Modeling the relationship between progression-free survival and overall survival: The phase 2/3 trial

Abstract

The standard phase 2 trial design has changed dramatically over the last decade. Randomized phase 2 studies have essentially become the standard phase 2 design in oncology for a variety of reasons. The use of these designs is motivated by concerns regarding the use of historical data to determine if a new agent or regimen shows promise of activity. However, randomized phase 2 designs come with the cost of increased study duration and patient resources. Progression-free survival (PFS) is an important endpoint used in many phase 2 designs. In many clinical settings, changes in PFS with the introduction of a new treatment may represent true benefit in terms of the gold standard outcome, overall survival (OS). The phase 2/3 design has been proposed as an approach to shorten the time to discovery of an active regimen. In this a paper design considerations for a phase 2/3 trial are discussed and presented in terms of a model defining the relationship between OS and PFS. The design is also evaluated using 15 phase 3 trials completed in SWOG between 1990 and 2005. The model provides a framework to evaluate the validity and properties of a employing a phase 2/3 design. In the evaluation of SWOG trials, 3 of 4 positive studies would have also proceeded to the final analysis and 10 of 11 negative studies would have stopped at the phase 2 analysis, if a phase 2/3 design had been used. Through careful consideration and thorough evaluation of design properties, substantial gains could occur using this approach.

Introduction

The standard phase 2 trial design has changed dramatically over the last decade. Randomized phase 2 studies have essentially become the standard phase 2 design in oncology for a variety of reasons. The use of these designs is motivated by concerns regarding the use of historical data to determine if a new agent or regimen shows promise of activity. These concerns stem from the preponderance of failed phase 3 trials in cancer research. When systematic differences exist between the study population and the historical control population or in the assessment of outcomes between the two populations, then evaluations of efficacy may be subject to bias, resulting in false leads or missed opportunities. While overall survival (OS) generally remains the primary endpoint in most phase 3 trials, progression-free survival (PFS) instead of response rate is increasing used in the phase 2 setting. As noted by Zhang et al (1), PFS assessment can be subject to bias based on the assessment schedule, consistency of evaluators, and a number of other factors.

Randomized Phase 2 studies can demand significant time and patient resources to conduct. (2,3) They are typically two to four times larger than single arm trials, and relative to phase 3 studies, they generally require similar levels of review and include the same degree of effort to initiate and conduct. Therefore, a well-designed randomized phase 2 trial may require a significant effort and time to complete, delaying the time to a definitive answer.

To address the afore-mentioned efficiency concerns, numerous authors have promoted a combination of a randomized phase 2 and phase 3 studies. (4–11) In essence, a randomized phase 2/3 design is a randomized phase 3 design with a very early look which can only stop for futility, but not for early signs of efficacy. (6) This early interim analysis may use an alternative endpoint other than the primary endpoint for the phase 3 trial; for example PFS may be used for the first interim analysis, when the primary endpoint for the final analysis is OS. At this interim analysis the go/no go decision conforms closely to the positive/negative conclusion from a typical randomized phase 2 trial, and as such there is a higher probability of stopping early for futility than with the typical early interim analysis.

In general, the most clinically meaningful outcome continues to be OS. However, as discussed by Korn and Crowley (12) and Villaruz and Socinski (13), PFS is becoming an endpoint thought to have clinical merit in its own right. In this article we discuss design considerations for a phase 2/3 study using PFS as the primary endpoint for the phase 2 component and OS as the primary endpoint for the phase 3. This necessitates making certain assumptions about the relationship between PFS and OS. Design options and qualifications are evaluated using a motivating example. In addition, to explore the validity of the proposed model, PFS and OS data from published phase 3 studies involving an FDA approved agent, or thought to be practice changing, are used. The paper concludes with an evaluation of the properties when applied to phase 3 trials completed by SWOG. To anchor this discussion of phase 2/3 designs we propose the following as the basic foundation for designing a phase 2/3 trial.

