## Introduction

Historically, drugs have been marketed at excessive doses (i.e., doses well onto the plateau of the efficacy dose-response relationship) with some patients experiencing adverse events (AEs) unnecessarily (Herxheimer, 1991 ICH-E4, 1994). Over the last 5 years, a greater effort has been made to ensure that the best benefit to risk assessment is obtained for each new drug (Andrews and Dombeck, 2004 Bush et al., 2005). The benefit to risk assessment of marketed drugs has been improved, in some...

## Preclinical Toxicology Studies

Before going into human trials, candidate drugs and biologic undergo extensive safety evaluation in several species of animal. The legal requirements in the United States are spelled out in regulations promulgated by the Food and Drug Administration for the filing of an Investigational Drug Exemption (IND U.S. Federal Register, 1988). The regulations call only for sufficient preclinical studies to assure the safety and rights of the human subjects who take part in Phase I, II, and III studies....

## Fixed Dose versus Dose Titration Designs

A fixed-dose design is in contrast to a dose-titration design. In a fixed-dose design, once a patient is randomized to a dose group, the patient would take the same dose of study drug throughout the entire dosing period. In a dose titration design, a patient is randomized to a dose regimen with a starting dose, then the dose for a patient can be changed over time. In a dose-titration study, subjects are randomized to start with a low dose, and depending on either patient's response to the drug,...

## Extensions

Several extensions of the basic methods described above have been studied in the literature. We briefly summarize a few below. 1. Multiple test procedures based on general contrasts are given in Ruberg (1989), Tamhaneet al. (1996), Dunnett and Tamhane (1998), andTamhane et al. (2001). The first three papers use the difference measure approach. Specifically, when using the difference measure approach for the MinED problem, a general contrast for testing Hi xi < x0 + 8 is given by Ci Ci0(Y0 +...

## Similar Models

The four-parameter logistic model as described in O'Connell et al. (1993) is given by the following equation Rj The value of the response for patient i Di The level of the drug for patient i jj1 The response when there is no drug present j2 The maximal attributable effect of the drug + j1 j3 The dose, which produces the response halfway between j1 and j2 j4 This parameter is related to the steepness of the slope si The random error term for patient i. As can be seen from Eq. (9.7), the...

## Schedule Dependence

There is no clearly recognized definition of what constitutes schedule dependence. One way it might be defined is if the same total dose is given with different dosing schedules and the cumulative response varies then this is schedule dependence. On the other hand if the time of peak drug effect changes with dose then this would not be usually called schedule dependence. Nevertheless, changes in the timing and magnitude of neutropenia with different dosing schedule of anticancer drugs have been...

## Exponential Power Model

This model is intended to capture a possible sub-linear or a convex dose-response relationship. It is defined, for 9' (E0, E1, 8) as As before, E0 represents the basal level corresponding to d 0 and 8 > 0 (< 0) controls the rate of increase (decrease) in the effect. Because E0 is a scale parameter in the exponential model in Eq. (10.6), the model contrast can be determined from the standardized model being a function of 8 alone. An initial estimate for 8 can then be obtained from knowledge...

## Preface

This book emphasizes dose selection issues from a statistical point of view. It presents statistical applications in the design and analysis of dose-response studies. The importance of this subject can be found from the International Conference on Harmonization (ICH) E4 Guidance document. Establishing the dose-response relationship is one of the most important activities in developing a new drug. A clinical development program for a new drug can be broadly divided into four phases - namely...

## References

Categorical Data Analysis, 2nd ed. New York Wiley. Armitage, P. 1955. Tests for linear trends in proportions. Biometrics 11 375-386. Bauer, P., and Budde, M. 1994. Multiple testing for detecting efficient dose steps. Biomet-rical Journal 36 3-15. Bauer, P., Rohmel, J., Maurer, W., and Hothorn, L. 1998. Testing strategies in multi-dose experiments including active control. Statistics in Medicine 17 2133-2146. Chen, Y.I., and Wolfe, D.A. 1990. A study of distribution-free tests...

## Pharmacokinetics

Most drugs have inter- and intra-subject variability in PKparameters of at least 20 to as much as several fold. Overlap in systemic exposure across various dose levels occurs when the variability in PKparameters is large (e.g., > fourfold in clearance) or if the increment in each dose escalation is low. If significant treatment-emergent events occur during a given dose escalation, it may be reasonable to repeat the same dose in the next group or proceed with a minimal dose increase. A major...

## Antiinfective Drugs

The most successful extrapolation of dose directly from preclinical studies to humans occurs with anti-infective drugs. Candidates for potential use as anti-infective drugs are routinely tested against cell cultures of specific infectious agents. The concentration of drug needed to inhibit or kill the infective agent is determined by serial dilution of the candidate compound against specific cultures. This provides a spectrum of activity for the candidate drug. It also provides the mean...

## Motivation

As discussed in Chapter 1, the main purpose of Phase II studies is dose finding and most of these studies are designed to help estimate the dose-response relationships. On the other hand, Phase III studies are designed to confirm findings from early phases, and results from Phase III studies are used for submission to regulatory agencies for drug approval. Hence, Phase III studies are designed for decision making. In terms of hypotheses testing, ways of controlling the family-wise error rate...

## New Drug Development Process

Most of the drugs available in pharmacy started out as a chemical compound or a biologic discovered in laboratories. When first discovered, this new compound or biologic is denoted as a drug candidate. Drug development is a process that starts when the drug candidate is first discovered, and continues until it is available to be prescribed by physicians to treat patients (Ting, 2003). A compound is usually a new chemical entity synthesized by scientists from drug companies (also referred as...

