Random F simulation:

Randomly generated dose toxicity curves based on the simulation procedure proposed by Oron & Hoff (2013). R code for Scenario Randomizer provided by Dr. Assaf P. Oron.
Random Dirichlet vectors was used to generate dose toxicity curves. In eacch scenario, a set of l increments (including the increments between 0 and $F(d_1)$) was simulated as a single multivariate Dirichlet random variable. The value of F at $d_i$ in scenario j can be written as $$F^{(j)}(d_i)=\sum_{k=1}^i X_k^{(j)}, \mathbf{X}^{(j)} \sim Dirichlet(\alpha_1, \alpha_2, ...,\alpha_l)$$ The parameters $\alpha_1, \alpha_2, ...,\alpha_l $ were randomly and independently drawn for each scenario.

Reference

Oron, A. P., & Hoff, P. D. (2013). Small-sample behavior of novel phase I cancer trial designs. Clinical Trials, 10(1), 63-80.

Random seed (integer) for random scenario simulation

Number of simulations

Number of scenarios randomly chosen (smaller than half of number of simulations)

Number of dose levels (integer)

Target toxicity rate $p_T$

Minimum value of the Dirichlet parameter at any level

Peak mean Approximate relative size of the jump in Dirichlet parameters around the density mode.

Peak sd Quantifies the mode's sharpness

Unacceptab dose Doses with more than 40% (default) toxicity will be excluded.

the smallest advantage (in closeness to 'targ') that the MTD has over other levels.

**if nonzero, the candidate set of F values will be raised to a random power in (warpFac0.1/targ,warpFac1/targ) before final vetting**

