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## Biostatistics practical exercise Using the t test to determine how long to condu

Bailey, Tori, Host/Executive Producer has reference to this Academic Journal, PHwiki organized this Journal 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 Cali as long as nia State University, Long Beach 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 in addition to 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. Bio 260, FDA t test calculations example 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 as long as 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 as long as 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 in addition to 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 as long as those infected to the value as long as normal infected individuals. The initial cost to recruit the subjects, pay the subjects in addition to administer the ABT007 is $5,000,000. The cost of each year’s monitoring in addition to testing is $1,000,000. 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 as long as 20 years. Bio 260, FDA t test calculations example Clinical trial of ABT007: The total expected profit from ABT007 will be 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 as long as 20 years. Initial cost = $5M, cost each year of trial = $1M. Bio 260, FDA t test calculations example 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 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to decide when it will end in order to maximize profit. Year 1 begins: Executives hold a party in addition to wish you all luck since your work is the future of the company in addition to you are the hope of all people with Lurgi ( in addition to may make profit as long as the company's shareholders). 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example SE of infected tcalc = tcrit = Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,9 = 1.833 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,9 = 1.833 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example SE of infected tcalc = tcrit = Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,18 = 1.734 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,18 = 1.734 tcrit = 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 in addition to 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 ef as long as ts. - Marketing department predicts that the market is now 50% smaller. 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example SE of infected tcalc = tcrit = Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,30 = 1.697 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,30 = 1.697 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example SE of infected tcalc = tcrit = Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,40 = 1.684 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,40 = 1.684 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example SE of infected tcalc = tcrit = Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,50 = 1.676 tcrit = 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 in addition to 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 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 Bio 260, FDA t test calculations example tcrit = t0.05,df = t0.05,50 = 1.676 tcrit = 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 in addition to 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 as long as 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 in as long as med doctors will not prescribe it so the market is 50% smaller. - Administering to study subjects invalidates their data. 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 Bio 260, FDA t test calculations example Clinical trial of ABT007: Task of your division is to monitor the trial in addition to 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 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 Bio 260, FDA t test calculations example SE of infected tcalc = tcrit = 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 in addition to 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 in addition to Learners do Results (n=40) - Some paused at 135V in addition to expressed concern. - Only 1 person stopped be as long as e 300V. - 26/40 Teachers went all the way to 450V in addition to 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 merely by being told to by perceived authority figures in addition to that this power is enhanced in groups. Explains (but may or may not excuse) the unethical behavior by Nazi in addition to Abu Ghraib guards under orders from superiors. We "scientists" must be careful in scientific situations because we are the "experts" in addition to are authority figures, we must be careful of the power we have even if we don't realize it.

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