

 


©2012 Samuel Oschin Comprehensive Cancer Institute CedarsSinai Medical Center All rights reserved 
I. Contents
I. Contents
II. Installing EWOC
III. Preparing the data file
IV. Running EWOC
1. Required parameters
Probability of dose limiting toxicity (θ)
Probability of exceeding the Target dose (α)
Minimum dose
Maximum dose
Data file
2. Optional fields
Title
Minimum dose increment
Output
Bayesian confidence interval
Marginal posterior distribution plot
Cohort size
Tree of doses
Variable Alpha Increment
Sequence of doses with no DLTs
3. Prior Distributions
For the Target dose
For the probability of DLT at the Initial dose
4. Actions
Next dose
Cancel
Save parameters
Open parameter file
View Data File
V. Output
1. Example 1
Next dose
Bayesian confidence interval
Marginal posterior distribution plot
Tree of doses
Exporting output
Discrete doses
2. Example 2
VI. Simulations
1. Simulation
2. Required entries
Target Probability of DLT (θ)
Probability of Exceeding Target Dose (α)
Variable Alpha Increment
Sample Size for Each Trial
Number of Simulated Trials
3. Optional entries
Seed for Pseudorandom Number (optional)
Sequence of doses with no DLTs
Number of doses in sequences
4. Scenario
(i) Continuous Dose
Minimum Dose
Maximum Dose
True MTD
Probability of DLT at Initial Dose
(ii) Discrete Doses
A) Specify Level of MTD
Number of Discrete Dose Levels
Dose Level of True MTD
Probability of DLT at Initial Dose
B) Probability of DLT at Dose Levels
5. Example 3 (Continuous dose)
Output
6. 4 (Discrete doses)
VII. References
EWOC 3.1 is a standalone Windows 7/ Vista /XP application. EWOC 3.1 is freeware which can be downloaded from the official EWOC website. Click "EWOC 3.1 Application Software" and follow the instructions.
EWOC 3.1 is composed of the executable code "EWOC 3.1.exe" and is accompanied with two text files to allow you to test it ("parameter.in" and "5fuLONG.txt"), and this User�s Guide. These four files will be installed in the folder you specify.
III. Preparing the data file
Before running EWOC, a data
file containing at least one line must be created. To create a data file, any
text editor (e.g., NOTEPAD ) can be used. The data
file has the following structure:
 Each line corresponds to one patient.
 Each line must begin with two numbers separated by spaces.
 Anything that appears after the dose (the "second number") is treated as a comment and, therefore, disregarded by EWOC. Comments must not extend to a second line.
For example, the data line from the file 5fuSHORT.txt
and the data line from the file 5fuLONG.txt
are both valid and equivalent, as interpreted by EWOC, whereas each line from the file 5fuWRONG.txt is invalid.
The design of a new trial will generally start with a data file containing one or more lines corresponding to the data obtained from patients treated at the initial dose. Since it is assumed that the initial dose is a safe dose, no DLT should be observed at the starting dose. If a dose level of 140 ng/m^{2 }is decided to be an appropriate starting dose for a given trial, the data file will look like the previous example. As the trial progresses, the data file will have as many lines as patients with known response to treatment.
Once all the data is entered save it in a file, preferably in the same folder in which EWOC was installed. If you are designing a new trial, it is convenient not to exit NOTEPAD while you run EWOC, so you can change the contents of your data file and see how different starting doses affect the dose escalation. In this case, save your revised data file each time so EWOC will have access to the updated version.
The following description assumes that the support of the MTD γ is the interval [X_{min}, X_{max}]. In other words, dose levels are selected continuously in this interval. A description for running a trial in the case of a set of discrete doses can be found in the Discrete Doses section below.
 Double click the icon to start EWOC.
 To start the Dialog click the mouse on the main menu item "State" and then "Dialog", or, using the keyboard, type "Alt+s" followed by "d".
 The EWOCDIALOG will then appear.