Adaptive designs

Standard 3+3 design/ 3+3^L design (Storer, 1989; Ji and Wang, 2013): The maximum-tolerated dose (MTD) is the highest dose at which no more than one dose limiting toxicities (DLT) are observed among 6 subjects.
1. Check the number of patients at the current dose.
  1. No subjects; treat three patients at the current dose and got to 2.
  2. Three subjects; enroll three more patients at the current dose and go to 3.
  3. Six subjects; go to 3.
2. Among 3 patients,
  1. If none experience DLT, escalate to the next higher dose. Go to 1. (If the current dose is the highest dose, stay at the current dose and go to 1.)
  2. If one subject experiences DLT, stay at the current dose. Go to 1.
  3. If two or more subjects experience DLT and the previous lower dose d* has 6 subjects, stop the trial and declare MTD is dose d*; otherwise, de-escalate to the previous lower dose (d*) and go to 1. (If the current dose is the lowest dose, stop the trial; MTD is lower than the lowest dose level.)
3. Among 6 patients,
  1. If none experience DLT, escalate to the next higher dose. Go to 1. (If the current dose is the highest dose, stop the trial; MTD is higher than the highest dose level.)
  2. If one subject experiences DLT, escalate to the next higher dose. Go to 1. (If the current dose is the highest dose, stop the trial; MTD is the current dose.)
  3. If two or more subjects experience DLT and the previous lower dose d* has 6 subjects, stop the trial and declare MTD is dose d*; otherwise, de-escalate to the previous lower dose (d*) and go to 1. (If the current dose is the lowest dose, stop the trial; MTD is lower than the lowest dose level.)
3+3^H design (Ji and Wang, 2013): The MTD is the highest dose with the toxicity rate less than or equal to 2/6.
1. The same with standard 3+3 design 1.
2. The same with standard 3+3 design 2.
3. Among 6 patients,
  1. If no more than one subject experiences DLT, escalate to the next higher dose. Go to 1. (If the current dose is the highest dose, stop the trial; MTD is higher than the highest dose level.)
  2. If two subjects experience DLT, escalate to the next higher dose. Go to 1. (If the current dose is the highest dose, stop the trial; MTD is the current dose.)
  3. If three or more subjects experience DLT and the previous lower dose d* has 6 subjects, stop the trial and declare MTD is dose d*; otherwise, de-escalate to the previous lower dose (d*) and go to 1. (If the current dose is the lowest dose, stop the trial; MTD is lower than the lowest dose level.)
Accelerated titration design (ATD) (Simon et al., 1997):
1. Titration phase: one subject is treated at the lowest dose. If the subject doesn't experience DLT, a new subject is treated with the next higher dose until a subject experiences DLT. Then, the trial switches to the second phase. (cohort size=1)
2. Traditional 3+3 design phase (cohort size=3 per dose level).
Biased coin design (BCD) (Durham & Flournoy, 1994): BCD is based on the theory of random walk and assigns patients to a dose level one at a time (cohort size=1).
- Early stoping/ Dose exclusion rule: Pr(toxicity rate at dose i > $p_T$) | data) > 0.95. It is based on posterior probability of toxicity probability (no. of toxicity x~Binamial(n,p), prior of p~Beta(1,1))
  - Early stoping: stop the trial if the first dose level is eliminated.
  - Dose exclusion(safety) rule: dose level i and all higher doses no longer assigned
- If the j subject experiences DLT, de-escalate to the previous lower dose for the (j+1)th subject. If the current dose is the lowest dose (d=1), stay at the lowest dose for the next subject.
- If the j subject does not experiences DLT, we flip a biased coin with probability of heads equal to $p_T/(1-p_T)$. If a head is observed, escalate to the next higher dose for the next subject, otherwise stay at the current dose, where p_T is the prespecified target toxicity rate. If the current dose is the highest dose, stay at the highest dose for the next subject.
- MTD determination (dose selection based on isotonic estimate of toxicity probability closet to target toxicity rate)
  1. Go to NextGenDF and sign in.
  2. After all subjects are treated, input the number of toxic and the number of treated for each dose to 'Decide MTD'. Note the posterior probability was assumed that beta(x+0.005, n-x+0.005) at each dose i when using isotonic regression.
k in a row (KIR) design (Gezmu, 1996; Wetherill, 1963) : Subjects are assigned to a dose level one at a time with cohort size=1. The last k (k>1) subjects are used to make the decision of dose assignment, where k is subject to target toxicity rate $p_T=1-(0.5)^{1/k}$.