## Trial Design Recommendations

Based on a review of all the simulation results, and considering the stated trial objectives and assumptions, we made these design recommendations Analysis method Regression-based estimation should be used, except for the confirmation of efficacy, where ANCOVA has a modest advantage. Allocation of patients to dose groups There was no consistent advantage to either equally balanced or end-weighted allocation, so either could be used. Dose spacing An MTD group should be included in the design...

## Concluding Remarks

Dose finding or dose selection happens mostly during Phase II or Phase III clinical development. The primary challenge for designing a Phase II dose-response clinical study is the lack of knowledge about how the drug works because this is the first time the test drug is studied in patients with the target disease. Again, Phase II studies are designed primarily for exploratory purposes and hence the main statistical method is estimation, and scientists tend to use model approaches in analyzing...

## Action Effect and Response

It is helpful to describe the pharmacological and pathophysiological consequences of drug exposure with three terms that are often considered synonyms (Holford and Peck, 1992). Action Refers to the mechanism at the primary target for the drug molecule, usually a receptor or enzyme, e.g., stimulation of an adrenergic beta-receptor in bronchial smooth muscle. Effect Describes the pathophysiological consequence of the drug action. There are typically several effects that might be observed, e.g.,...

## Comparison of the Four Parameter Logistic Model to the Emax Model When p4

Given the four-parameter logistic model R p2 + (9.10) Re-arranging the terms yields D-p4 (P1 - P2) R P2 + -- x - - (9.12) (D-1)04 x (01 - 02) R 02 + ----v , y2 (9.13) yields an Emax model with an inverse dose transformation Note that due to the inverse transformation of the dose, the Emax model parameters are interpreted in terms of the inverse dose. For example, E0 would be the response when the inverse dose is zero.

## Competitive Binding Assays

The concept of competitive binding arises from the standard first-order chemical kinetics and this was most fully developed by Sir John Gaddum in the 1930's (Burgen and Mitchell, 1978). The idea here is that there are receptor sites on animal tissue. An agonist is a small molecule that fits into the receptor site and triggers the tissue to do something. If the tissue is a smooth muscle, it contracts. If it is glandular, it secretes some specific hormone. In animal preparations, as a whole, it...

## Review of Basic Elements of Pharmacokinetics

The time course of drug concentration in plasma and other tissues of the body is determined by rates of input, distribution and elimination. The input process will vary with the route of administration but most often can be adequately described by a single first-order or zero-order mechanism (sometimes with a lag time before the onset of appearance of drug at the site of measurement, e.g., plasma). It is helpful to distinguish between the extent of absorption, or bioavailability, of a dose and...

## When the Response is Ordinal

Consider the data in Table 13.1 where five ordered categories ranging from death to good recovery were used to describe the clinical outcome of patients who suffered from subarachnoid hemorrhage. The five outcome categories make up the Glasgow Outcome Scale (GOS). Three doses of an investigational drug (low, medium, and high) and a vehicle infusion (placebo) were included in the trial. For this type of data, one can either model the probability of an ordinal response as a function of the dose...

## An Example Using Partitioning Based Stepwise Methods

A dose-response trial study with four active doses of an experimental compound versus a placebo was reported by Stewart and Ruberg (2000). The experiment was planned to study the effectiveness of the drug of different doses in preventing nausea and vomiting for patients undergoing surgery. The response variable was complete response, that is, no emetic episodes over a 24-hour observation period. The data are as follows. 12. Partitioning Tests in Dose-Response Studies with Binary Outcomes Dose...

## Proofof Activity Analysis in the Dose Finding Example

We now re-analyze the data presented in Section 10.1 using the MCP-Mod approach outlined in Section 10.5.1. The set of candidate models includes Emax, linear in log-dose, linear, exponential and quadratic (umbrella shape). Based on preliminary discussions, the logistic model is not included in this candidate set. Initial estimates for the different models are provided in Section 10.3. The test contrasts were obtained using the true parameter values for the corresponding standardized model,...

## General Approach to Power Calculation

When testing a null hypothesis H0 e < 0 against an alternative hypothesis Ha e > 0, where e is the treatment effect (difference in response), the Type I error rate function is defined as a(e) Pr reject H0 when H0 is true . Similarly, the type-II error rate function j is defined as j(e) Pr fail to reject H0 when Ha is true . For hypothesis testing, we need to know the distribution of the test statistic T, 0(T), under H0. For sample size calculation, we need to know its distribution under a...

## Appendix SAS Code for Performing Various Analyses

SAS code for performing various analyses with data in Table 13.1 data one 1 1 59 1 2 25 1 3 46 1 4 48 1 5 32 2 1 48 2 2 21 2 3 44 2 4 47 2 5 30 3 1 44 3 2 14 3 3 54 34 64 3 5 31 proc freq data one *CMH test with scores entered in the data weight count tables group*dose*outcome cmh1 run proc freq data one *CMH test with mid-rank scores weight count tables group* dose*outcome cmh1 scores ridit run proc catmod data one order data *mean response model weight count population dose response 1 2 3 4 5...

## Po q0

Simulation results with 3+3 STER Table 14.10. Simulation results with 3+3 STER Note True MTD 50, mean simulated MTD 41. Mean number of DLTs 3.3 Prob. of MTD Percent recommendations of dose as MTD. Note True MTD 50, mean simulated MTD 41. Mean number of DLTs 3.3 Prob. of MTD Percent recommendations of dose as MTD. Consequently, the total number of expected DLTs is given by J2 f 1 N Pi, Table 14.10 is another example as in Table 14.9, but the simulation results are from STER rather...