EWOCDIALOG is organized in three groups of fields: (1) required parameters, (2) optional fields, (3) prior distributions; and five action buttons: (1) next dose, (2) cancel, (3) save parameters, (4) open parameter file, and (5) View.
1. Required parameters
Probability of dose limiting toxicity (θ)
The proportion of patients expected to experience a medically unacceptable, doselimiting toxicity (DLT) if administered the Target dose (or maximum tolerated dose, MTD). Its value, generally between 0.1 and 0.5, depends on the nature of the DLT. It would be set relatively high when the DLT is a transient, correctable or nonfatal condition, and low when it is lethal or life threatening. In the dialog window above, the default value is θ = 0.33.
Probability of exceeding the Target dose (α)
The probability that the dose selected by EWOC is higher than the Target dose. Low values make the escalation cautious, high values cause larger steps. In the beginning of a trial, there is a higher level of uncertainty about the Target dose. Consequently, at the onset of a phase I trial, the probability of exceeding the Target dose is typically set to a low value (e.g., 0.25) in order to minimize the possibility of harming patients by administering doses much greater than the Target dose. In the dialog window above, the default value is a = 0.25. As the trial progresses, uncertainty about the Target dose declines and the likelihood of administering a dose considerably higher than the Target dose decreases. Thus, one should consider gradually increasing a during the course of the trial. When the probability of exceeding the Target dose is set to 0.5, it implies that underdosing a patient (treating with a dose lower than the Target dose) is just as bad as overdosing.
Minimum dose
This is the lower bound X_{min} of the support of the MTD γ. The dose to be given to the first patient in the trial is always greater than or equal to X_{min}. Note that the dose given to the first cohort of patients is not necessarily equal to X_{min} but there must be strong evidence that it is a safe dose. EWOC will never assign doses below X_{min}. In the dialog window above, the default value is X_{min} = 0.0.
Maximum dose
This is the upper bound X_{max} of the support of the MTD γ. The highest allowable dose in the trial must be less than or equal to X_{max}. EWOC will never assign doses above X_{max}. In the dialog window above, the default value is X_{max} = 1.0.
Data file
The name of the data file. If the data file and EWOC code are not in the same folder or directory, the full path should be provided. Name and full path should not be longer than 100 characters.
2. Optional Fields
Title
TUp to 100 characters can be used to label the Marginal posterior distribution plot and the Tree of doses.
Minimum dose increment
Controls how the doses are rounded or truncated. Changes in dose level will be in integer multiples of the selected minimum increment. For example, when the Initial dose is 140 units, a Minimum dose increment of 25 units could possibly produce the sequence of doses: 140, 215, 265, 290 ... From a theoretical perspective, dose varies continuously from X_{min} to X_{max}. In practice, due to dilution or measurement limitations, it may be possible to obtain only discrete dose levels. When left equal to zero, the next dose will be rounded to three decimal places.
Output
The following five output options, which are detailed in the Output section, are currently available:
Bayesian confidence interval:
The interval which most likely contains the true Target dose. For example, if [223.2, 425.0] is a Bayesian confidence interval at the 95% level, then the probability that the Target dose lays between 223.2 and 425.0, given the available data, is 0.95. The length of the interval measures the uncertainty about the Target dose. The most frequently used level is 95%. EWOC can calculate levels between 4 and 98%.
Marginal posterior distribution plot:
Conveys the accumulated information about the Target dose. A Bayesian confidence interval is depicted only when the previous box was also checked.
Cohort size:
This option allows you to design a trial with cohorts of p patients at each dose level, p =1, 2, 3. The default is one patient. To select either two or three patients, click the right corner for the dropdown box, and then select either two or three to make the selection, which will then be highlighted. In the example, we selected cohorts of size p = 2.