- Early stoping/ Dose exclusion rule:Pr(toxicity rate at dose i > $p_T$) | data) > 0.95. It is based on posterior probability of toxicity probability (no. of toxicity x~Binamial(n,p), prior of p~Beta(1,1))
  - Early stoping: stop the trial if the first dose level is eliminated.
  - Dose exclusion (safety) rule: dose level i and all higher doses no longer assigned
- If the j subject experiences DLT, de-escalate to the previous lower dose for the (j+1)th subject. If the current dose is the lowest dose (d=1), stay at the lowest dose for the next subject.
- If the last k (k>1) patients were treated at dose level d and none of them experience toxicity, escalate to the next higher dose; otherwise stay at the current dose, where k is selected as the smallest integer, but not less than $log(0.5)/log(1-p_T)$. If the current dose is the highest dose, stay at the highest dose for the next subject.
- MTD determination (dose selection based on isotonic estimate of toxicity probability closet to target toxicity rate)
  1. Go to NextGenDF and sign in.
  2. After all subjects are treated, input the number of toxic and the number of treated for each dose to 'Decide MTD'. Note the posterior probability was assumed that beta(x+0.005, n-x+0.005) at each dose i when using isotonic regression.
Bayesian continual reassessment method (CRM) Design (O'Quigley, Pepe, & Fisher, 1990; Cheung, 2011; Cheung, 2013; Sweeting, Mander, & Sabin, 2013):
- The CRM design (O'Quigley, Pepe, & Fisher, 1990) assumes that the toxicity probability p(d_i) increases monotonically with increasing dose $d_i$. The dose selected for the next patient depends on the distance between the posterior mean p*(d_i) at all of the doses and p_T. This simulation was conducted based on R package of dfcrm packages (Cheung, 2013) or bcrm (Sweeting, Mander, & Sabin, 2013), which includes one-parameter toxicity probability models, such as the hyperbolic-tangent model, a logistic model, and a power model. In addition, the prior distributions for the parameter in toxicity probability models are gamma, uniform and lognormal.
- Free software. You can use (I), (II) or (III) for conducting an oncology phase I trial.
  1. MD anderson Cancer Center-BMA-CRM simulator
    1. Go to the Software Download Site of MD anderson Cancer Center.
    2. Download BMA-CRMsimulator_V2.2.2.zip; extract file from zip and install it.
    3. Open BMA-CRM simulator and choose 'Trial Conduct' to run an oncology phase I trial. Note that when you conduct a simulation and evaluation in the website of Optimal Selection of Adaptive Designs, please check the Bayesian Continual Reassessment Method (bcrm package) and select 'power $d^{\alpha}$' dose response model and lognormal distributaion of prior $\alpha$ with mean 0.
  2. dfcrm packages (Cheung, 2013) in R software.
    1. Open R and install 'dfcrm' package.
    2. 'crm' function is used to compute a dose for the next patient in a phase I trial according to the CRM.
    3. For example, prior toxicity probabilities: p.tox0; target toxicity rate: target.tox=0.3; patient outcomes: tox=c(0,0,1); dose levels assigned to patients: level=c(1,1,1); method for parameter estimation: method = 'bayes'; dose response model: model ='empiric'; distribution of prior a: normal with mean 0 and variance 1.34.
      Please click dfcrm help for more information.
      Note that this is equal to a power model with lognormal prior for bcrm .
      - > #install.packages('bcrm')
      - > library(dfcrm)
      - > p.tox0 <- c(0.05, 0.10, 0.20, 0.30, 0.35, 0.40, 0.45)
      - > out<-crm(prior=p.tox0, target=0.3,tox=c(0,0,1),level=c(1,1,1), method = 'bayes', model ='empiric', scale = sqrt(1.34))
      - > out$mtd #Next recommended dose level for next cohort
      Note that when you conduct a simulation comparison in the website, please select 'power $d^{\alpha}$' dose response model and lognormal distributaion of prior $\alpha$ with mean 0 and variance $s^2$.
    4. Use crm function with empiric model, scale=s value and Bayes method to conduct an oncology phase I trial. Note that when you conduct a simulation and evaluation in the website of Optimal Selection of Adaptive Designs, please select 'power $p^{\alpha}$' dose response model and lognormal distributaion of prior $\alpha$ with mean 0 and variance $s^2$.
  3. bcrm packages (O'Quigley, Pepe, & Fisher, 1990; Sweeting, Mander, & Sabin, 2013) in R software.
    1. Open R and install 'bcrm' package and 'rjags' package. JAGS software is required to install first for two parameter dose response model.
    2. Use bcrm function to conduct an oncology phase I trial.