Design Considerations for Phase 2/3 Trials

The standard randomized phase 2 design using PFS as the primary endpoint will target larger improvements than the follow-on phase 3 using OS, and employ type I error rates between 10–20%. (14) While such a design may be based on improvement in PFS, interpretation of trial results often take into consideration multiple pieces of information such as OS, response, and toxicity. In contrast, a phase 2/3 requires the specification of one rule. The phase 2 component of a phase 2/3 trial is a modification of the stand-alone phase 2 design, using similar effect sizes and error rates. The first interim analysis in a phase 2/3 trial is considered the phase 2 analysis, with the analysis time determined based on the number of events defined by the phase 2 parameters. Futility is established at this interim analysis if the alternative hypothesis is rejected at 1-power of the phase 2 or equivalently, if the study fails to reject the null hypothesis at the type I error rate of the phase 2. Therefore in the design of a phase 2/3 trial it is important to evaluate the proposed model and design choices as a unified study rather than simply combining phase 2 and 3 study designs.

Steps to design a phase 2/3 trial:

1. Determine if the setting is appropriate

2. Define the assumed relationship between the phase 2 and phase 3 endpoints

3. Define the phase 2 and phase 3 study parameters: target effect measure and size, type I and type II error rates

4. Evaluate phase 2 designs in terms of feasibility/timeliness of analysis and impact on phase 3 design properties

5. Evaluate the properties of the phase 2/3 design and adjust design parameters if necessary

Methods

Each specific step to design a phase 2/3 study is discussed below. Step 1 is discussed in terms of key considerations. Step 2 is discussed by presenting a possible model to define the association between PFS and OS. The discussion of Step 3 uses this model to determine the study parameters. The discussion of this step is further given by example of where a phase 2/3 design might be appropriate. A literature review of phase 3 studies reporting on PFS and OS is used to evaluate the proposed model. Finally, to evaluate the performance of a phase 2 interim analysis on completed phase 3 studies, a “phase 2 analysis” is performed on phase 3 studies led by SWOG between 1990 and 2005 which included OS as the primary outcome.

Determine if the setting is appropriate

The first step, determination of appropriateness, is less based on statistics and trial design issues than on subject matter knowledge. Specifically, within in a disease setting and treatment type, there has to exist an intermediate outcome (such as PFS) for which it is expected that a treatment effect on this outcome represents an effect on the primary outcome (such as OS). It would seem that the most appropriate setting would be in more advanced disease with limited numbers of effective therapies available for post-progression treatment. Of note, one could design a phase 2/3 study using the same endpoint for the phase 2 component as for the overall trial; however there will not be the same reduction in time and patient savings relative to using an earlier endpoint for the phase 2 component. In terms of evaluating the feasibility of this approach, the event rate is likely quite important because the basis for using such a design is time savings. If the rates are low, then in order for the sample size to in the phase 2 range, the phase 2 analysis would require a temporary closure to accumulate enough events. In this case, it is important to consider how feasible it would be to conduct such a study, because such an interim analysis may be more informative than the standard interim analysis and could impact the integrity of the trial.(15,16)

Define the assumed relationship between the phase 2 and phase 3 endpoints

Given that continuation of a phase 2/3 design past the phase 2 interim analysis is based solely on a rule defined for the phase 2 endpoint, it should be the case that differences in the phase 2 outcome capture the effect of treatment on the phase 3 outcome. In the context of PFS and OS, this assumption would indicate that all or almost all of the treatment benefit occurs before progression, and most of the difference in OS is due to differences in progression. This assumption is consistent with the criteria put forward by Prentice (17) in specifying the necessary conditions for a surrogate endpoint. Specifically, a key component of the criteria is that the surrogate endpoint captures any relationship between the treatment and the primary endpoint.

