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Phase II Stopping Rules That Employ Response Rates and Early Progression

John R. Goffin, Dongsheng Tu

From the Juravinski Cancer Centre, McMaster University, Hamilton; and the National Cancer Institute of Canada Clinical Trials Group and Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada

Corresponding author: John R. Goffin, Juravinski Cancer Centre, 699 Concession St, Hamilton, Ontario L8V 5C2; e-mail: john.goffin{at}hrcc.on.ca

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION AUTHORS' DISCLOSURES OF... AUTHOR CONTRIBUTIONS Appendix REFERENCES

 
Purpose Phase II oncology trials traditionally have used response rate (RR) as the primary end point, but newer targeted agents require the consideration of alternative end points. High rates of early progressive disease (EPD) suggest inadequate drug activity and may be useful in the early stopping of trials. This study used a simulation to define a set of rules to assess a combined end point of RR and EPD.

Methods The simulation assumed a two-stage trial with a specified error and power. It randomly generated the true response rate, r, of the agent under study and its true rate of early progressive disease, epd, for each run of the simulation. Two pairs of parameters were specified: (r_nul, epd_nul) and (r_alt, epd_alt). A drug was considered uninteresting for further development if r was less than or equal to r_nul and epd was greater than or equal to epd_nul (ie, the null hypothesis) and interesting for further development if r was greater than or equal to r_alt or epd was less than or equal to epd_alt (ie, the alternate hypotheses). Thresholds for the required number of patients with responses, n_r and EPD, n_p, were generated for each set of parameters.

Results Thresholds for n_r and n_p that satisfied the specified error rates were generated. There was at least an 89% likelihood that a study would be stopped at the first stage of accrual if r and epd were uninteresting.

Conclusion The simulation was able to establish stopping rules by combining the RR and the EPD that achieved the desired error rates. High rates of early stopping suggest that this design could shorten phase II trials of inactive agents.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION AUTHORS' DISCLOSURES OF... AUTHOR CONTRIBUTIONS Appendix REFERENCES

 
Drug development in oncology has become increasingly resource-intensive, even as more agents come under study.^1,2 The phase II study has a limited ability to discriminate drugs that are suitable for phase III study,^3,4 and improvement of the efficiency of phase II studies could accelerate drug development.

The conventional use of response rate (RR) in phase II trials is tied to the assumption that such responses are associated with better survival. Data generally support this association,^5-8 but some drugs induce minimal response in particular settings while still improving survival.^9,10 In addition, stable disease is likely to be associated with an improvement in survival.^6,11-14 Recent drug development has been directed toward more targeted therapies. Some of these drugs are likely to cause cell death, but other agents—drugs termed cytostatic—may be more likely to induce only stabilization of disease and, as such, will require different considerations when activity is assessed.¹⁵

To monitor for at least a minimal signal of disease stabilization, one can employ the end point of early progressive disease (EPD) in phase II trials. This may be defined as progression of disease at the first point of disease remeasurement after treatment. Drugs that allow a significant proportion of the population to undergo early disease progression are potentially unattractive.

Traditional, two-stage, phase II designs with one binary end point, as developed by Fleming,¹⁶ Gehan,¹⁷ and others¹⁸ can be used to assess RR or proportions of EPD. Zee et al¹⁹ proposed a new design that would incorporate both RR and proportions of EPD as the end points in a phase II trial. The goal was to increase the likelihood of early termination of trials with agents that showed excessive early progression and a limited rate of response. The desired alternate hypothesis was to find drugs with greater than minimally specified RR or less than the specified EPD rate. Although attractive in concept, the authors found from simulations that the power of the studies with the decision rule from this design was less than that set in the design.²⁰

Chang et al²¹ considered a two-stage design of phase II trials with both RR and the EPD rate in the context of a window-of-opportunity study. Their study employed an "and" in the alternate hypothesis and included the expectation that drugs should have both a good RR and a minimal EPD rate to be attractive in a previously untreated population. They indicated that their design may be used to assess cytostatic agents or previously treated patients by switching the null and alternative hypotheses. However, their design allows for early acceptance of seemingly interesting drugs at the end of the first stage, which is not a standard practice in phase II oncology trials.

This article develops stopping rules for phase II trials by using the same framework as Zee et al.¹⁹ It employs both RR and EPD rate and can be used to assess drugs in the setting of advanced disease. An approach that is based on simulations was adopted.