## Simultaneous Confidence Intervals

Bretz et al. (2003) proposed stepwise confidence intervals for the ratios Xi xi f 0 based on Fieller's (1954) method. Consider the r.v. which is t-distributed with v df. By solving the inequality Ti < tva, which is an event of probability 1 - a, we get the following 100(1 - a) lower confidence bound on Xi where ai t2aS2 ni (0 < i < k). For identifying the MinED Bretz et al. (2003) embedded these marginal 100(1 -a) confidence intervals into the following step-down procedure, which does not...

## Discussion

In this section, we compare the methodology proposed in this paper with that currently practiced by the U.S. Food and Drug Administration (FDA). For simplicity assume a single dose or drug. Then the FDA's criterion for efficacy consists of the proof of statistical significance and of clinical significance. Denoting the means for the control and the drug by i0 and i1, respectively, the statistical significance criterion is met if H0 i < 0 is rejected in favor of the one-sided alternative H1 1...

## The Relevance of Considering Integral of Effect as the Outcome Variable

The most obvious applications of PK PD are to describe the time course of a drug effect or clinical response such as changes in blood pressure or pain. However, many clinical responses are more closely related to the cumulative effects of the drug. For example, the healing of a peptic ulcer is the consequence of cumulative inhibition of gastric acid secretion and increase in pH allowing tissue repair. The time course of changes after each dose may be important for acute symptomatic relief of...

## Escalation and A B Designs

In this section, we describe two types of designs that are used in dose-finding studies in oncology and other areas. Both designs do not need specification of the total sample size, since, ideally, experimentation is continued until the MTD is exceeded by one dose level. The escalation design is defined as follows. Subjects are assigned in groups of size m starting with the lowest dose. Let CU be an integer such that 0 < CU < m. Let X(dj) be the number of toxicities in a cohort of subjects...

## Clinical Development for Life Threatening Diseases

In drug development, concerns for drugs to treat life-threatening diseases, such as cancer or AIDS, can be very different from those for other drugs. In the early stage of developing a cancer drug, patients are recruited to trials under open-label treatment with test drug and some effective background cancer therapy. Under this circumstance, doses of the test drug may be adjusted during the treatment period. Information obtained from these studies will then be used to help suggest dose regimen...

## Clinical Trial Objectives Used for the CTS Project

For the CTS project work, the following clinical trial objectives were adopted (1) Confirm that the candidate is efficacious on the primary efficacy measure. (2) Estimate the target doses the candidate doses expected to give the target response levels (TVs) for efficacy and tolerability. (3) Estimate a dose range that is potentially clinically noninferior to the reference agent for efficacy and tolerability. A fourth trial objective, not covered due to space limitations, related to evaluating...

## Comparing Two Success Probabilities in a Single Hypothesis

In this section, we briefly review the tests for comparing two unknown success probabilities, p0 and p1. Let us first consider testing the null hypothesis of equality There are exact tests and large sample approximate tests available for testing this simple null hypothesis. Let n0 and n1 represent the sample sizes in the two groups. Let X0 and X1 be the numbers of successes and x0 and x1 be the observed numbers of successes in each group. Then X0 Binomial(n0, p0) and X1 Binomial(n1, p1). For...

## Conclusions

This chapter reviewed the Emax model for dose-response analyses in clinical trials. The model was introduced, parameters interpreted, and sensitivities of the Emax model curve to changes in the parameters reviewed. Study design considerations, estimating starting values, and data analysis examples using the Emax model were also reviewed. Understanding the dose response is a fundamental part of the choosing the right dose. The Emax model is flexible, the parameters are readily interpretable, and...

## Selection of Control

Three types of treatment controls can be considered in clinical trial designs (1) historical control, (2) placebo control and (3) active control. Historical controls are based on data from other studies or the published literature, and they are usually less credible than placebo or active controls. Hence, historical controls are rarely used in clinical trials for new drug development. An active control is a treatment that is already on the market. Usually this is the standard treatment...

## X0J

For L< x1 < U, where f 1 p --p- is the odds ratio, L max(0, x n0), and U min(n1, x). A difference on the linear scale, i.e., S, is now replaced by a nonlinear odds ratio f. Figure 12.1 shows the relationship between S and f for a few values of p0. Notice that p1 < p0 is equivalent to f < 1, and the distribution reduces to Eq. (12.3) when p1 p0, or, f 1. It can also be shown that for f > 0, the distribution in Eq. (12.6) has monotone likelihood ratio in X1. That is, for f' > f, h(x )...

## Modeling Dose Response

Let pij be the probability that a subject in the ith dose group (i 1, 2, 3, 4) will have a response in the jth (j 1,2, , 5) category. For each dose group, pjs Table 13.1. Responses measured on the Glasgow Outcome Scale from a trial comparing three doses of a new investigational treatment with a control (Chuang-Stein and Agresti, 1997) Table 13.1. Responses measured on the Glasgow Outcome Scale from a trial comparing three doses of a new investigational treatment with a control (Chuang-Stein and...

## New Drug Application

When there is sufficient evidence to demonstrate a new drug is efficacious and safe, an NDA is put together by the sponsor. An NDA is a huge package of documents describing all of the results obtained from both nonclinical experiments and clinical trials. A typical NDA contains sections on proposed drug label, pharmacological class, foreign marketing history, chemistry, manufacturing and controls, nonclinical pharmacology and toxicology summary, human pharmacokinetics and bioavailability...