Tree of dosees:
Shows the recommended doses for the next two, three, and four cohorts of ρ patients depending on the number of DLTs observed for that cohort. The default is the next two patients if the box is checked. To select either three or four cohorts, click the mouse on the tiny arrows at the right corner of the box, and then click either three or four to make the selection, which will then be highlighted. In the above dialog, we requested a tree of doses for the next two cohorts of two patients each. Note that it is very important to have the boxes for Cohort size and Tree of Doses highlighted to obtain the appropriate graphs.
Variable Alpha Increment:
The probability of exceeding target dose (α) can be gradually increased during the course of the trial to meet the need of a relatively higher probability of exceeding target dose as the trial progresses and the uncertainty about the target dose declines. In the dialog below, we start with α = 0.25, then increase a in increments of 0.05 every time we calculate the dose for the next cohort of 2 patients, up to a maximum value of α = 0.5.
Sequence of doses with no DLTs:
This option requests a sequence of consecutive doses assuming that no patient exhibited DLT. This is useful to clinicians when trying to find out how many patients it would take to achieve a certain dose level assuming that no patient experienced DLT. In the dialog above, we are requesting a sequence of dose levels for the first 10 patients.
3. Prior Distributions
We do not recommend changing the defaults for the prior distributions unless you know what you are doing. The Prior distributions will be discussed in more detail elsewhere.
For the Target dose
The default is the uniform distribution between X_{min} and X_{max}. Alternatively, a Beta distribution with specified mode and standard deviation can be selected.
For the probability of DLT at the Initial dose
The default is the uniform distribution between zero and θ, the probability of dose limiting toxicity at the Target dose. The upper limit field changes automatically as θ does. To make them different from each other, change the upper limit field AFTER each change made in θ.
4. Actions
Next dose
Parameter values are checked for validity (e.g., valid range and existence of specified files). If everything seems right, the Next dose is calculated and reported in the "Escalation With Overdose Control  Results" window. Confidence interval, plots and trees are computed and drawn when requested. Errors will be indicated in special windows. Warnings are printed in the results window. While computations are being made, the "Running..." window appears. To stop the computations when the "Running..." window is present, end the EWOC task using the Task Manager (click the right mouse button on the Windows Start Menu).
Cancel
Closes the EWOCDialog.
Save parameters
Saves the contents of the EWOCDialog into a userspecified file. Once saved, this file can be opened at any time with the Open parameter file button. When Save parameters is clicked, a dialog window appears in which you may specify a name for the file, or you can click "cancel" to go back to EWOC dialog without saving parameters.
Open parameter file
Opens a previously saved parameter file. A parameter file can be opened at any time. When Open parameter file is clicked, a dialog window appears in which you may specify a name for the file. Clicking the cancel option in this window will link you back to EWOC dialog without opening any parameter file.
View Data File
Opens a previously saved data file. A data file can be opened at any time. When View button is clicked, a dialog window appears in which you may specify a name for the data file. Clicking the cancel option in this window will link you back to EWOC dialog without opening any data file. The data file will be opened in notepad program where you can make changes on the data file.
1. Example 1
This is the example of the FUtrial described in Babb et al. (1998). The target probability of DLT is θ = 0.33 and the minimum and maximum dose levels allowable in the trial are X_{min} =140 and X_{max} = 425. A minimum dose increment of 20 is selected. Suppose we use a probability of exceeding the target dose α = 0.25 and a variable α increment of 0.25. The result EWOCDialog is given below
Next dose
Suppose the data file "5FU_Long.txt" containing information on the first cohort of two patients is used,
If the Next Dose button is clicked (or you hit Enter) on the EWOCDIALOG shown above, the recommended dose for the third or next cohort of two patients is calculated.