In order to describe the relationship between PFS and OS, we use the model proposed by Goldman and colleagues (18). The model is a mixture of survival distributions specified in terms of the time to progression (TTP), time to death without progression (S_pre), and time to death following progression (S_post). Figure 1 depicts this model with \lambda_{P}^{c}\left( t\right) ,\lambda_{Pre}^{c}\left( t\right),\lambda_{Post}^{c}\left( t\right) representing the hazard rates at time t for the survival distributions for TTP, S_Pre, and S_Post, for the control treatment (c=0) and the experimental treatment (c=1). The observed values for PFS and OS are: PFS = min{TTP, S_pre) and OS = S_Pre if a patient dies before progression and OS = TTP+S_Post, if the patient progresses before death. It follows, that if TTP and S_Pre are exponentially distributed, then so is PFS with hazard rate of \lambda_{P}^{c}+\lambda_{Pre}^{c}. However, as was shown in (18), in this model OS is not exponentially distributed even when there are constant rates of transition between the states defined by progressive disease or death, so that hazard rates for survival are not constant over time. The hazard ratio (HR) for OS in this model is the HR averaged over the observation time period.

Figure 1.

Proposed model for the association between progression and death

As depicted in Figure 1, treatment has an indirect effect on survival time through its effect on time to progression and a direct effect on death. If the main effect of treatment is through an indirect effect on survival due to an effect on progression, then progression represents a surrogate, and λ_Pre is zero, or close to zero. However, perhaps even with a small risk of death before progression, it could well be assumed that \lambda_{Pre}^{c} does not vary across treatment arms, and then the PFS HR is smaller than the TTP HR. Additionally, if \lambda_{Pre}^{c}\left( t\right) is a function of time, then the PFS HR is not constant over time.

Define the phase 2 and phase 3 study parameters

Design of the phase 2 and phase 3 components require specification of the effect measure and target effect size, and the type I and type II error rates. The phase 2 parameters will be defined in terms of the phase 3 design. In this setting, the type I and type II error for the phase 2 component are more accurately stated in terms of the phase 3 endpoint: that is, the phase 2 type I error occurs if the null hypothesis that there is no difference in PFS is rejected when there is in fact no difference in OS. Likewise a phase 2 type II error occurs if the conclusion is that there is no difference in PFS when in fact there is a difference in OS.

Since the phase 2 interim analysis is much more aggressive than standard interim analysis boundaries, this analysis has a greater impact on the study design properties. For example if both phase 2 and 3 designs specify 90% power, the adjusted power is 81%. (6) Therefore, depending on the power of the phase 2, the adjusted power of the phase 3 could be significantly decreased.

Determination of the effect measures and sizes for the two outcomes is more complicated. Quite often, while studies are designed to evaluate the HR between two treatment arms, clinically meaningful benefits are defined in terms of the difference in medians or percentage alive at a given time point. Under the model proposed, the multiplier that defines the relationship between the hazard ratio for PFS and OS is a time-varying function of the post-progression hazard rate and the hazard rates for PFS on both treatment arms. When the hazard rate for survival post-progression is larger, that is when time between progression and death is shorter, the multiplier is closer to one and the hazard ratios for PFS and OS are more similar. It follows that in this situation, the ratio of medians is smaller than the average HR.

Assuming PFS is a perfect surrogate for OS, the HR for OS (\Lambda _{OS}) at time t can be shown to be product of the HR for PFS (\Lambda _{PFS}) and a function of the survival functions for PFS and survival post progression as follows:

• \Lambda _{OS} &=&\Lambda _{PFS}\ast c,\ c<1..

Here the multiplier is generally less than 1, implying that the Λ_PFS is generally some factor larger than \Lambda _{OS}. However, given that the target in clinical terms is usually both a hazard ratio and a difference in medians, the approach we use here is to “attribute” the targeted absolute difference in median OS to PFS to determine clinically meaningful hazard ratios. This does ignore that OS does not have proportional hazards in this model.

This model, while likely also not correct, highlights that in design and analysis the true model is generally unknown, but for practicality and consistency across studies, standard analysis approaches such as use of the log-rank test statistic or Cox regression are generally used. It is most likely that the deviations from proportional hazards and constant hazards will result in a reduction in power, but by averaging over the times, a meaningful measure is given. Again, this emphasizes the importance of evaluating the design using the proposed analysis approach.