## Issues Relating to Clinical Development Plan

As mentioned in Chapter 1, one important step in early clinical development of a new drug is to draft a clinical development plan (CDP). Various clinical studies are designed and carried out according to this plan, and the CDP is updated over time based on newly available information. Estimation of dose-response relationship should be one of the very important components in CDP. Considerations and plans regarding dose finding should be in place starting from the nonclinical development stage....

## Trials with Multiple Agents

It is common in oncology to treat patients with drug combinations. Often, the dose of one agent is fixed and the goal is to find the MTD of the other agent administered in combination. Sometimes, two or three doses of one of the agents are selected with the goal of finding the MTD of the second agent for each dose of the first agent. For example, Rowinsky et al. (1996) described a trial where five doses of topote-can and two doses of cisplatin were selected for the study. Since topotecan and...

## Clinical Trial Objectives

An obvious objective for the first Phase II trial is to confirm the candidate's basic pharmacology (efficacy and safety). This proof of concept (POC) objective could be achieved by a simple two-group study, using some relatively high dose (near the maximally tolerated dose, MTD) versus placebo, with a sample size appropriate to the measures' variability and anticipated effect sizes. However, based on prior knowledge about the compound class, it is almost certain that the candidate will have the...

## I33Drug Formulation Development

As discussed earlier, a potential new drug can be either a chemical compound or a biologic. If the drug candidate is a biologic, then the formulation is typically a solution, which contains a high concentration of such a biologic, and the solution is injected into the subject. On the other hand, if the potential drug is a chemical compound, then the formulation can be tablets, capsules, solution, patches, suspension, or other forms. There are many formulation problems that require statistical...

## Models for Describing the Time Course of Response

The guiding principle for exposure response is the belief that drug concentration is the primary causal factor in generation of a response (Holford and Sheiner, 1981). This differs from the apparent belief expressed by statisticians who analyze dose response as if the dose was the primary causal factor whether allopathic (response increases with increasing dose) or homeopathic (response decreases with increasing dose). The concentration belief system leads to a simple partition of processes...

## Dose Allocation Dose Spacing

As depicted in Figure 7.2, with very limited information about the drug candidate, after allocating a placebo control, a high dose that is close to MTD, it will be very difficult to select the medium or low doses. The challenge is that at an early stage, there is no information as to what the underlying dose-response curve should be. Is it curve 1, curve 2, curve 3 or some other form When there is very limited data to help allocating doses, we may consider the potential use of other information...

## Linear in Log Dose Model

The linear in log-dose model is defined, for 9' (E0, 8) as where a value c > 0 is added to d to avoid problems with the placebo (d 0) arm. E0 is the basal effect and 8 is the slope associated with log(d + c). As with the Emax model, an increasing effect (8 > 0) model will be assumed. Clearly, the linear in log-dose model is a location-scale model which can be expressed as f (d, 9) E0 + 8f 0(d), with the standardized model being equal to so that the determination of the appropriate model...

## Multiple Center Studies

Clinical trials are commonly conducted at a number of different investigator sites or centers. The main reason for this practice is to ensure timely enrollment of sufficient number of patients. Another benefit of multiple center studies is that results obtained from these studies can represent a wider variety of patient background. This means that a multiple center study including various type of centers are more desirable, and the conclusion is not heavily dependent on one single center. In...

## Why Exposure Response is More Informative

The exposure response approach is capable of describing and explaining the time course of response after a single dose or multiple doses. Unlike the usual dose response approach, which is usually defined by a primary endpoint at a single time, the concept of time is a necessary and fundamental part of understanding pharmacological effects and therapeutic responses to a drug. Dose response can be considered as the least informative form of exposure-response relationship. The time course of...

## Core SAS Code for the Emax Model Analysis of the Blood Pressure Example Data in Section

Proc nlmixed data bp_01 parms e0 100 ed50 10 emax -12 n 2 s2e0i 225 s2emaxi 36 s2ed50i 12.25 err 4 e0_ (e0 + e0i) if dose 0 then do pred e0_ end else do denom ((ed50+ed50i)*) + (dosen) pred e0_ + numer denom end random e0i emaxi ed50i normal( 0, 0, 0 , s2e0i, 0, s2emaxi, 0, 0, s2ed50i ) bp_01 was the name of the SAS data set used. The dataset contained the patient's dose values and their corresponding diastolic blood pressure (mmHg). The parm option specifies the initial values for the...

## Objective 3 Estimation of a Potentially Clinically Noninferior Dose Range

For the inactive (TI 0) profile, the 10 type 1 error rate used for Objective 1 provides a minimum Objective 3 success rate of 90 , with these 90 of trials correctly declaring the efficacy dose to be above the top tested dose. The other two criterion components further improve the success rate, e.g., to approximately 95 with N 400 in five groups. 122 8. Clinical Trial Simulation Trial 0 25 50 75 100 125 0 25 50 75 100 125 Figure 8.7. Assigned dose levels and estimated NI ranges for 40 sample...

## Premarketing Clinical Development

If a chemical compound or a biologic gets through the selection process from animal testing and is shown to be safe and efficacious to be tested in human, it progresses into clinical development. In drug development for human use, the major distinction between clinical trials and nonclinical testing is the experimental unit. In clinical trials, the experimental units are human beings, and the experimental units in nonclinical testing are nonhuman subjects. As mentioned earlier, the results of...

## Estimation of the MTD After the Trial

Designs that use fixed sample size require specifying an estimation procedure to use after the trial is completed. It had been shown by simulations that the isotonic regression based estimator works better than other estimators (Stylianou and Flournoy 2002 Ivanova et al. 2003). The isotonic regression estimator is essentially the maximum likelihood estimator for the isotonic model of the data. Let N(dj, n) be the number of patients assigned to dose dj and X(dj, n) the number of toxicities at dj...