If 200 ng/m^{2} is given to the next cohort of two patients, and if one of them had DLT, the data file will look like
Checking the Bayesian confidence box at 95% level, the Marginal posterior distribution plot, the Cohort size of two patients, the Tree of doses for next four cohorts, and clicking Next Dose will produce the following results:
Marginal posterior distribution plot
The Marginal posterior distribution (yaxis) versus Dose (xaxis) plot. It can be viewed as a probabilistic summary about the Target dose and conveys all the information accumulated from the previous patients. The first line at the top displays the title. The second line contains the date and number of the patient for whom the dose is being calculated. The second line continues with the Probability of dose limiting toxicity (θ) and the Probability of exceeding the Target dose (α). The EWOC recommended dose, is shown in red and italicized. The fundamental property of the EWOC recommended dose is that the area under the curve between it and X_{min} is the chosen Probability of exceeding the Target dose (α). The Probability that the EWOC recommended dose exceeds the Target dose is shown in black and italicized. The 95% Bayesian confidence interval bounds are shown in blue. The limits of this interval are determined so that the area under the curve is 95% of the total area and it contains the most likely values for the Target dose. Four numbers are displayed below the xaxis: X_{min} and X_{max} (closest to the xaxis), Mode, and EWOC recommended dose (in red).
Tree of doses
Suppose that the first two patients are given dose level 140, and none of them had DLT, and that the second pair of patients were given a dose level of 200, and one of them had a DLT. Suppose we use a probability of exceeding the target dose α = 0.25 and a variable α increment of 0.05. Suppose we want to have a tree of doses for the next four cohorts of 2 patients. The corresponding EWOCDialog is given below
The corresponding tree of doses is
The graph displays the recommended doses for the next four cohorts considering all possible outcomes. It assumes that patients 1 and 2 had no DLT when given a dose of 140 ng/m^{2}, and there was one DLT for patients 3 and 4 when given a dose of 200 ng/m^{2}.
Exporting output
The Marginal distribution plot and Tree of doses are generated as bitmap files. To print or make them available to other applications, click on the window containing the desired output, then click on "Edit" in the main menu and highlight the "Select all" option. Click again on "Edit" in the main menu and highlight the "Copy" option. The output is now available in the Clipboard and can be pasted as an image or into a document using your favorite image or text editor (e.g., Photoshop, Word, WordPerfect).
Discrete doses
If the trial is based on a prespecified set of discrete doses d1 < d2 < ... < d_{k}, then assuming that d_{i+1}  d_{i} = d for all i =2,..,k1, set X_{min} = d1 and X_{max} = d_{k} + d. The EWOC algorithm will treat the dose as continuous in the interval [d_{1}, d_{k+d}] and the recommended dose by EWOC is always rounded down to the nearest dose. For example, if the doses available in the trial are 50 ng/m^{2}, 150 ng/m^{2}, 250 ng/m^{2}, 350 ng/m^{2}, 450 ng/m^{2}, then X_{min} = 50 ng/m^{2} and X_{max} = 550 ng/m^{2}. 50 ng/m^{2} might be the dose given to the initial cohort of patients, which will be entered in the data file and 100 ng/m^{2} should be entered in the Minimum Dose Increment tab of the EWOC dialog box.
2. Example 2
Suppose you want to design a phase I trial where the target probability of DLT is θ = 0.33. The doses available in the trial are 50 ng/m^{2}, 150 ng/m^{2}, 250 ng/m^{2}, 350 ng/m^{2}, 450 ng/m^{2}. The first patient in the trial will be given dose 50 ng/m^{2} and you want to treat one patient at a time. Suppose we use a probability of exceeding the target dose α = 0.25 and and no α increment of 0.05. Suppose we want the tree of doses for the first 4 patients. The result EWOCDialog is given below
The resulting Tree of doses is
Note that in computing the dosing schema, when a sequence of DLTs are observed at X_{min}, and especially if the variable alpha is used, EWOC may produce incoherent results. Recall that EWOC assumes no DLTs can occur at X_{min}. When this assumption is violated and alpha is incremented the resulting dosing estimates may be incoherent. In practice, if a DLT were to be observed at X_{min}, the study should be halted and redesigned.