Evaluate of feasibility and design properties

To demonstrate the evaluation of feasibility of design properties, the motivating example employed here is treatment of extensive stage small cell lung cancer (E-SCLC). The standard of care for E-SCLC has essentially been a platinum-agent (cisplatin) in combination with etoposide for more than 20 years. (19) Median survival is around 9–10 months, and median progression-free survival is around 5 months. Moreover, to date, only topotecan has been approved by the Food and Drug Administration for the second line treatment of SCLC, and its efficacy is quite modest. This highlights a setting where there is a desperate need to improve care and to do so quickly.

Using this example in E-SCLC, candidate designs for the phase 2 component of a randomized phase 2/3 were determined and compared with a stand-alone phase 2 and phase 3. A design targeting a 3-month improvement in median survival would be considered clinically valuable. Therefore, these designs targeted a 33% improvement in median survival, from 9 months to 12 months. Appling the 3 month difference to PFS, this would be equivalent to a 60% improvement in median PFS, from 5 to 8 months. The sample sizes were determined based on a uniform accrual rate of 20 patients/month. Four follow-up scenarios were considered: no, 3, 6, and 9 months of follow-up. A stand-alone randomized phase 2 would likely employ 9 months of follow-up. Table 1 details the required events and sample size for varying levels of type I and type II error rates.

Table 1.

Phase 2 Trial Designs for SCLC

Type I, type II error	Events	Sample Size (Analysis time)
		No follow-up	3 months follow-up	6 months follow-up	9 months follow-up
15%,15%	78	198 (10 mths)	150 (11 mths)	124 (13 mths)	108 (15 mths)
15%,10%	97	218 (12 mths)	180 (12 mths)	150 (14 mths)	132 (16 mths)
15%, 5%	130	266 (14 mths)	218 (15 mths)	192 (16 mths)	172 (18 mths)
10%,10%	120	256 (13 mths)	206 (14 mths)	178 (15 mths)	160 (17 mths)
10%, 5%	155	294 (16 mths)	252 (16 mths)	220 (18 mths)	200 (20 mths)
5%, 5%	197	350 (18 mths)	298 (19 mths)	268 (20 mths)	248 (22 mths)

Table 1 demonstrates that a phase 2/3 design is quite feasible in this setting with a relatively short time to the phase 2 analysis, and modestly small sample sizes even for the setting with no follow-up. In fact, because of the rapid event rate, for all of the designs the phase 2 interim analysis with no temporary closure for additional follow-up occurs at the same time or before the designs with follow-up, including the stand-alone randomized phase 2 design.

As discussed above, design of the phase 3 component of a phase 2/3 requires the choice of either a study with lower adjusted power or an increase in the phase 3 power to recover the power loss from the phase 2 analysis. A stand-alone phase 3 design with 81% power would require 506 patients with an expected analysis time of 38 months, whereas a phase 2/3 with adjusted 81% power (90%*90%) would require 638 patients with an analysis time of 44 months. A stand-alone phase 3 design with 86% power would require 570 patients with an expected analysis time of 41 months, whereas a phase 2/3 with adjusted 86% power (95%*90%) would require 764 patients with an analysis time of 51 months. These designs use the design parameters stated above, a 1-sided 2.5% log-rank test for significance (assuming exponential survival) and 12 months of follow-up. Therefore, using a stand-alone phase 2 with 10% error rates (see Table 1), a stand-alone phase 2 followed by a phase 3 with 81% power would require 666 patients (160+506) and a total study period of 55 months, whereas the phase 2/3 would require 638 patients and total study period of 44 months. Similarly, a phase 3 with 86% power would require 730 patients (160+570) and a total study period of 58 months for the stand-alone studies and 764 patients and a total study period of 51 months for the phase 2/3. Therefore this demonstrates in the given setting, a phase 2/3 design would reduce the time to a definitive answer relative to the traditional phase 2 followed by phase 3 designs.

