Hutson, 2003 Safety and efficacy outcome

Tropical Journal of Pharmaceutical Research, December 2003; 2 (2): 197-206

© Pharmacotherapy Group, Faculty of Pharmacy, University of Benin, Benin City, Nigeria. All rights reserved.

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Research Article

A sequential test procedure for monitoring a singular safety and efficacy outcome

Alan D. Hutson University at Buffalo, Department of Statistics, Farber Hall Room 249A, 3435 Main St., Buffalo, NY 14214-3000.

Abstract

In this note we describe a modification of the sequential probability ratio test (SPRT) developed for the purpose of “flagging” a significant increase in the mortality rate of a treatment relative to a control while ensuring that double-blinding and the Type I error for the primary test of efficacy, also based on mortality rates, is not compromised.

Key words: Interim analysis; safety monitoring; sequential testing.

Φ To whom correspondence should be addressed: E-mail: [email protected]

197 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome

Introduction time monitoring of AE reports? To generate a formal statistical rule to tackle this problem Drug trials go through different phases. In requires the principal investigators to design phase I trials the primary concern is safety, the trial around the efficacy outcome in the the subjects are typically healthy volunteer traditional sense, while the DSMB needs to and patient studies, and the primary determine what are the unacceptable objective is to determine the maximum differences between the new therapy and tolerated dose (MTD). This is followed by a control in the opposite (unsafe) direction. phase II trial, which build upon the results of the phase I trial. The primary goal of a In this note we develop a one-sided safety phase II trial is to determine the optimal monitoring rule based upon a modification of method of administration and examine Wald's classical sequential probability ratio potential efficacy. If the phase II trial test (SPRT)1. This rule is to be used in demonstrates that the drug may be conjunction with a randomized block design reasonably safe and potentially effective a where the hypothesis involving efficacy is a phase III trial may be carried forth. The simple comparison of two mortality primary goal of a phase III trial is to compare proportions of the form H : p = p versus 0 1 2 the effectiveness of the new treatment with H : p

In a majority of phase III clinical trials subject 1. Mortality can be evaluated within a fixed measurements can be divided into distinct time period shortly following treatment, efficacy and safety variables. With the 2. It is one-sided in the sense that a safety exception of truly sequential trials the problem is not flagged if the new primary efficacy variables are usually treatment appears efficacious, analyzed at a few well defined points in time 3. Requires the input of members of the (typically based upon calendar time or DSMB to determine what an unsafe rate accrual milestones). In contrast, safety is might be for the new therapy relative to monitored continuously through the control given the design parameters of generation of adverse event (AE) reports to the trial, the respective internal review board (IRB) 4. Is continuously sequential in terms of and review by the principal investigator (PI), blocks of subjects being the unit of time, with summary data safety monitoring board 5. It is easily explained to non-statisticians (DSMB) reports generated at regular through the use of examples, intervals, e.g. quarterly or bi-yearly. In a 6. Maintains the Type I error control for the majority of high-risk clinical trials the DSMB test of efficacy conditioned upon the will also monitor the flow of AE reports in relative safety of the experimental real-time. therapy.

In the specific case of double-blind controlled The motivation of this methodology stemmed trials of a new treatment versus standard of from the request of our DSMB to generate a care, or placebo, how might one monitor safety monitoring rule based upon statistical safety “continuously” and efficacy at distinct methods for the DCA-MALA clinical trial of points in time when the primary safety and 2 malaria in Ghana . This trial was designed efficacy variable is mortality. In addition, if as a randomized, double-blind, placebo- the DSMB wishes to remain blinded to controlled single-center trial. The trial was treatment assignment unless there is a true originally designed to enroll n=1500 safety issue, what type of information is subjects, but was terminated earlier due to needed in order for them to make an financial reasons. For this specific trial of informed decision in conjunction with real dichloroacetate (DCA) versus placebo the

198 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome measure of efficacy was 28-day mortality, blocks, and N =n + n denote the number of i 1i 2i and the primary measure of safety was also subjects in block i, i=1, 2,···K, where N =N/K. 28-day mortality. Ultimately the DSMB i wanted a simple statement after each block For the purposes of our safety monitoring of subjects completed the trial: “remain plan we set the null “efficacy” hypothesis to blinded at this point in time” or that the “blind correspond to the original study design and be broken at this point in time.” Unblinding the alternative “safety” hypothesis to the study is used to mean group summary correspond to unsafe rates of the new statistics will be analyzed and presented in therapy relative to control. Let p and p an unblinded fashion. This does not 1 2 necessarily mean that data at the individual denote the event rates of the new therapy subject level is unblinded. Also note that the and control group, respectively. Then the principal investigators would remain blinded safety data monitoring rule(SDMR) consists even if the DSMB were to take an unblinded of testing look at this trial. The use of this rule still H :
= efficacy (p , p ), allowed us to monitor secondary measures 0 0 1 2 of safety in the standard way3-4. In addition, H :
= safety(p ,p ), 1 1 1 2 adverse events involving mortality were still monitored on a case-by-case basis (in a after blocks of N = n + n subjects complete blinded manner). i 1i 2i the study. The DSMB chairperson is then