    3. For example, Sample size: nmax=30; prior toxicity probabilities: p.tox0; power dose response model: ff='power'; distribution of prior a: lognormal(0,1.34); target toxicity: target.tox=0.3; start dose: start=1. The use of the posterior mean estimate of the posterior distribution to choose the next dose: pointest='mean'. Please click bcrm help or see page 9 of Sweeting et al. (2013) for more information.
      - ># One-parameter dose response model
      - > #install.packages('bcrm')
      - > library(bcrm)
      - > p.tox0 <- c(0.05, 0.10, 0.20, 0.30, 0.35, 0.40, 0.45)
      - > bcrm(stop = list(nmax =30), p.tox0 = p.tox0, ff = 'power', prior.alpha = c(3, 0, 1.34),
        target.tox = 0.30, start = 1, pointest = 'mean')
      - ># two-parameter dose response model
      - > #install.packages('bcrm')
      - > #install.packages('rjags')
      - > #install.packages('R2WinBUGS')
      - >library(bcrm)
      - >library(rjags)
      - >library(R2WinBUGS)
      - > p.tox0 <- c(0.05, 0.10, 0.20, 0.30, 0.35, 0.40, 0.45)
      - > mu<-c(2.15,0.52)
      - > Sigma<-rbind(c(0.84^2,0.134),c(0.134,0.80^2))
      - > bcrm(stop = list(nmax =30), p.tox0 = p.tox0, cohort=3, ff='logit2',prior.alpha=list(4,mu,Sigma), target.tox=0.3, constrain=TRUE,start=1, pointest='mean',method='rjags')
Escalation with overdose control (Babb et al., 1998; Sweeting, Mander, & Sabin, 2013):
1. Open R and install 'bcrm' and 'rjags' package. JAGS software is required to install first.
2. For example, sample size: nmax=30; prior toxicity probabilities: p.tox0; two-parameter logistic dose response model: ff='logit2'; distribution of prior a: Bivariate Lognormal(mu,Sigma); target toxicity: target.tox=0.3; start dose: start=1. The predicted proportion of patients who receive an overdose is equal to 0.25: pointest=0.25. The use of rjags (MCMC calculations) for optimisation method: method='rjags'. Please click bcrm help for more information.
  - > #install.packages('bcrm')
  - > #install.packages('rjags')
  - > #install.packages('R2WinBUGS')
  - >library(bcrm)
  - >library(rjags)
  - >library(R2WinBUGS)
  - > p.tox0 <- c(0.05, 0.10, 0.20, 0.30, 0.35, 0.40, 0.45)
  - > mu<-c(2.15,0.52)
  - > Sigma<-rbind(c(0.84^2,0.134),c(0.134,0.80^2))
  - > bcrm(stop = list(nmax =30), p.tox0 = p.tox0, cohort=3, ff='logit2',prior.alpha=list(4,mu,Sigma), target.tox=0.3, constrain=TRUE,start=1, pointest=0.25,method='rjags')
Escalation based on toxicity intervals (Neuenschwander, et al., 1998; Sweeting, Mander, & Sabin, 2013):
1. Open R and install 'bcrm' and 'rjags' package. JAGS software is required to install first.
2. For example, Sample size: nmax=30; prior toxicity probabilities: p.tox0; two-parameter logistic dose response model: ff='logit2'; distribution of prior a: Bivariate Lognormal(mu,Sigma); target toxicity: target.tox=0.3; start dose: start=1. The use of rjags (MCMC calculations) for optimisation method: method='rjags'. Toxicity intervals: Underdosing [0,0.2], Target dosing (0.2, 0.35], Excessive toxicity (0.35, 0.60], Unacceptable toxicity (0.60, 1.00] set tox.cutpoints=c(0.2,0.35,0.60). The losses associated with each toxicity interval, Underdosing = 1, Target dosing =0, Excessive toxicity=1, Unacceptable toxicity=2. Please click bcrm help for more information.
  - > #install.packages('bcrm')
  - > #install.packages('rjags')
  - > #install.packages('R2WinBUGS')
  - >library(bcrm)
  - >library(rjags)
  - >library(R2WinBUGS)
  - > p.tox0 <- c(0.05, 0.10, 0.20, 0.30, 0.35, 0.40, 0.45)
  - > mu<-c(2.15,0.52)
  - > Sigma<-rbind(c(0.84^2,0.134),c(0.134,0.80^2))
  - > bcrm(stop = list(nmax = max.n), p.tox0 = p.tox0, cohort=3, ff = 'logit2', prior.alpha = list(4,mu,Sigma), target.tox = 0.3, constrain=TRUE,start=1, method='rjags', tox.cutpoints=c(0.2,0.35,0.6),loss=c(1,0,1,2))
Modified toxicity probability interval (mTPI) design (Ji, Li, & Bekele, 2007; Ji, Liu, Li, & Bekele, 2010):
- Early stoping/Dose exclusion rule: Pr(toxicity rate at dose i > $p_T$) | data) > 0.95. It is based on posterior probability of toxicity probability (no. of toxicity x~Binamial(n,p), prior of p~Beta(1,1))
  - Early stoping: stop the trial if the first dose level is eliminated.
  - Dose exclusion (safety) rule: dose level i and all higher doses no longer assigned
- The action of dose-finding depends on the unit probability mass (UPM) for the toxicity probability intervals, (0, $p_T-\epsilon_1)$,($p_T-\epsilon_1, p_T+\epsilon_2$) and ($p_T+\epsilon_2$, 1). The UPM of the three intervals are computed based on a beta/binomial model and one compares UPMs among three intervals.
  - If the UPM for under-dosing interval (0, $p_T-\epsilon_1)$ is largest, escalate to the next higher dose.
  - If the UPM for equivalence interval ($p_T-\epsilon_1, p_T+\epsilon_2$) is largest, stay at the current dose.