Evaluation of PFS and OS in literature review

In the literature review of phase 3 studies, 8 breast cancer (20–27), 13 colorectal (28–40), 11 kidney (41–51), 4 leukemia (52–55), 10 lung and mesothelioma (56–65), 1 lymphoma (66), 6 myeloma (67–72) and 2 prostate cancer (73–74) publications were identified. To evaluate the relationship between PFS and OS, the absolute difference in median PFS and OS, the ratio of median PFS values and the PFS HR, and the ratio of median OS values and the OS HR were compared using linear regression. These data are presented in Figure 2. Panel A presents the association between the difference in median PFS and OS. The blue line represents equality between change in OS and PFS and the red line presents the regression of the difference in median OS on the difference in median PFS. The regression coefficient for PFS is 0.89 and is statistically significant at level < 0.0001. Panel B presents the association between the PFS HR and the OS HR. Again, the blue line represents equality and the red the regression line. While the magnitude of association was significantly less than the association with the absolute difference in medians, the PFS HR was statistically associated with the OS HR at level 0.04, with a regression coefficient of 0.28. Panels C and D present the comparisons of the ratio of medians to the HRs for PFS and OS. Both values were highly statistically significant at level <0.0001 with coefficients of 0.72 for the PFS comparison and 0.70 for the OS comparison, indicating the HRs for PFS and OS are reasonably well represented by the ratio of medians.

Figure 2.

Comparison of measures of PFS and OS in literature review

Panel A: A comparison of the absolute difference in median PFS with the absolute difference in median OS.

Panel B: A comparison of the HR for PFS with the HR for OS

Panel C: A comparison of the ratio of median PFS values with the HR for PFS

Panel D: A comparison of the ratio of median OS values with the HR for OS

The blue lines represent equality between the X and Y axis, the purple lines represent the fitted regression values.

Phase 2/3 Evaluation of SWOG trials

SWOG provided an opportunity to evaluate this approach on real data. Fifteen phase 3 trials which included OS as the primary endpoint and had data on either PFS or relapse-free survival run through SWOG between 1990 and 2008 were identified. (75–88) Table 2 includes a description each of these trials, including the disease setting, treatments, and design properties. Of these trials four were positive and the remaining 11 studies failed to reject the null hypothesis.

Table 2.