	METHODS

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The simulation lets r be the true response rate of the agent that is being studied and epd its true rate of early progressive disease. In this simulation, one assumes that two pairs of parameters, (r_nul, epd_nul) and (r_alt, epd_alt), can be specified that would render a drug uninteresting for further development if r is less than or equal to r_nul and epd is greater than or equal to epd_nul and interesting for further development if r is greater than or equal to r_alt or epd is less than or equal to epd_alt. That is, we are interested in testing the following hypotheses in a phase II trial: the null hypothesis of r being less than or equal to r_nul and epd being greater than or equal to epd_nul versus the alternate hypothesis of r being greater than or equal to r_alt or epd being less than or equal to epd_alt.

This article considers the following two-stage procedure for testing the above hypotheses: In the first stage, n₁ are entered. Then, n_1r and n_1p are assumed to be the number of patients who responded and the number who had early progression among these n₁ patients, respectively. The trial would be stopped at this stage if n_1r is less than or equal to n_1r-nul and n_1p is greater than or equal to n_1p-nul, in which n_1r-nul and n_1p-nul are two thresholds determined during the design of the study. Otherwise, n₂ additional patients are entered in the second stage of the study. Let n_2r and n_2p be respectively the number of patients who responded and who had early progression among these n₂ patients. The drug will be declared interesting at the end of the second stage if n_1r + n_2r n_1r-alt + n_2r-alt or n_1p + n_2p n_1p-alt + n_2p-alt, in which n_2r-alt and n_2p-alt are another two thresholds determined during the design of the study.

Simulations were performed with TreeAge Pro Healthcare software (Williamstown, MA) to determine thresholds (program available on request). For each simulation, the following parameters were prespecified: design parameters (r_nul, epd_nul) and (r_alt, epd_alt), desired power and error of the study, and the number of patients in the first stage (n₁) and second stage (n₂). For each set of potential thresholds, 1,000,000 simulations were run to assess the error and power of the study as the frequency of rejection of the null hypothesis. The final set of thresholds was selected as the one which yielded the error and power closest to that specified. When the error or power could be better than specified, this was permitted if it did not worsen the other error. The r and epd in each of the simulations were generated by using one of the following two methods:

The full-space method, for simulations of the alternative hypothesis, used a weighted probability (that was based on the space created by the selected [r_alt, epd_alt] parameters) to randomly select a value for r or epd from within the range of interest. Thus, either r greater than or equal to r_alt or epd less than or equal to epd_alt is generated. The remaining parameter then is randomly selected from the values that satisfy r + epd 1.

For simulations of the null hypothesis, the same method was used, but r and epd both were required to satisfy r less than or equal to r_nul and epd greater than or equal to epd_nul.

The borderline-value method assumed that extremely desirable values for r and epd were unlikely and that the inclusion of such values in assessed populations would under-power a study to detect drugs with borderline r or epd characteristics. In the borderline-value method, cohorts to assess the alternate hypothesis were generated by randomly assignment of r as r_alt or epd as epd_alt. The nonprecedent parameter then was randomly assigned a value within its noninteresting range (ie, r r_alt or epd epd_alt) such that r + epd 1. Cohorts for the null hypothesis assessment were generated as described for the full-space method.

	RESULTS

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Thresholds Created by the Full-Space Method
Table 1 indicates the patient thresholds required for acceptance or rejection of the null hypothesis after stage 1 and 2, when drugs of interest were assumed to have r greater than or equal to r_alt or to have epd less than or equal to epd_alt. Power was specified at .80; error was specified at .05; 15 patients were assessed in each stage.

In all assessments of these thresholds by the full-space method, the error rates achieved were better than required. Table 1 also indicates the expected average study size when a drug met either the criteria of interest or disinterest. As expected with the low value, studies in which uninteresting drugs were assessed had greater than 96% likelihood of stopping at the first stage; this provided a corresponding average accrual number just greater than 15, which was the number of patients recruited at stage 1.

Thresholds Created by the Borderline-Value Method
Despite the apparent high power in Table 1, drugs with r or epd of marginal but passable levels of interest may not be detected. The borderline-value method generated drugs with either r equal to r_alt and epd greater than epd_alt or with epd equal to epd_alt and r less than r_alt. Table 1 lists thresholds generated by the full-space method that have poor power to detect such borderline drugs.