  - If the UPM for the overdosing interval ($p_T+\epsilon_2$, 1) is largest, de-escalate to the previous lower dose.
- Conduct mTPI design for an oncology phase I trial.
  1. Go to NextGenDF and sign in.
  2. Select 'Decision' sheet.
  3. Input sample size, target probability, $\epsilon_1$ and $\epsilon_2$ to 'generate decision table'.
  4. Determine dose level for next cohort based on the subjects response and decision table.
  5. After all subjects are treated, input the number of toxic and the number of treated for each dose to 'Decide MTD'. Note the posterior probability was assumed that beta(x+0.005, n-x+0.005) at each dose i when using isotonic regression.
Bayesian Optimal Interval Design (BOIN) design (Liu, and Yuan, 2015):
1. Open R and install 'BOIN' package.
2. Consider a phase I trial aiming to find the MTD with a target toxicity rate of 0.3. The maximum sample size is 30 patients in a cohort size of 3. Please click BOIN Tutorial for more information.
  - >install.packages('BOIN')
  - >library(BOIN)
  - >get.boundary(target=0.3, ncohort=10, cohortsize=3)
3. MTD determination (dose selection based on isotonic estimate of toxicity probability closet to target toxicity rate)
  Note, the posterior probability assumed that beta(x+0.05, n-x+0.05) at each dose i when using isotonic regression.
  - >n<-c(6,6,9,9)
  - >x<-c(0,0,1,3)
  - >select.mtd(target=0.3,npts=n,ntox=x)
T-statistic design (Ivanova et al., 2008; Bolognese, 2016):
- Early stoping/ Dose exclusion rule: Pr(toxicity rate at dose i > unacceptable toxicity level | data) > cutoff. It is based on posterior probability of toxicity probability (no. of toxicity x~Binamial(n,p), prior of p~Beta(1,1))
  - Early stoping: stop the trial if the first dose level is eliminated.
  - Dose exclusion (safety) rule: dose level i and all higher doses no longer assigned
  - Default: unacceptable toxicity level=0.35, cutoff=0.8.
- $T_i = (P_i-P_T)/sqrt( (P_i*(1-P_i)/n_i )$
  - $P_i$= the estimated proportion of toxicity at dose i.
  - 2 dose escalation when T < cutpoint 1.
  - 1 dose escalation when T in [cutpoint 1, cutpoint 2).
  - Stay at the current dose when T in [cutpoint 2, cutpoint 3).
  - 1 dose de-escalation when T in [cutpoint 3, cutpoint 4).
  - 2 dose de-escalation when T >= cutpoint 4.
  - Defual: cutpoint 1=-2; cutpoint 2=-1; cutpoint 3=1; cutpoint4=2.
- MTD determination (dose selection based on isotonic estimate of toxicity probability closet to target toxicity rate)
  1. Go to NextGenDF and sign in.
  2. After all subjects are treated, input the number of toxic and the number of treated for each dose to 'Decide MTD'. Note the posterior probability was assumed that beta(x+0.005, n-x+0.005) at each dose i when using isotonic regression.
Isotonic regression was used to estimate toxicity probability for MTD determination: pava{Iso} or you can choose cirPAVA{cir} in R.
- > library(Iso) # alternative library(cir)
- ># Perform the isotonic transformation using PAVA with weights being posterior variances
- ># The posterior mean p.mean and variance p.var from the beta distribution $(x_i+a, n_i-x_i+b)$ at dose i, where a=0.005, b=0.005
- > iso.p<-pava(y=p.mean, w=1/p.var) # alternative function cirPAVA(y=p.mean,wt=1/p.var)
- > iso.p+1E-10 ## by adding an increasingly small number to tox prob at higher doses, , it will break the ties and make the lower dose level the MTD if the ties were larger than pT or make the higher dose level the MTD if the ties are smaller than pT
Comprehensive score
For each method, we expect the best design to have $\%Sel_{MTD}$ as high as possible and $\%(n_{<MTD}+n_{>MTD})/n$ as small as possible. So a larger $I_{MTD}$ indicates a design with more reliability. The index of MTD $$I_{MTD}=\frac{\%Sel_{MTD}}{\%(n_{<MTD}+n_{>MTD})/n}$$ For the selected design, the values of $I_{MTD}$ were transformed to a continuous rank index of MTD between 0 and 1. The continuous rank index of MTD is defined as $$R_{MTD}=\frac{ I_{MTD}-min(I_{MTD}) }{max(I_{MTD})-min(I_{MTD})}$$ If $max(I_{MTD})=min(I_{MTD})$, $R_{MTD}$ will be 1/(number of methods) Likewise, to measure the safety of a design, the continuous rank index of overall toxicity probability is defined as $$R_{OT}=\frac{ |P_{OT}-max(P_{OT})| }{max(P_{OT})-min(P_{OT})}$$ where a smaller overall toxicity probability $P_{OT}$ indicates a design with more safety, i.e. a higher $R_{OT}$ indicates a design with more safety. If $max(P_{OT})=min(P_{OT})$, $R_{OT}$ will be 1/(number of methods) Comprehensive score is defined as $$S_{w}=w*R_{MTD}+(1-w)*R_{OT}$$ where $w$ is a weight that adjusts the importance given to $R_{MTD}$ over $R_{OT}$.