SWOG Trial Description

Study		Design							Observed Data
		N	Years		Control Arm Outcomes	Target HROS	α	Power	Accrual		Control Arm Outcomes	Stop Time	Result
	Disease		Accr	FUP					Years
S879782	Early stage cervical	240	5.5	4	5-yr OS: 60%	1.78	0.05	0.85	262	6.3	5-yr OS: 66%	Final	Positive
(GYN)					5-yr PFS: 56%	(1.5)^					5-yr PFS: 62%
S900881	stomach or GI junction	550	5.5	2	Med OS: 30m	1.4	0.025	0.9	573	7	Med OS: 27m	Final	Positive
(GI)					Med RFS: 20m						Med RFS: 19m
S930887	Advanced NSCLC	400	2.5	1	Med OS: 6m	1.33	0.05	0.88	415	1.5	Med OS: 6m	Final	Positive
					Med PFS: 2m						Med PFS: 2m
S931380	high risk stage I/II	3000	3.75	5	5-yr OS: 93%	1.45*	0.05	0.9	3126	3.1	5-yr OS: 88%	Final	Negative
(Breast)					5-yr DFS: 86%						5-yr PFS: 80%
S932175	Multiple myeloma	500+	4	3	Med OS: 3y	1.33	0.05	0.81	519	9.8	Med OS: 4.9y	Final	Negative
(Mmyel)					Med PFS: 1.3y						Med PFS: 1.8y
S941585	high risk stage II and stage III colon	1500	6.5	3.5	Med OS: 9.3y	1.35	0.05	0.95	1004	5	Med OS: 10.9y	Interim	Negative
(GI)					Med DFS: 8.5y						Med DFS: 9.4y
S942079	Colorectal	700	3.5	1.5	Med OS: 15m	1.33	0.025	0.9	723	4.1	Med OS: 13m	Final	Negative
(GI)					Med PFS: 6m						Med PFS: 5m
S943886	Non-Hodkin	206+	5	2	2-yr OS: 40%	1.5	0.05	0.82	194	10	2-yr OS: 74%	Final	Negative
(Lymph)					2-yr DFS: 30%						2-yr DFS: 73%
S950976	Advanced NSCLC	400	1.33	1	Med OS: 8m	1.5	0.025	0.94	415	1.8	Med OS: 9m	Final	Negative
(Lung)					Med PFS: 4m						Med PFS: 4m
S991683	advanced refractory prostate	620	3.5	1	Med OS: 18m	1.33	0.025	0.8	716	3.3	Med OS: 16m	Final	Positive
(GU)					Med PFS: 4m						Med PFS: 3m
S0001	glioblastoma and gliosarcoma	375	5	2	Med OS: 12m	1.4	0.05	0.925	179	4.2	Med OS: 10m	Interim	Negative
(Brain)					Med PFS: 5m						Med PFS: 4m
S000388	Advanced NSCLC	500	1.67	1	Med OS: 8m	1.375	0.025	0.88	376	2	Med OS: 9m	Interim	Negative
(Lung)					Med PFS: 4m						Med PFS: 4m
S002377	Stage III, NSCLC	672+	3.5	2.5	Med OS: 21m	1.33	0.025	0.89	250	4.2	Med OS: 32m	Interim	Negative
(Lung)					Med PFS: 7m						Med PFS: 10m
S012478	Extensive stage 1st line	620	4	1	Med OS: 10m	1.33	0.025	0.9	656	4.3	Med OS: 9m	Final	Negative
(Lung)	SCLC				Med PFS: 5m						Med PFS: 5m
S020584	advanced pancreas	704	5	1	Med OS: 6m	1.33	0.0125	0.92	743	2.2	Med OS: 6m	Final	Negative
(GI)					Med PFS: 3m						Med PFS: 3m

^*S9313 had DFS as a primary endpoint with HR=1.3 and no interim futility testing. A trial with the same characteristics but OS as a primary endpoint would use HR=1.45.

^{^}S8797 was powered for HR=1.78, but interim futility testing was based on HR=1.5.

⁺Based on number randomized

NSCLC = Non-small cell lung cancer

GI = gastrointestinal

^17-29 Reference number – see bibliography

Of the 15 trials, 6 trials were identified as occurring in disease settings where there would likely be little gain in time and patient accrual using this approach, given the assumed progression-free survival times in the control arms. Specifically, S8797 with a 5-year PFS rate of 56%, S9313 with a 5-year DFS rate of 96%, S9415 with a median DFS of 8.5 years, and S9321 with a median PFS of 1.3 years, S9438 with a 2-year DFS rate of 30%, and S9008 with a median RFS of 20 months were identified as poorer candidates for a phase 2/3 design using OS as the primary endpoint and PFS as the phase 2 endpoint, and perhaps these populations are better addressed by separate phase 2 and phase 3 studies. It is possible that in these disease settings there are better endpoints that would alleviate this issue and allow for the use of a phase 2/3 design.

Table 3 summarizes the actual the number of events, sample size, percentage of actual accrual and the phase 2 decision for each power/type I error combination. In general the phase 2 decision was consistent across the range of error rates. Of the trials identified as poor candidates, two of the trials would have essentially gone to full accrual (S8797 and S9438) and the remaining 4 studies (S9313, S9415, S9321, and S9008) would have generally made it to at least 50% accrual before the phase 2 analysis, with S9313 accruing over around 2,000 patients and S9415 accruing around 1,000 patients by the analysis.

Table 3.