notified of the results after each test is Statistical Methods carried out per block. We strongly recommend that the values for p and p We will employ a version of a sequential test 1 2 for the purpose of generating a safety corresponding to H0 be chosen based upon monitoring rule, which will basically flag a the original study design pertaining to problem for the DSMB with respect to a efficacy. For example, in the DCA-MALA disproportionate amount of mortalities for a trial the mortality rates from which the trial was designed were p = 0.19 and p =0.25, new therapy relative to the standard of care 1 2 or placebo. Note that this rule does not for DCA and placebo, respectively. For H , 1 terminate the clinical trial, it only suggests the “safety” hypothesis, the DSMB with the unblinding the trial for the purpose of more guidance of a simulation study deemed intense scrutiny. The sequential test is p =0.28 to be an unacceptable death rate in based upon a modification of the SPRT, 1 initially developed by Wald1, and is a the DCA arm given a placebo death rate of p =0.25, and accounting for statistical noise. procedure for testing a simple null 2 hypothesis versus a simple alternative The mathematical details for the efficacy and hypothesis continuously in time. With safety “functions” are contained in Appendix respect to the new safety monitoring plan, A. Through simulations we illustrated that if “continuously in time” will refer to blocks of the placebo death rate is lower than subjects who complete the trial as opposed anticipated the decision to recommend to testing after individual subjects complete unblinding the trial will be earlier given the the trial. Therefore, in order to implement same relative differences in adverse event rates, e.g. p =0.18 to p =0.15 for DCA this rule effectively the design of the trial 1 2 should be of the form of a randomized block relative to placebo. Note that the unblinding design. Let N=n +n denote the total number 1 2 rule can be easily modified to accommodate of subjects for the new treatment plus the other types of outcomes such as mean standard treatment, K denote the number of differences.

199 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome

Test Statistic. Denote the estimates of the the test terminates earlier and we accept H0, proportions p and p as yet the test would terminate quickly if there is 1 2 -8 a safety concern. Setting =0.20 and =10 ^ corresponds to the stopping bounds of p1i = number of mortalities in the new A=9.9999 and B=0.00001. Therefore, if the therapy arm/n test errs it will err on the conservative side in 1i terms of unblinding the study early. The ^ parameters  and  may be adjusted by the p2i = number of mortalities in the DSMB in order to relax or tighten the monitoring rule during the course of the control arm/n , study. 2i

Using the candidate choices of =0.20 and where i=1, 2,···, K, and again K denotes the -8 number of blocks. The safety monitoring test =10 (approximately null) in the DCA- ^ MALA trial it was determined through statistic
is then simply a function of simulation that
would never be less than B i p1i i ^ prior to the first planned interim analysis at and p2i updated after every block i. For 50% accrual. If this scenario did occur it the DCA-MALA study we set B=75 and would have indicated that DCA is n =n =10 based upon efficacy considera- substantially more effective than originally 1i 2i anticipated and that the safety of DCA in tions. Note that n and n have to be large 1i 2i terms of the mortality rates shouldn't be of enough to produce a meaningful value for
. i concern to the EAC at that current point in The details for the calculation of
are time. Therefore, we propose that if
statistical theory dictates that A ≤ control such that
reverses its path and 1− α β crosses A. This rare event (given a long- and B ≥ . The crude stopping β 1− α term past history of treatment efficacy) would not stop the trial, however, the 1− α β recommendation to unblind the trial at that bounds A = and B = work well β 1− α point in time would be made to the DSMB Chair. It would then have to be determined for our purpose. This is demonstrated via whether this run was due to chance alone, or the the simulation study in Section 3. The some deterministic cause such as a bad parameters  and  correspond roughly to batch of drug. traditional fixed sample size Type I and Type

II error rates. Hence, we will typically Simulation Study choose  to be much smaller than  if the primary goal is safety monitoring. For the The following simulation study is used to DCA-MALA trial we determined that the illustrate the proportion of times out of appropriate levels would be to set =0.20 -8 10,000 simulations that the decision to and =10 such that it would be unlikely that “remain blinded”or “unblind the study” would

200 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome occur over possible choices of -7 Table 1: Simulation Results =0.05,0.10,0.20 and =10 , 0.05, 0.10 for a clinical trial with sample size fixed at n=1500,  = .05 and  = 10-7 broken into K=75 blocks. The decision to  (p ,p ) Median Decision 1 1 2 “reset the trial” the trial, as described above, p p Sample Unblind Remain 1 2 is built-in to the simulation study. The Size Blinded numbers are similar to the operating 0.15 0.25 1500 0.5% 95.5% characteristics of the DCA-MALA trial, 0.20 0.25 1500 6.3% 93.7% however, there are no planned interim 0.25 0.25 1240 54.4.0% 45.6% analyses. In addition, the median time that
0.30 0.25 340 97.6% 2.4% crosses A or B is given. For any specific trial 0.20 0.15 280 99.2% 0.8% of interest a similar simulation study should 0.15 0.10 240 99.8% 0.2% be undertaken in order to determine the appropriate parameter values for  and . Table 2: Simulation Results