Reference

Babb, J., Rogatko, A. & Zacks, S. (1998). Cancer phase I clinical trials: Efficient dose escalation with overdose control. Statistics in Medicine, 17(13), 1103-1120.

Bolognese, J. (2016). Consideration of the T-Statistic adaptive dose-finding design for estimating maximum tolerated dose. 2016 Joint of Statistical Meetings, McCormick Place Convention Center, Chicago, USA. https://ww2.amstat.org/meetings/jsm/2016/onlineprogram/AbstractDetails.cfm?abstractid=318637

Cheung, Y. K. (2011). Dose finding by the continual reassessment method: CRC Press.

Cheung, K. (2013). dfcrm: Dose-finding by the continual reassessment method. R package version 0.2-2. https://CRAN.R-project.org/package=dfcrm

Durham, S., & Flournoy, N. (1994). Random Walks for Quantile Estimation. In S. Gupta & J. Berger (Eds.), Statistical Decision Theory and Related Topics V (pp. 467-476): Springer New York.

Gezmu, M. (1996). The geometric up-and-down design for allocating dosage levels. (PhD degree), American University.

Ivanova A., Bolognese, J., & Perevozskaya I. (2008). Adaptive dose finding based on t-statistic for dose-response trials. Statistics in Medicine, 27(10), 1581-1592.

Ji, Y., Li, Y., & Bekele, B. N. (2007). Dose-finding in phase I clinical trials based on toxicity probability intervals. Clinical Trials, 4(3), 235-244.

Ji, Y., Liu, P., Li, Y., & Bekele, B. N. (2010). A modified toxicity probability interval method for dose-finding trials. Clinical Trials, 7(6), 653-663.