## Design Considerations for Phase II Dose Response Studies

Dose-response studies are usually carried out in Phase II. At this point, there is often a considerable amount of uncertainty regarding any hypothetical dose- response curves. It is typical at this time that the MTD is known from Phase I studies, and it may also be assumed that efficacy is nondecreasing with increasing doses. Even so, the underlying dose-response curve can still take many possible shapes. Under each assumed curve, there are various strategies of allocating doses. For example,...

## Conclusion and Discussion

In dose-response studies, when the purpose is to test for one or a few doses that are more efficacious than placebo, the principle of partitioning provides a powerful testing procedure for constructing multiple tests which control theFWER strongly. In this chapter, two partitioning test procedures for binary responses are introduced. One is a predetermined step-down method and the other is a sample determined step-down method. Choice of the appropriate procedure depends on the anticipated dose...

## The A B Escalation with Dose Deescalation

Basically, the general A + B design with dose de-escalation is similar to the design without dose de-escalation. However, it permits more patients to be treated at a lower dose (i.e., dose de-escalation) when excessive DLT incidences occur at the current dose level. The dose de-escalation occurs when more than D A (where D > C) or more than E (A + B) patients have DLTs at dose level i. In this case, B more patients will be treated at dose level i - 1 provided that only A patients have been...

## Simulations

We now investigate, via simulation, the performance of the MCP-Mod dose finding methodology described in Section 10.5.1. Following the design of the case study of Section 10.1, we consider the comparison of the five dose levels d 0, 0.05, 0.2, 0.6, and 1, with a single endpoint measured per patient. The outcome is assumed to be independently distributed as N( _d, a2). We set a 0.65, motivated by the residual standard deviation from the case study in Section 10.1. We restrict the simulations to...

## Choice of Prior Distributions

In this section, we address the issue of the choice of prior distributions. Specifically, we extend the class of restrictive priors used in Sections 5.2 and 5.3 by relaxing some of the constraints placed on (p0, y ). We show through simulations that a candidate joint prior distribution for (p0, y) with negative a priori correlation between these two components results in a safer trial than the one that assumes independent priors for these two parameters while keeping the efficiency of the...

## More Complex Dose Finding Trials 461 Trials with Ordered Groups

Sometimes patients can be stratified into two populations with possibly different susceptibility to toxicity. For example, UGT1A1 genotype might predict the occurrence of severe neutropenia during irinotecan therapy (Innocenti et al. 2004). In a study conducted by Innocenti et al. (2004), three out of six patients with the TA indel 7 7 genotype developed grade 4 neutropenia compared to 3 among 53 other patients. The two populations are referred to as ordered since it can be said that the...

## Parallel Line Assays

The phrase three-point assay was an attempt to establish quick and accurate tests of potency for digitalis preparations in the 1920s (see Burns, 1937). This assay used a standard of known potency and two titrations of the test material. A straight line was drawn between the two test results on a semi-log paper, another line was drawn parallel to that, through the result for the standard, and the relative potency was computed. Modern pharmacological studies use more than two doses of the test...

## Basic Properties of Group Upand Down Designs

Let D di, , dK be the set of dose levels selected for the study. Let P (d) denote the probability of toxicity at dose d, pj P(dj). We assume that P(d) is an increasing function of d. The group up-and-down design is defined as follows. Subjects are treated in cohorts of size s starting with the lowest dose. Let X(dj) be the number of toxicities in the most recent cohort assigned to dose dj, X(dj) Bin(s,pj). Let cL and cU be two integers such that 0 < cL < cU < s. Assume that the most...

## Multiple Arm Dose Response Trial

To characterize the response curve, multiple groups at different dose levels including a control group are usually studied. Such a multiple-arm trial is informative for the drug candidates with a wide therapeutic window. Whether a model-based or a nonparametric approach is adopted, any prior information about dose-response curve such as linear or monotonic is helpful. This prior information not only allows user to decide a more powerful test statistic (e.g., linear contrasts of the means), but...

## Correlated Priors

For simplicity of notation, p0, y , and v will denote both random variables and arguments of the corresponding densities. Let p0 be a random variable defined on (0,0) and v N(b, a 1) truncated to the interval b, to). Given p0 and v, let y N(x(p0, v), a2) truncated to the interval (a, v) with a < x(p0, v) < v and a < b. Denote by gx(.)(Y) the marginal distribution of y. This density depends on the functional form of x(p0, v) specified below. Model Mi. p 0 and y are independent with p 0...

## Why the Clearance Volume Parameterization is Preferred

Pharmacokinetic models can be expressed in a variety of parameterizations, e.g., volumes and half-lives or volumes and clearances. From a mechanistic perspective, the volume and clearance parameterization is preferable because the parameters can be directly linked to structural and functional properties of the body. Half-lives (e.g., of drug elimination) should be considered as secondary or derived parameters dependent on the more fundamental parameters of clearance and volume (Eq. (6.3))....

## Basic Concepts

Initially, the development of a new chemical entity is influenced by its anticipated pharmacological actions in patients as suggested by its effects in animal models as well as its toxicology and PK profile in animals (Lesko et al., 2000 Peck et al., 1994). The severity of the disease state and the availability of effective and safe alternative treatments are also key factors in formulating a development plan. Each new chemical entity is evaluated against key parameters of a target profile....