This module allows you to simulate trials and generate design operating characteristics for either a continuous dose or a discrete set of increasing doses d_{i}, i=1,...,k. For a continuous dose, the user specifies the minimum and maximum allowable dose, the value of the true MTD θ_{true} , and the probability of DLT at the minimum dose ρ_{0}. For a discrete set of k doses, the user can either specify the probability of DLT at each dose level or specify the probability of DLT at the initial dose and the dose level j such that d_{j} is the true MTD, γtrue. Let d_{0} = X_{min}, d_{k+1} = X_{max}. Here, we assume that the support of the MTD is [X_{min}, X_{max}], X_{min} < d_{1} < d_{2} < ... < d_{k} < X_{max}, and d_{i+1}  d_{i} is constant for all i = 0, ...,k.
1. Simulation
To start a simulation, click on "State" from the main menu item, then "Simulation".
The simulation dialog pops up.
2. Required entries
Target Probability of DLT (θ)
The proportion of patients expected to experience a medically unacceptable, doselimiting toxicity (DLT) if administered the Target dose (or maximum tolerated dose, MTD). Its value, generally between 0.1 and 0.5, depends on the nature of the DLT. It would be set relatively high when the DLT is a transient, correctable or nonfatal condition, and low when it is lethal or life threatening. In the example above, the default value is θ = 0.33.
Probability of Exceeding Target Dose (α)
The probability that the dose selected by EWOC is higher than the Target dose. Low values make the escalation cautious, high values cause larger steps. Typical values are 0.2 or 0.25. In the example above, the default value is α = 0.25.
Variable Alpha Increment
In the beginning of a trial, there is a higher level of uncertainty about the Target dose. Consequently, at the onset of a phase I trial, the probability of exceeding the Target dose is typically set to a low value (e.g., 0.2, 0.25) in order to minimize the possibility of harming patients by administering doses much greater than the Target dose. As the trial progresses, uncertainty about the Target dose declines and the likelihood of administering a dose considerably higher than the Target dose decreases. Thus, one should consider gradually increasing alpha during the course of the trial. When the probability of exceeding the Target dose is set to 0.5, it implies that underdosing a patient (treating with a dose lower than the Target dose) is just as bad as overdosing. Typical values are 0.05. Set it to 0.0 if a fixed alpha is desired. When a positive increment value is used, alpha increases up to a maximum value of 0.5. In the above example, the default value is 0.0.
Sample Size for Each Trial
This is the total number of patients you expect to enroll in the trial. In the above example, the default value is n = 6.
Number of Simulated Trials
This is the number of trials m to replicate to derive the design operating characteristics. Use a small number of trials (10 or 20) to estimate the time it would take to run the program. We recommend using 500 to 1000 trials obtain design operating characteristics. In the above example, the default value is m = 2.
3. Optional entries
Seed for Pseudorandom Number (optional)
Use any integer between 1 and 2147483646 to initialize the seed for random number generator. In the above example, the default value is 0.
Sequence of doses with no DLTs
Checking this box will return a sequence of consecutive dose assignments provided that no patient experienced DLT.
Number of doses in sequences
Specify how many consecutive doses to observe. In the above example, the default value is 10.
4. Scenario
You must select either Continuous Doses or Discrete Doses.
Minimum Dose
This is the minimum dose level that can be assigned to a patient. In the above example, the default value is X_{min}=0.
Maximum Dose
This is the maximum dose level that is anticipated in the trial. In the above example, the default value is X_{max}=1.
True MTD
This is the assumed true value of the MTD. Enter any number between X_{min} and X_{max}. In the above example, the default value is θ_{true}=0.5.
Probability of DLT at Initial Dose
This is the probability of DLT at dose X_{min}. Enter a value between 0 and θ. In the above example, the default value is ρ_{0}=0.05.
(ii) Discrete Doses
You must select either "Specify Level of MTD" or "Probability of DLT at Dose Levels".
Number of Discrete Dose Levels
Enter the number of available discrete dose levels. In the above example, the default value is k=4.