Results of phase 2 interim analysis in SWOG phase 3 trials

			1	2	3	4	5	6	7	8	9
Study	Final	Power:	85%	85%	85%	90%	90%	90%	95%	95%	95%
	Result	Type I error:	10%	15%	20%	10%	15%	20%	10%	15%	20%
S8797	Positive	(accrual goal : 264, actual size: 268)
		Events	109	87	71	133	109	91	173	145	125
		N	262	262	262	262	262	262	262	262	262
		Accrual (%)	99%	99%	99%	99%	99%	99%	99%	99%	99%
		Phase II stop	No	No	No	No	No	No	No	No	No
S9008	Positive	(accrual goal : 600, actual size: 606)
		Events	97	78	64	119	97	82	155	130	112
		N	263	221	202	316	263	227	366	324	302
		Accrual (%)	44%	37%	34%	53%	44%	38%	61%	54%	50%
		Phase II stop	No	No	No	No	No	No	No	No	No
S9308	Positive	(accrual goal : 440, actual size: 432)
		Events	45	36	30	55	45	38	72	61	52
		N	119	110	98	138	119	110	152	143	127
		Accrual (%)	27%	25%	22%	31%	27%	25%	35%	33%	29%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
S9313	Negative	(accrual goal : 3240, actual size: 3176)
		Events	50	40	33	61	50	42	79	67	57
		N	1796	1598	1455	1957	1796	1618	2180	2050	1860
		Accrual (%)	55%	49%	45%	60%	55%	50%	67%	63%	57%
		Phase II stop	No	No	No	No	No	No	No	No	No
S9321	Negative	(accrual goal : 500, actual size: 575)
		Events	70	56	46	86	70	59	112	94	81
		N	205	174	166	234	205	184	298	253	227
		Accrual (%)	41%	35%	33%	47%	41%	37%	60%	51%	45%
		Phase II stop	Yes	No	Yes	Yes	Yes	Yes	Yes	No	Yes
S9415	Negative	(accrual goal : 1600, actual size: 1135)
		Events	207	166	136	253	207	174	330	277	238
		N	844	763	704	965	844	787	1004	1004	919
		Accrual (%)	53%	48%	44%	60%	53%	49%	63%	63%	57%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
S9420	Negative	(accrual goal : 700, actual size: 730)
		Events	59	47	39	72	59	49	94	79	68
		N	135	114	105	148	135	122	186	161	141
		Accrual (%)	19%	16%	15%	21%	19%	17%	27%	23%	20%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
S9438	Negative	(accrual goal : 206, actual size: 204)
		Events	88	70	58	107	88	74	140	118	101
		N	194	174	155	194	194	183	194	194	194
		Accrual (%)	94%	84%	75%	94%	94%	89%	94%	94%	94%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
S9509	Negative	(accrual goal : 440, actual size: 432)
		Events	45	36	29	55	45	38	71	60	51
		N	129	118	110	147	129	119	164	152	140
		Accrual (%)	29%	27%	25%	33%	29%	27%	37%	35%	32%
		Phase II stop	Yes	No	No	Yes	Yes	No	Yes	Yes	No
S9916	Positive	(accrual goal : 744, actual size: 770)
		Events	26	21	17	32	26	22	41	35	30
		N	100	92	87	117	100	93	128	122	114
		Accrual (%)	13%	12%	12%	16%	13%	13%	17%	16%	15%
		Phase II stop	No	No	No	No	No	No	No	No	No
S0001	Negative	(accrual goal : 400, actual size: 183)
		Events	47	38	31	58	47	40	76	64	55
		N	65	63	54	79	65	63	108	94	73
		Accrual (%)	16%	16%	14%	20%	16%	16%	27%	24%	18%
		Phase II stop	Yes	No	No	Yes	Yes	No	Yes	Yes	Yes
S0003	Negative	(accrual goal : 550, actual size: 397)
		Events	69	55	45	84	69	58	109	92	79
		N	148	121	105	160	148	122	191	169	157
		Accrual (%)	27%	22%	19%	29%	27%	22%	35%	31%	29%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
S0023	Negative	(accrual goal : 672, actual size: 284)
		Events	45	36	30	55	45	38	72	61	52
		N	109	92	86	136	109	93	160	140	130
		Accrual (%)	16%	14%	13%	20%	16%	14%	24%	21%	19%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
S0124	Negative	(accrual goal : 680, actual size: 671)
		Events	84	67	55	102	84	70	133	112	96
		N	148	130	123	168	148	136	218	180	165
		Accrual (%)	22%	19%	18%	25%	22%	20%	32%	26%	24%
		Phase II stop	No	No	No	No	No	No	No	No	No
S0205	Negative	(accrual goal : 704, actual size: 766)
		Events	84	67	55	102	84	70	133	112	96
		N	173	157	146	200	173	161	239	211	191
		Accrual (%)	25%	22%	21%	28%	25%	23%	34%	30%	27%
		Phase II stop	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes

Of the positive trials 3 of 4 would have continued at the phase 2 analysis across all scenarios. S9308, the positive study that stopped at the phase 2 analysis was positive for both OS and PFS at the final analysis, with median PFS of 2 versus 4 months and median OS of 6 versus 8 months. The PFS HR used in the analysis was 2, which is likely too large. Evaluating this study with a HR of 1.6 (equivalent to a 1.2 month improvement), the study would have continued in all scenarios except in the phase 2 setting with 85% power and 20% type I error.

Of the negative trials, 10 of 11 would have stopped at the phase 2 analysis for the majority of scenarios. Interestingly, S0124 would have never stopped early, and at the final analysis while OS was not significantly different between the treatment arms, PFS was significantly different between the treatment arms. Results were mixed in S9509 and S0001 with the studies failing to stop for futility based on the evaluation with all scenarios with 20% type I error rates for S9509 and those with 85% and 90% power for S0001. In addition, both studies would have failed to stop with the 85% power, 20% type I error combination.

Because the phase 2 power has a large impact on the adjusted phase 2/3 power, our recommendation is to use at least 90% power for the phase 2 design. Then, the choice of the type I error will be based on both acceptability of the proportion of negative studies that will proceed to the phase 3 portion of the study and the sample size and timing of the phase 2 analysis. The evaluation of the SWOG studies indicates that a false positive rate of 20% may be too liberal.

Discussion

While this manuscript focuses upon the statistical properties of a new clinical trial design, it is also important to note that this design has already been used in clinical oncologic research. For example, SWOG S1203, an on-going study, employs early monitoring based on complete response while the primary outcome is event-free survival. In addition, coauthors on this paper, acting as consultants for Threshold  Pharmaceuticals, recommended this design for the conduct of a randomized clinical trial of doxorubicin versus the combination of doxorubicin and TH302, a prodrug of the DNA alkylator bromo-isophosphoramide mustard. The company reported that this design enabled them to raise sufficient capital to fund this registration trial.

The evaluation of SWOG studies presented in this paper was based on the proposed model for PFS and OS. However, we note that numerous authors have discussed modeling the relationship between PFS and OS. (89–94) The proposed model used in this paper is just one such possible model. We find the model to be an intuitive one for the setting described. For the design of a phase 2/3 study, the study team should assess the disease setting and potential outcomes to be used and then determine which model is most approach for the design.

It is important to note that while a phase 2/3 design has a high likelihood of stopping at the phase 2 analysis under the null hypothesis, implementation of a phase 2/3 design does mean that the study sponsor and team are prepared for the study to continue to the phase 3 portion. In addition another possible downside to this approach is that a separate publication of the phase 2 study will not occur, as it is inappropriate to publish the results of interim analyses of an on-going study.

Conclusions

The phase 2/3 design has been suggested as an approach to speeding up drug development. While not applicable in all settings, use a of phase 2/3 design with PFS and OS, as described in this manuscript, could reduce the time to discovery not only in study time but also by removing the development time between a phase 2 and a phase 3 trial. Through careful consideration and thorough evaluation of design properties, substantial gains could occur using this approach.