## XiXij Op1 N0

var(Sij - XiXij) (Xi) - 27 N- and > denote convergence in distribution. Note that E (Su) E (52) 1 -I 1 (T-a)da 1 + e (1 e ) E(Xij) -E(Sij), and E(x2 ) 'j l ' Xi Xi a 2(X . ) var (Sij- ( e (S -) - 2XiE (SijXij) + X2 E (x2)) E (Xij) E2(Xij)y 'J ' ' y 'JJ> Example In a four-arm (the active control, lower dose of test drug, higher dose of test drug and combined therapy) Phase II oncology trial, the objective is to determine if there is treatment effect with time-to-progression as the primary...

## Simulation Project Methods 2 Analysis and Evaluation Criteria

The evaluation criteria for the trial objectives are described in this section. Both linear regression and analysis of variance methods were implemented, to allow a better method (as measured by the percentage of correct trials) to be identified for proposed inclusion in the trial protocol. Analysis of covariance (ANCOVA) Based on an ANCOVA of the change from baseline for the efficacy measure (with baseline as covariate) and an ANOVA of the AE incidence (no covariate), the key statistics are...

## The Time Course of Placebo Response and Disease Natural History

In the analysis of clinical trials, it is usual to consider the placebo response as if it was indistinguishable from the natural history of the disease. However, it is often plausible to assume that the disease and the placebo response will have different time courses. Slowly progressive diseases, e.g., those that change 10 to 20 over the time course of the trial can be approximated by a linear function even if the profile over longer periods has a more complex shape. It is also reasonable to...

## Covariates in the Emax Model

In a dose-response setting there is the possibility that one or more covariates could significantly account for patient variation in the response to a drug. In a situation where a covariate may influence the response, it can be beneficial to incorporate that covariate in the Emax model. For example, if it is desired to allow for gender differences in the ED50 parameter, the Emax model can be modified as in Eq. (9.6), R E0 + -Di X Emax-- + si (9.6) In Eq. (9.6), a fifth parameter is added to the...

## Sample Determined Step Down Method

Consider the set of partitioning hypotheses Hq Doses i (i e I) are not effective but doses j (j I) are effective for all I c 1, ,k . The partitioned parameter space for k 2 is illustrated in the left plot of Figure 12.3. Similarly, a level-a test for H0I, Doses i (i e I) are not effective, is a level-a test for . As there are 2k potential null hypotheses, applying a multiple comparison method to each of the H0I would be computationally inefficient especially when k is large. Sample-determined...

## Parallel Designs versus Crossover Designs

In a fixed-dose parallel group design, a patient receives the same treatment for the duration of the trial. In contrast, in a crossover design, each patient receives a sequence of treatments during two or more study phases. Multiple sequence groups are used. Each has a different order of treatments, to account for any trends (such as disease progression or seasonal variation). For instance, in a 2 x 2 crossover design, a subject is randomized into one of two sequences. For one sequence, the...

## Review of Basic Elements of Pharmacodynamics

Pharmacodynamics describes the concentration-effect relationship. The concentration is usually considered to be at the site of action and drug effects occur immediately in proportion to concentration. Delayed effects in relation to concentrations at other sites (e.g., plasma) are discussed below. The law of mass action predicts the equilibrium occupancy of a receptor by a drug binding to the receptor-binding site with affinity defined by Kd, the equilibrium dissociation constant (Eq. (6.4))....

## Fully Sequential Designs for Phase I Clinical Trials

In a clinical setting, assigning subjects one at a time may be necessary due to time and logistical constraints. The biased coin designs (Durham et al. 1994 1995) use the most recent outcome and a biased coin to determine the assignment of the next patient. These designs lose efficiency since they use the information from the most recent patient only. The moving average design (Ivanova et al. 2003) uses information from several subjects that have been assigned at the current dose and hence is...

## Special Application ofDunnetts Procedure for Binary Response

Chuang-Stein and Tong (1995) examined three approaches for comparing several treatments with a control using a binary outcome. The first approach relies on the asymptotic theory applied to the Freeman and Tukey (1950) transformation of the observed proportions. The second finds an acceptance region based on the binomial distributions estimated under the joint null hypotheses. The third approach applies Dunnett's procedure to the binary data. The authors found that for sample sizes typical of...

## Comparison of Success Probabilities in Dose Response Studies

In dose-response studies, there are usually multiple composite null hypotheses of interest. Let the notation be the same as before, with the subscript denoting the dose group. For example, let pi, i 0, 1, 2, ,k denote the success probabilities of the placebo, the lowest dose, the second lowest dose, , and the highest dose respectively. Suppose a dose i is considered effective if pi > p0 + 8, i 1, ,k, where 8 is a pre-specified non-negative quantity that reflects practical significance. Then,...

## Contents

1 Introduction and New Drug Development Process 1 1.2 New Drug Development 1.3 Nonclinical 1.3.2 Toxicology Drug 1.3.3 Drug Formulation 1.4 Premarketing Clinical 1.4.1 Phase I Clinical 1.4.2 Phase II III Clinical 1.4.3 Clinical Development for Life-Threatening Diseases 12 1.4.4 New Drug 1.5 Clinical Development Plan 1.6 Postmarketing Clinical Development 1.7 Concluding Remarks 2 Dose Finding Based on Preclinical Studies 18 2.2 Parallel Line 2.3 Competitive Binding 2.4 Anti-infective 2.5...

## Estimation of Target Doses

Once an adequate dose-response model has been chosen and successfully fitted to the data, one may proceed to estimate the target dose(s) of interest. In this chapter, we restrict our attention to the estimation of the minimum effective dose (MED), although the ideas are equally applicable when estimating other target doses. Following Ruberg (1995), the MED is defined as the smallest dose, which shows a clinically relevant and a statistically significant effect. Let A denote the clinically...