However, the power and error met the specified values with the use of thresholds designed for such borderline-value drugs, as indicated in Table 2. Compared with the thresholds generated in Table 1, the borderline-value method generated threshold pairs for the alternate hypothesis that were more generous; n_1r+ n_2r is lower and n_1p+ n_2p is higher. Thus, if the borderline-value thresholds are applied to assess a population of drugs generated by the full-space method, the power increases to greater than .97 in all cases, and the errors remain essentially unchanged (data not shown).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION AUTHORS' DISCLOSURES OF... AUTHOR CONTRIBUTIONS Appendix REFERENCES

Two different methods to determine patient thresholds for response and EPD are described. The full-space method simulates drugs, and r and epd are chosen from throughout the ranges relevant to the null or alternate hypothesis. It is attractive in its absence of bias or presupposition about the characteristics of the drugs under study. As indicated in Table 1, thresholds were generated that met the specified error rates. The power is greater than required so that the thresholds detect drugs with either a favorable RR or a favorable EPD rate. A lesser power could have been chosen but would have been without gain, as the error was sufficiently low.

Thresholds generated by the full-space method may dismiss drugs of marginal activity that still meet the alternate hypothesis, as listed in Table 1. In contrast, the borderline-value method creates thresholds that assume marginal activity for a drug and achieves the specified power and error rates (Table 2). A sensitivity analysis (Table 4) on the basis of the borderline method shows small changes in error rates. Thresholds did not change in every case, partly because of the model's intent on preserving power. A larger sample size did not necessarily lead to better power; the parameter set (n₁ = 20, n₂ = 20; null hypothesis, r 0.05 and epd 0.6, versus alternate hypothesis, r 0.2 or epd 0.4) did not result in a need for the program to reconcile overlapping thresholds for the null and alternate hypotheses, an instance that contributes to improved error at the expense of β error.

In addition, Table 3 lists thresholds created by drugs that have borderline characteristics for both cohorts of interest and of disinterest. The rules fail to meet the specified error rate, which could only be improved at the expense of power.

Although extremely good drugs are unlikely to exist, poor drugs are more frequently encountered; RRs near zero are observed in early trials, and the EPD rate can be high in advanced or pretreated disease. Therefore, the value of rules designed to sensitively detect drugs of only borderline disinterest is doubtful. The utility of the parameters of Table 3 is in indicating the limits of such rules.

Other cohorts of drugs could be used to generate thresholds that have distributions that favor particular portions of the space of interest or disinterest. The difficulty is in knowing what RR or EPD rate distribution would be likely. For practical reasons, we favor the thresholds capable of detecting drugs of borderline interest as generated for Table 2.

The initial paper that added EPD to the assessment of phase II trials was found later by its authors to have poorer power than intended.^19,20 That paper differs from the present paper in the employment of multiple pairs of threshold criteria that reject the null hypothesis. Because the alternate hypothesis is designed to detect drugs with either interesting parameter, a single pair suffices. However, that initial paper indicated the importance of the detection of drugs with minimal but sufficient activity, and it supports the use of rules of Table 2.

Unlike this article, Chang et al²¹ designed a trial to allow acceptance of a drug after the first stage of accrual, which may be appropriate for extremely active drugs or limited resources. In a heterogeneous population, many investigators prefer to accrue additional patients. This will modestly improve the confidence intervals around outcome rates and will allow better planning of phase III studies for drugs with marginal activity. Correspondingly, desired error rates may be difficult to achieve after only the first stage of accrual; after stage 1, in Table 2, error rates were .06, .11, .11, and .12 respectively.

The consequence of rejection of the null hypothesis at stage 1 can be shown. Chang et al²¹ indicate that their hypotheses can be reversed and give one example with the hypotheses set as in the present paper. By using specified parameters (power = .8; alpha = .05; n₁ = 21, n₂ = 21; null hypothesis, r 0.4 and epd 0.3, versus alternate hypothesis, r 0.6 or epd 0.1), their method rejects the null hypothesis at stage 1 if n_1r is greater than or equal to 15 or if n_1p equals 0, accepts the null hypothesis if n_1r is less than or equal to seven and if n_1p is greater than or equal to five, and it otherwise accrues stage 2. At the second stage, if n_1r + n_2r 23 or n_1p + n_2p 6, the null hypothesis is rejected; otherwise, it is accepted and achieves = .0494 and power = .804. With the same parameters, our borderline model accepts the null hypothesis at stage 1 if n_1r is less than or equal to 10 and if n_1p is greater than or equal to five and otherwise continues to stage 2. At the second stage, if n_1r + n_2r 21 or if n_1p + n_2p 8, the null hypothesis is rejected, and = .0145 and power = .890. The thresholds given by Chang et al,²⁰ thus, are more likely to reject the null hypothesis at stage 1 but are less likely to do so at stage 2. This results, most likely, from their method that allows early rejection of the null hypothesis at stage 1 and thus needs to provide less liberal rejection criteria at stage 2 to achieve the desired error.