Ji, Y., & Wang, S.-J. (2013). Modified toxicity probability interval design: a safer and more reliable method than the 3+ 3 design for practical phase I trials. Journal of Clinical Oncology, 31(14), 1785-1791.

Liu, S., & Yuan, Y. (2015). Bayesian optimal interval designs for phase I clinical trials. Journal of the Royal Statistical Society: Series C (Applied Statistics), 64(3), 507-523.

Neuenschwander, B., Branson, M., & Gsponer T. (2008). Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27(13), 2420-2439.

O'Quigley, J., Pepe, M., & Fisher, L. (1990). Continual Reassessment Method: A Practical Design for Phase 1 Clinical Trials in Cancer. Biometrics, 46(1), 33-48.

Simon, R., Freidlin, B., Rubinstein, L., Arbuck, S. G., Collins, J., & Christian, M. C. (1997). Accelerated titration designs for phase I clinical trials in oncology. Journal of the National Cancer Institute, 89(15), 1138-1147.

Storer, B. E. (1989). Design and analysis of phase I clinical trials. Biometrics, 45(3), 925-937.

Sweeting, M., Mander, A., & Sabin, T. (2013). bcrm: Bayesian Continual Reassessment Method Designs for Phase I Dose-Finding Trials. Journal of Statistical Software, 54(13), 1-26.

Wetherill, G. B. (1963). Sequential Estimation of Quantal Response Curves. Journal of the Royal Statistical Society. Series B (Methodological), 25(1), 1-48.

Optimal Selection of Adaptive Designs in Phase I Oncology Clinical Trials

Random seed (integer) for random scenario simulation

Number of simulations

Number of scenarios randomly chosen (smaller than half of number of simulations)

Number of dose levels (integer)

Target toxicity rate \(p_T\)

Minimum value of the Dirichlet parameter at any level

Peak mean Approximate relative size of the jump in Dirichlet parameters around the density mode.

Peak sd Quantifies the mode's sharpness

Unacceptab dose Doses with more than 40% (default) toxicity will be excluded.

the smallest advantage (in closeness to 'targ') that the MTD has over other levels.

if nonzero, the candidate set of F values will be raised to a random power in (warpFac*0.1/targ,warpFac*1/targ) before final vetting

Simulation trials

Target toxicity probability \(p_T\)

Maximum sample size (N)

Start dose level

Number of simulation trials

Random seed (integer) for simulation 6 is recommended if BOIN design is selected

True toxicity probability at each dose level

Dose 1

Dose 2

Dose 3

Dose 4

Dose 5

Dose 6

Dose 7

Dose 8

Dose 9

Dose 10

Cohort size (mcohort)

Dose response model (model) - empiric (power) model: \(d^{exp(\alpha)}\), logistic: logistic model

Intercept of the logistic model (intcpt)

Dose-skipping restrictions (restrict) The next cohort can only be escalated one dose level above the current cohort. If FALSE, dose assignments are purely model-based

Standard deviation of the normal prior of the model parameter (scale)

Dose 1

Dose 2

Dose 3

Dose 4

Dose 5

Dose 6

Dose 7

Dose 8

Dose 9

Dose 10

Cohort size (cohort)

Dose-skipping constraint (constrain) The next cohort can only be escalated one dose level above the current cohort. THe input of start dose level will not be applied if constrain=FALSE.

Dose 1

Dose 2

Dose 3

Dose 4

Dose 5

Dose 6

Dose 7

Dose 8

Dose 9

Dose 10

Dose response model: Two-parameter model may need about 35 minutues with sample size of 30 and 1000 simulation trials per scenario if selected. Note that the optimisation method: exact method for one-parameter; rjags (MCMC) method for two-parameter model.