## Estimating the Starting Dose in Phase I

A strategy has been proposed to determine the highest recommended starting dose of new therapeutics in adult healthy volunteers (FDA, 2002). The draft guidance presents a fairly simple method of estimating the starting dose. The maximum recommended starting dose (MRSD) in adult healthy subjects is to be derived from the no-observed adverse effect levels (NOAELs) in toxicology studies of the most appropriate species, the NOAELs converted to human equivalent doses (HED), and a safety factor is...

## Exposure Response

Almost all clinical trials include responses measured over time. It is valuable to understand how these responses arise as a function of treatment dose and time. It is particularly important in planning and interpreting Phase IIB (dose response) and Phase III (confirmation of effectiveness) trials. This chapter describes how the dose-response relationship can be understood in pharmacological terms. It reviews the basic principles of clinical pharmacology (pharmacokinetics, pharmacodynamics, and...

## Uncertainties Affecting Clinical Trial Planning

Three major uncertainties about the DRRs were relevant to trial planning. (1) The DRRsfor the reference agent. The reference agent could not be included in this trial, for reasons beyond the scope of this discussion. Thus, the trial needed to be based on the strong (and to a large extent untestable) assumption that the reference and proposed trials' patient populations, methods, etc., would be similar enough to justify comparison of the placebo-adjusted results. The prior reference agent trial...

## Multiple Comparisons

In typical dose-response studies, more than two treatment groups are included in a clinical trial. When this is the case, it is important to understand the questions related to the objectives of the study To show a trend such that higher doses tend to have better responses or To show a particular dose is better than placebo Depending on the objective of a study, appropriate multiple comparison adjustment need to be made so that the probability of making a Type I error can be controlled under a....

## Number of Doses to be Tested

In order to cover a wide range of doses, it is desirable to study as many doses as possible. However, the number of doses that can be tested in a given study is limited. There are practical constraints in determining the number of treatment groups. Most trials with sufficient number of patients are multicenter trials. As mentioned earlier, different centers may have different recruitment rates, and imbalance in number of patients between treatment groups may exist. If this happens, the...

## Objective 2 Accuracy of Target Dose Estimation

8.3.2.1 Tolerability Target Dose Because the same data models for tolerability were used for all TI, only random differences were seen among the four TI. There was essentially no impact of allocation strategy on estimation success, as measured by the percentage of trials with a close enough estimate ( 25 ). Similarly, the differences between the regression and ANCOVA-based estimation were small. There were negligible differences among the three dose spacing patterns including an MTD group,...

## Objective 1 Power for Confirming Efficacy

For the TI 0 candidate (no efficacy), the percentages of correct trials were approximately 90 for all design and analysis combinations, confirming that the 10 Type 1 error rate was preserved as desired. For the active candidates (TI > 0), the percentage of positive trials (i.e., the power for confirming efficacy) generally increased with larger total trial size (N) and decreased as the selected number of patients was spread over more groups. Table 8.2 shows results for the TI 1 data model,...

## Phase I Clinical Trials

In a Phase I PK study, the purpose is usually to understand PK properties and to estimate PK parameters (e.g., AUC, Cmax, Tmax, to be described in next paragraph) of the test drug. In many cases, Phase I trials are designed to study the bioavailability of a drug, or the bioequivalence among different formulations of the same drug. Bioavailability means the rate and extent to which the active drug ingredient or therapeutic moiety is absorbed and becomes available at the site of drug action (Chow...

## Phase I Oncology Dose Escalation Trial

For non-life-threatening diseases, since the expected toxicity is mild and can be controlled without harm, Phase I trials are usually conducted on healthy or normal volunteers. In life-threatening diseases such as cancer and AIDS, Phase I studies are conducted with limited number of patients due to (1) the aggressiveness and possible harmfulness of cytotoxic treatments, (2) possible systemic treatment effects, and (3) the high interest in the new drug's efficacy in those patients directly. Drug...

## Postmarketing Clinical Development

An NDA serves as a landmark of the drug development. The development process does not stop when an NDA is submitted or approved. However, the objectives of the process are changed after the drug is approved and is available on the market. Studies performed after the drug is approved are typically called postmarketing studies, or Phase IV studies. One of the major objectives in postmarketing development is to establish a better safety profile for the new drug. Large-scale drug safety...

## Quadratic Model

This model is intended to capture a possible non-monotonic dose-response relationship, in either a concave (umbrella or inverted-U) shape, or a convex (U) shape. The full three-parameter model, with 9' (E0, j1, j2), is defined as f (d, 9) Eo + jid + j2d2 (10.8) If j2 > 0, the model corresponds to a U-shape, while j2 < 0 gives an umbrella-shape. A simple variation of the model above would result from replacing d with log(d) in Eq. (10.8). Since dopt -j1 2 j2 is the dose corresponding to the...

## Safety and Tolerability

The use of randomization, blinding and a concurrent placebo-controlled group reduces the bias in safety assessments during the FIH study. Prespecified safety definitions (e.g., definition of dose-limiting toxicities and MTD) and stopping rules for dose escalation also ensure that safety and tolerability data are collected in an objective manner. Many have proposed that FIH studies be open-label and without concurrent placebo controls. For objective measures that are less susceptible to bias by...

## Dose Selection for Phase II

In addition to examining dose or concentration response information from studies specifically designed to provide it, the entire database should be examined for possible desirable or undesirable PD effects that could be related to dose or concentration. If possible have an estimate from Phase I studies of the smallest dose that could provide any benefit. If quantifiable, select reasonable PD parameters to measure in Phase II in order to gain further information on the variability in PD and an...