By applying the rules of Zee et al¹⁹ to 39 completed, phase II trials that were assessed by RR only, Dent et al²² found that rules that incorporated EPD were more likely to stop apparently ineffective drugs at the first stage of accrual. Conversely, after stage 2, the method of Zee et al¹⁹ suggested activity in two instances, whereas the method of Fleming¹⁶ did not. The disputed drugs were not additionally studied, so activity could not be confirmed. The study of Dent et al²² demonstrates the potential for more frequent early stopping of inactive drugs as well as the unconfirmed possibility that rules that incorporate EPD may be more sensitive to drug activity.

Another potential benefit to the use of EPD, as suggested by Zee et al,¹⁸ is that its presence can be determined at first tumor measurement, even if responses can not be fully assessed; this information may allow rapid commencement of stage 2 of accrual after stage 1 is completed, which would allow avoidance of the delay induced by waiting for potential responses.

Although the described method capably arrests the study of inactive drugs after stage 1, the "or" alternate hypothesis may best be applied to situations in which only modest drug activity is expected. Cytostatic agents or populations with poor rates of expected response (eg, pancreatic cancer) still may accrue benefit from nonprogressive disease, and low EPD rates may indicate drugs worthy of further consideration. Alternatively, drugs active against specific biologic subsets of disease (eg, trastuzumab) may demonstrate some responses but otherwise demonstrate little stable disease if assessed in unselected populations. In the above situations, the demands of an "and" alternate hypothesis may result in drug discard. Conversely, the ethics of window-of-opportunity studies demand that only the most active drugs continue to stage 2, which supports the use of an "and" hypothesis.

The assessment of EPD in addition to response could shorten phase II studies through early stopping when the EPD rate is undesirably high. Although EPD may also increase the sensitivity of phase II studies to drug activity, this must be confirmed and will depend on the criteria of the alternate hypothesis. This article creates rules for an alternate hypothesis that allows a drug to be considered interesting if the criteria are met for either a sufficiently high RR or a sufficiently low rate of EPD. It is hoped that the use of such rules may improve drug development.

	AUTHORS' DISCLOSURES OF POTENTIAL CONFLICTS OF INTEREST

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION AUTHORS' DISCLOSURES OF... AUTHOR CONTRIBUTIONS Appendix REFERENCES

 
The author(s) indicated no potential conflicts of interest.

	AUTHOR CONTRIBUTIONS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION AUTHORS' DISCLOSURES OF... AUTHOR CONTRIBUTIONS Appendix REFERENCES

 
Conception and design: John R. Goffin, Dongsheng Tu

Collection and assembly of data: John R. Goffin

Data analysis and interpretation: John R. Goffin, Dongsheng Tu

Manuscript writing: John R. Goffin, Dongsheng Tu

Final approval of manuscript: John R. Goffin, Dongsheng Tu

	Appendix

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION AUTHORS' DISCLOSURES OF... AUTHOR CONTRIBUTIONS Appendix REFERENCES

 
Detailed Methods Section of Phase II Stopping Rules That Employ Response Rates and Early Progression. The simulation lets r be the true response rate of the agent under study and epd its true rate of early progressive disease. Assume that one can specify two pairs of parameters, (r_nul, epd_nul) and (r_alt, epd_alt), which would render a drug uninteresting for further development if r is less than or equal to r_nul and epd is greater than or equal to epd_nul and less interesting for further development if r is greater than or equal to r_alt or epd is less than or equal to epd_alt. That is, in a phase II trial, we are interested in the testing of the following hypotheses: the null r less than or equal to r_nul and epd greater than or equal to epd_nul versus alternate hypothesis: r greater than or equal to r_alt or epd less than or equal to epd_alt.