Dose Level of True MTD
Enter an integer corresponding to the true dose level of the MTD. For example, if you entered 7 discrete dose levels, and you assume that the true MTD is dose level 4, enter the number 4. In the above example, the default value is 3.
Probability of DLT at Initial Dose
This is the probability of DLT at dose level 1. Enter a value between 0 and θ. In the above example, the default value is ρ_{0}=0.05.
B) Probability of DLT at Dose Levels
Use this option only if you did not select the option "Specify Level of MTD". Enter pairs x,y, where x is the dose level and y is the corresponding probability of DLT at that dose level. In the above example, there are 4 dose levels and the true probabilities of DLTs at each level are 0.05, 0.15, 0.23, 0.37, respectively.
5. Example 3 (Continuous dose)
We want to design a cancer phase I trial with a target probability of DLT θ = 0.33, and a fixed probability of exceeding the target dose α = 0.25. A maximum of 24 patients will be enrolled to the trial. Dose levels are between 100 and 500 mg and the first patient receives the dose 100 mg. We want to obtain design operating characteristics by simulating 500 trials assuming that the true MTD is 150 mg and the probability of DLT at the initial dose is 0.05.
The simulation dialog box corresponding to the input parameters and scenario is shown below.
also entered 20 for the seed of the random number generator. Now, click Run.
Note: The program will become nonresponsive while running. Please wait while it finishes the computations.
Output
The results of the simulation are printed in a new window
Escalation With Overdose Control  Results
These are also stored in the text file "simulationResults.txt" located in the same directory as the executable program EWOC 3.1. The file contains information on the input parameters and the summary statistics.
Input parameters and scenario:
Alpha= 0.25
Minimum dose= 100.00
Maximum dose= 500.00
True MTD= 150.00
True Rho= 0.05
Sample size per trial= 24
Number of trials= 500
Seed= 20
Simulation results: Estimated MTD= 147.15
Estimated root MSE= 11.17
Pct DLTs= 0.34
Time to run simulation is: 4193 sec
8 sec per trial
The estimated MTD is is the estimated MTD of the ith trial. is the dose recommended for the n+1st patient in the ith trial.
The estimated bias is defined as
The estimated root MSE is defined as
Pct DLTs is the proportion of patients who experienced DLT from all trials.
6. Example 4 (Discrete doses)
We want to design a cancer phase I trial with a target probability of DLT θ = 0.33, and a fixed probability of exceeding the target dose α = 0.25. A maximum of 24 patients will be enrolled to the trial. Dose levels available for the trial are 100, 200, 300, 400, and 500 mg and the first patient receives the dose 100 mg. We want to obtain design operating characteristics by simulating 500 trials assuming that the true MTD is 300 mg and the probability of DLT at the initial dose is 0.05.
The simulation dialog box corresponding to the input parameters and scenario is shown below.
We also entered 20 for the seed of the random number generator. Now, click Run. Similar to Example 3, the output file contains information on the input parameters and the summary statistics.
Input parameters and scenario:
Alpha= 0.25
True MTD= 3.00
True Rho= 0.05
Sample size per trial= 24
Number of trials= 500
Seed= 20
Percent DLTs= 0.25
Simulation results:
Dose  Probability of Toxicity  Percent Patients at Dose Level  Percent DLTs at Dose Level  Pct of Trials with Dose Level as the MTD 

1.  0.05  0.068  0.017  0.000 
2.  0.14  0.363  0.128  0.282 
3.  0.33  0.518  0.336  0.666 
4.  0.61  0.051  0.645  0.052 
5.  0.83  0.000  1.000  0.000 
Time to run simulation is 3556 sec, 7 sec per trial.
Probability of Toxicity is the true probability of DLT at the corresponding dose level. Percent Patients at Dose Level is the proportion of patients that were allocated to each dose level from all trials.
Percent DLTs at Dose Level is the proportion of patients that experienced DLT at each dose level.
Pct of Trials with Dose level as the MTD is the proportion of trials that recommend each dose level as being the MTD.
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