Dose response model (ff) power: \(d^{\alpha}\), logit1: 1-parameter logistic, ht:Hyperbolic tangent

Distribution of the prior \(\alpha\) (prior.alpha)

mean on the log scale (u)

variance on the log scale (>0)

shape (a>0)

scale (b>0)

min (a)

max (b, a<b)

Bivariate lognormal prior for \(\alpha_1\) and \(\alpha_2\)

Prior mean vector

mean for log(log(\(\alpha_1\)))

mean for log(\(\alpha_2\))

Prior variance-covariance matrix

variance (>0) for log(log(\(\alpha_1\)))

variance (>0) for log(\(\alpha_2\))

Covariane

Point estimated method (pointest) mean: posterior mean (exact method) or plugin: plug-in mean (approximate method)

This method may need about 35 minutues with sample size of 30 and 1000 simulation trials per scenario.

Dose escalation scheme controls the probability that a patient will receive an overdose is less than or equal to q. The rjags (MCMC) method will be used for computation.

Distribution of the prior \(\alpha\) (prior.alpha): Bivariate lognormal prior for \(\alpha_1\) and \(\alpha_2\)

Prior mean vector

mean for log(log(\(\alpha_1\)))

mean for log(\(\alpha_2\))

**if nonzero, the candidate set of F values will be raised to a random power in (warpFac0.1/targ,warpFac1/targ) before final vetting**

Random seed (integer) for simulation
6 is recommended if BOIN design is selected

Dose-skipping restrictions (restrict)
The next cohort can only be escalated one dose level above the current cohort. If FALSE, dose assignments are purely model-based

Dose-skipping constraint (constrain)
The next cohort can only be escalated one dose level above the current cohort. THe input of start dose level will not be applied if constrain=FALSE.

Dose response model:
Two-parameter model may need about 35 minutues with sample size of 30 and 1000 simulation trials per scenario if selected. Note that the optimisation method: exact method for one-parameter; rjags (MCMC) method for two-parameter model.

Dose response model (ff)
power: \(d^{\alpha}\), logit1: 1-parameter logistic, ht:Hyperbolic tangent

Point estimated method (pointest)
mean: posterior mean (exact method) or plugin: plug-in mean (approximate method)

Point estimated method (pointest): Feasibility bound between 0 and 0.5 for EWOC (not more than 1).
That is, the predicted proportion of patients who receive an overdose is equal to a specified value, q.

Cutpoints for toxicity intervals (tox.cutpoints)
For example, Underdosing (0,0.2], Target dosing (0.2, 0.35], Excessive toxicity (0.35, 0.60], Unacceptable toxicity (0.60, 1.00] set tox.cutpoints=c(0.2,0.35,0.60).

Loss function (loss)
is associated with each toxicity interval. For example, Underdosing = 1, Target dosing =0, Excessive toxicity=1, Unacceptable toxicity=2.

Equivalence interval (\(p_T-\epsilon_1,p_T+\epsilon_2\)) (EI):a amall range surrounding target toxicity probability \(p_T\)
For example, when \(p_T\)=0.25 and \(\epsilon_1=\epsilon_2=0.05\), EI is between 0.2 and 0.3. Any dose with toxicity probability in the EI is considered an acceptable MTD.

Early stopping parameter (n.earlystop)
If the number of patients treated at the current dose reaches n.earlystop, stop the trial and select the MTD based on the observed data. Recommend 9 to 18.

**Lower bound (LB) for toxicity probability (\(\phi_1\)=p.saf=LB*target)** The default value is p.saf=0.6*target.

**Upper bound (UB) for toxicity probability (\(\phi_2\)=p.tox=UB*target)** The default value is p.tox=1.4*target).

Cutoff probability for excessive toxicity (cutoff.eli)
Stop the trial if Pr(toxicity rate of the lowest dose > target | data) > cutoff.eli.

Cutpoints for T-statistic design
2 dose escalation when T < cutpoint 1; 1 dose escalation when T in [cutpoint 1, cutpoint 2); Stay at the current dose when T in [cutpoint 2, cutpoint 3); 1 dose de-escalation when T in [cutpoint 3, cutpoint 4); 2 dose de-escalation when T >= cutpoint 4.

Dose exclusion rule/ Eearly stopping
based on posterior probability of toxicity probability (prior~Beta(1,1))