This article considers the following two-stage procedure for the testing of the above hypotheses: In the first stage, n₁ are entered. If n_1r and n_1p are, respectively, the number of patients who responded and had early progression among these n₁ patients, the trial would be stopped at this stage if n_1r was less than or equal to n_1r-nul and if n_1p was less than or equal to n_1p-nul, in which n_1r-nul and n_1p-nul are two thresholds determined during the design of the study. Otherwise, n₂ additional patients are entered in the second stage of the study. Let n_2r and n_2p be, respectively, the number of patients who responded and had early progression among these n₂ patients. The drug will be declared as interesting at the end of the second stage if n_1r + n_2r n_1r-alt + n_2r-alt or n_1p+ n_2p n_1p-alt + n_2p-alt, in which n_2r-alt and n_2p-alt are another two thresholds determined during the design of the study.

Simulations were performed by using TreeAge Pro Healthcare software (Williamstown, MA) to determine thresholds (program available on request). For each simulation, the following parameters were prespecified: design parameters (r_nul, epd_nul) and (r_alt, epd_alt), desired power and error of the study, and the number of patients in the first stage and second stage. Patient cohorts for error assessment of thresholds were generated as integer pairs of actual r and epd by two methods: the full-space method and the borderline-value method.

In the full-space method, simulations of the alternative hypothesis randomly select a value for either r or epd from within the range of interest. The choice of precedence of r or epd was assigned randomly on the basis of a frequency assessment of the overall potential space in which a drug would have a value of r greater than or equal to r_alt and/or epd less than or equal to epd_alt. Thus, either r greater than or equal to r_alt or epd less than or equal to epd_alt is generated. The remaining (nonprecedent) parameter then was selected randomly from the values that satisfy r + epd 1. In Figure A1, for example, a pair of r and epd would be selected with equal probability from anywhere above and/or left of the line of border for values of interest (ie, a line defined by r_alt = 20% and epd_alt = 40%).

View larger version (25K): [in this window] [in a new window] [PowerPoint Slide for Teaching]   Fig A1. Patient thresholds to achieve specified error rates (Note: n = 30, 1-β = 0.8, = 0.05).

The borderline-value method assumed that extremely desirable values for r and epd were unlikely and that inclusion of such values in assessed populations would under-power a study to detect drugs with borderline r or epd characteristics. In the borderline-value method, cohorts for the assessment of the alternate hypothesis were generated by random assignment of r = r_alt or epd = epd_alt. The nonprecedent parameter then was randomly assigned a value within its noninteresting range (ie, r < r_alt or epd > epd_alt), such that r + epd 1. Cohorts for the null hypothesis assessment were generated as described for the full-space method.

Successive patient thresholds for n_r-alt and n_p-alt and for n_r-nul and n_p-nul were run through 10⁶ simulations of randomly generated r and epd values (by using either the full-space or borderline-value method) to determine the power or error that each would generate. Fig A1 demonstrates that the desired power can be achieved with different threshold pairs. With the parameters of = .05, power = .8, n = 30 in a single stage, r_alt = 0.20, r_nul = 0.05, epd_alt = 0.4, and epd_nul = 0.6, several pairs of n_r-alt and n_p-alt might be taken that achieve the required power. To miss the fewest number of drugs that fall near the borderline acceptable values, the method selects the most generous combination of the pairs, in this instance combining the n_r-alt = 8 from the program generated option 2 with the n_epd-alt = 10 from option 3. For power in the borderline value method, thresholds were taken when possible from pairs that did not encroach on the area of disinterest.

More than one pair could be taken for the error thresholds, as such pairs could encompass different areas of r_nul and epd_nul. The program preferentially selected thresholds in which neither n_r-nul nor n_p-nul overlapped with thresholds for the alternate hypothesis; in instances of overlap, thresholds were reconciled such that the thresholds for power were given precedence.

After the thresholds were determined for stages 1 and 2, cohorts were run through a two-stage trial by using 10⁶ simulations.

	NOTES

 
Supported by a grant from the Amgen Career Development Award (J.R.G.).

Presented in part at the 43rd Annual Meeting of the American Society of Clinical Oncology, June 1-5, 2007, Chicago, IL.

Authors' disclosures of potential conflicts of interest and author contributions are found at the end of this article.

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Submitted August 21, 2007; accepted January 3, 2008.

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• Problems Identified With Phase II Stopping Rules That Employ Response and Early-Progression Rates
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  JCO 2009 27: 646-647 [Full Text]

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