## Sensitivity of the ED 50 Parameter

The ED50 parameter is the dose of the drug which produces half the maximal effect. A higher ED50 value indicates a higher dose is needed to produce an effect. Figure 9.3 illustrates the effect of changes in the ED50 parameter on the Emax dose-response curve. Figure 9.3. Emax Model dose-response curves with differing ED50 values.

## General Considerations for Designing Clinical Trials

Figure 7.1 illustrates data collected from a typical dose-response study, often referred to as a randomized, double-blind, placebo-controlled, fixed dose, parallel group, and dose-response design. In such a study, patients are randomized into predetermined dose groups (often including a placebo, a low dose, one or several medium doses and a high dose). Patients take the randomized dose for the planned study duration. The efficacy and safety data obtained are analyzed to evaluate the...

## Subject Population and Endpoints

Every clinical trial starts with a clinical question. Based on this question, clinical trial team members work together to draft a clinical trial protocol. This protocol serves as the design document for the trial. The results obtained from a clinical trial will help address the key clinical question. Hence, the most important study design consideration is to understand the objective(s) of the given study, and the trial is designed to collect the necessary clinical data to help answer these...

## Gate Keeping Procedure

This procedure is also known as predetermined step-down or the hierarchy procedure (Bauer and Budde, 1994 Bauer et al., 1998). In short, this procedure follows a prespecified sequence. Testing will be conducted at the 0.05 level at each stage and it will continue as long as the p-value is significant at the 0.05 level. Testing will stop at the first instance when a p-value is above 0.05. This procedure is used very frequently when there is a prior belief of a monotone dose-response relationship...

## Review of Multiple Test Procedures

Various procedures based on different contrasts of the dose means have been proposed in the literature (Ruberg, 1989, Tamhane et al., 1996, Dunnett and Tamhane, 1998). Here we will only consider step-down procedures based on pairwise contrasts because (1) as shown by Bauer (1997), only pairwise contrasts yield procedures that control the FWE even when the dose response is not monotone, (2) they are simple to use, and (3) they can be easily extended to nonnormal data by using appropriate...

## Sensitivity of the N Parameter

The slope factor (Hill factor), determines the steepness of the dose-response curve. As the slope factor N increases, the dose range, defined as the ratio of ED90 to ED 10 tightens. Hence, the larger the value of N, the more sensitive the response is to changes in the dose of the drug. Figure 9.4 illustrates the effect of a change in the slope parameter N from 1 to 3 on the Emax model dose-response curve. Figure 9.5 illustrates the dose range (ED90 ED10) as a function of the slope factor based...

## Two Main Mechanism Classes for Delayed Effects

There are two qualitatively different mechanisms linking plasma concentration time course to subsequent actions, effects, and responses. First, the drug molecule must be distributed to the site of action, e.g., at the cell surface in the extracellular fluid adjacent to a receptor. Second, a chain of events involving turnover of physiological mediators such as cyclic AMP, gene transcription factors, and proteins is required before the action is translated into an effect or clinical response. In...

## Introduction to the Emax Model

The Emax model is a nonlinear model frequently used in dose-response analyses. The model is shown in Eq. (9.1) Ri The value of the response for patient i Di The level of the drug for patient i, the concentration may also be used in many settings E0 The basal effect, corresponding to the response when the dose of the drug is zero Emax The maximum effect attributable to the drug ED50 The dose, which produces half of Emax N The slope factor (Hill factor), measures sensitivity of the response to...

## Dose Escalation

It is not always necessary to escalate to doses as high as the MTD in the FIH studies. The highest single dose tested can also be defined as the pharmacologically active dose (PAD) giving the maximal effect in the absence of toxicity (Figure 3.3). However, the estimation of the PAD from preclinical pharmacology studies may not be possible if animal models of the disease are not available or the understanding of the fundamental biochemical or physiological aspects of the mechanism of action of...

## Clinical Development Plan

In the early stage of drug development, as early as in the nonclinical stage, a clinical development plan (CDP) should be drafted. This plan should include clinical studies to be conducted in Phases I, II and III. The CDP should be guided by the draft drug label. The drug label provides detailed information on how the drug should be used. Hence, a draft label at the early stage of drug development lays out the target profile for the drug candidate. Clinical studies should be designed to help...

## Hochbergs Stepup Procedure

This is also a sample-determined stepwise procedure, similar to that in Section 12.3.2. While Holm's step-down testing is a shortcut version of thepartition testing based on Bonferroni methods, Huang and Hsu 2005 show that Hochberg's step-up testing is also a special case, or shortcut version, of a partition testing based on Simes' test. Although more powerful than Bonferroni method Holm's procedure, Simes' test Hochberg's procedure control the Type I error rate familywise error rate at a only...

## Traditional or 3 3 Design

The most widely used design in oncology is the traditional design also known as the standard or 3 3 design. According to the 3 3 design, subjects are assigned in groups of three starting with the lowest dose with the following provisions If only three patients have been assigned to the current dose so far, then If no toxicities are observed in a cohort of three, the next three patients are assigned to the next higher dose level If one toxicity is observed in a cohort of three, the next three...

## Logistic Model

The logistic model is a four-parameter model, 9' E0, Emax, ED50, 5 , defined as f d, 9 E0 Emax 1 exp ED50 - d 5 10.10 E0 is the left-asymptote parameter, corresponding to a basal effect level not the placebo effect, though , Emax is the maximum change in effect from the basal level, and ED50 is the dose that gives half of the maximum change in effect. Finally, 5 is a parameter controlling the rate of change with dose in the effect and which has a graphical interpretation as the increment over...