t test to determine how long

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  1. 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

  2. Bio 260, FDA t test calculations 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 b-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 b-killer cells during infection, thereby reducing, but not eliminating, the deleterious effects.

  3. Bio 260, FDA t test calculations example About marketing ABT007: The # of b-killer cells in an infected person = 30 per ml The # of b-killer cells in an un-infected person = 15 per ml If the drug can be shown to lower the # of b-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.

  4. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml $2M per year if p<0.05, $4M per year if p<0.01, Sells for 20 years. 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 b-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.

  5. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml $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. Clinical trial of ABT007: The total expected profit from ABT007 will be?

  6. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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)

  7. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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).

  8. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells stat 0 $5M $2M $4M 1,000 0 - - - - 1 2 3 4 5 6 7 8 9

  9. Bio 260, FDA t test calculations example Un-infected person = 30 per ml, infected person = 15 per ml 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 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.

  10. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  11. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,9 = 1.833 tcrit = t0.01,df = t0.01,9 = 2.821 Stop study now: profit = $?

  12. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,9 = 1.833 tcrit = t0.01,df = t0.01,9 = 2.821 Stop study now: profit = -$6M Continue?

  13. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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.

  14. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  15. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,18 = 1.734 tcrit = t0.01,df = t0.01,18 = 2.552 Stop study now: profit = $?

  16. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,18 = 1.734 tcrit = t0.01,df = t0.01,18 = 2.552 Stop study now: profit = -$7M Continue?

  17. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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.

  18. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  19. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,30 = 1.697 tcrit = t0.01,df = t0.01,30 = 2.457 Stop study now: profit = $?

  20. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,30 = 1.697 tcrit = t0.01,df = t0.01,30 = 2.457 Stop study now: profit = -$8M Continue?

  21. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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

  22. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  23. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,40 = 1.684 tcrit = t0.01,df = t0.01,40 = 2.423 Stop study now: profit = $?

  24. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,40 = 1.684 tcrit = t0.01,df = t0.01,40 = 2.423 Stop study now: profit = -$9M Continue?

  25. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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

  26. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  27. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,50 = 1.676 tcrit = t0.01,df = t0.01,50 = 2.403 Stop study now: profit = $?

  28. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,50 = 1.676 tcrit = t0.01,df = t0.01,50 = 2.403 Stop study now: profit = -$10M Continue?

  29. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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.

  30. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  31. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,60 = 1.671 tcrit = t0.01,df = t0.01,60 = 2.390 Stop study now: profit = $?

  32. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,60 = 1.671 tcrit = t0.01,df = t0.01,60 = 2.390 Stop study now: profit = -$1M Continue?

  33. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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.

  34. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  35. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,60 = 1.671 tcrit = t0.01,df = t0.01,60 = 2.390 Stop study now: profit = $?

  36. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,60 = 1.671 tcrit = t0.01,df = t0.01,60 = 2.390 Stop study now: profit = -$2M No bonuses Continue?

  37. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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

  38. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  39. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,80 = 1.664 tcrit = t0.01,df = t0.01,80 = 2.374 Stop study now: profit = $?

  40. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,80 = 1.664 tcrit = t0.01,df = t0.01,80 = 2.374 Bonuses $14,000 each Stop study now: profit = $7M Continue?

  41. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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.

  42. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 SE of infected? tcalc =? tcrit = ?

  43. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,80 = 1.664 tcrit = t0.01,df = t0.01,80 = 2.374 Stop study now: profit = $?

  44. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 tcrit = t0.05,df = t0.05,80 = 1.664 tcrit = t0.01,df = t0.01,80 = 2.374 Bonuses $12,000 each Stop study now: profit = $6M

  45. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 OBSERVE: the SE decreases as sample size increases

  46. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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. bcells bcells bcells 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 OBSERVE: the tcalc statistic increases even though the difference in means stays the same, because SE decreases

  47. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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 tcrit = t0.05,df = t0.05,9 = 1.833 tcrit = t0.01,df = t0.01,9 = 2.821 tcrit = t0.05,df = t0.05,18 = 1.734 tcrit = t0.01,df = t0.01,18 = 2.552 tcrit = t0.05,df = t0.05,30 = 1.697 tcrit = t0.01,df = t0.01,30 = 2.457 tcrit = t0.05,df = t0.05,40 = 1.684 tcrit = t0.01,df = t0.01,40 = 2.423 tcrit = t0.05,df = t0.05,50 = 1.676 tcrit = t0.01,df = t0.01,50 = 2.403 tcrit = t0.05,df = t0.05,60 = 1.671 tcrit = t0.01,df = t0.01,60 = 2.390 tcrit = t0.05,df = t0.05,80 = 1.664 tcrit = t0.01,df = t0.01,80 = 2.374 OBSERVE: the tcrit statistic decreases as sample size increases

  48. Bio 260, FDA t test calculations example Infected person = 30 per ml, un-infected person = 15 per ml 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 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 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?

  49. 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?

  50. 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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