-7 In this specific simulation study the efficacy  = .1 and  = 10  (p ,p ) Median Decision hypothesis 0(p ,p ) was fixed at 0(0.20, 1 1 2 1 2 p p Sample Unblind Remain 0.25) as determined by a hypothetical trial 1 2 Size Blinded design. Assume that the DSMB decided the 0.15 0.25 1500 1.3% 98.7% safety hypothesis should be  (0.30, 0.25). 1 0.20 0.25 1500 11.2% 88.8% The simulations were then carried out given 0.25 0.25 800 63.6% 36.4% different scenarios of “true” mortality rates 0.30 0.25 260 98.5% 1.5% (p ,p ). The pairs (p ,p ) were set to 0.20 0.15 200 99.5% 0.5% 1 2 1 2 0.15 0.10 180 99.9% 0.1% (0.15,0.25), (0.20,0.25), (0.25,0.25), (0.30,0.25), (0.20,0.15), and (0.15,0.10), corresponding to the new treatment being Table 3: Simulation Results more efficacious than planned, the new treatment being efficacious as planned, the  = .2 and  = 10-7 new treatment being equivalent to placebo,  (p ,p ) Median Decision 1 1 2 the new treatment being worse than placebo p p Sample Unblind Remain 1 2 at the correct placebo rate, the new Size Blinded treatment being worse than placebo at a 0.15 0.25 1500 3.6% 96.4% lower placebo mortality rate, and the new 0.20 0.25 1500 19.8% 80.2% treatment being worse than placebo at a 0.25 0.25 440 72.8% 27.2% very low and unexpected placebo mortality 0.30 0.25 180 99.2% 0.8% rate, respectively. 0.20 0.15 140 99.7% 0.3% 0.15 0.10 120 99.6% 0.4% The simulation results are provided in Tables 1-9. Since we are primarily interested in Table 4: Simulation Results testing for safety the choice of  and  comes down to a tradeoff between stopping  = .05 and  = .05  (p ,p ) Median Decision times and Type I error for this application. 1 1 2 p p Sample Unblind Remain The column labeled “Median Sample Size” 1 2 indicates the median time at which a Size Blinded decision rule is to be implemented if the true 0.15 0.25 1500 0.4% 99.6% underlying mortality rates were p and p . If 0.20 0.25 1500 6.7% 93.7% 1 2 0.25 0.25 1220 54.8% 45.2% we were confident of the underlying truth 0.30 0.25 320 97.6% 2.4% with respect to p and p in terms of efficacy 0.20 0.15 260 99.2% 0.8% 1 2 then it becomes a question of trade-offs. 0.15 0.10 240 99.6% 0.6%

201 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome

Table 5: Simulation Results Table 7: Simulation Results

 = .1 and  = .05  = .05 and  = .1  (p ,p ) Median Decision  (p ,p ) Median Decision 1 1 2 1 1 2 p p Sample Unblind Remain p p Sample Unblind Remain 1 2 1 2 Size Blinded Size Blinded 0.15 0.25 1500 1.2% 98.8% 0.15 0.25 1500 0.4% 99.6% 0.20 0.25 1500 12.2% 87.8% 0.20 0.25 1500 7.1% 92.9% 0.25 0.25 760 64.1% 35.9% 0.25 0.25 1120 56.3% 43.7% 0.30 0.25 240 98.4% 1.6% 0.30 0.25 320 97.8% 2.2% 0.20 0.15 200 99.5% 0.5% 0.20 0.15 260 99.0% 1.0% 0.15 0.10 180 99.8% 0.2% 0.15 0.10 240 99.6% 0.4%

Table 6: Simulation Results Table 8: Simulation Results

 = .2 and  = .05  = .1 and  = .1  (p ,p ) Median Decision  (p ,p ) Median Decision 1 1 2 1 1 2 p p Sample Unblind Remain p p Sample Unblind Remain 1 2 1 2 Size Blinded Size Blinded 0.15 0.25 1500 4.0% 96.0% 0.15 0.25 1500 1.6% 98.4% 0.20 0.25 1500 21.2% 78.8% 0.20 0.25 1500 12.3% 87.8% 0.25 0.25 740 73.2% 26.8% 0.25 0.25 740 65.3% 34.7% 0.30 0.25 160 99.2% 0.8% 0.30 0.25 240 98.9% 1.1% 0.20 0.15 140 99.7% 0.3% 0.20 0.15 200 99.6% 0.4% 0.15 0.10 120 99.9% 0.1% 0.15 0.10 180 99.8% 0.2%

-7 Table 9: Simulation Results and =10 , e.g. see Table 3. A possible tradeoff would be to choose =0.1 and =0.1  = .2 and  = .1 in Table 8, where we would unblind the study  (p ,p ) Median Decision at rate 12.3% if we were close to the 1 1 2 p p Sample Unblind Remain proportions from which the study was 1 2 Size Blinded planned around, and unblind the study 0.15 0.25 1500 4.4% 95.6% 98.9% of the time if we were close to the 0.20 0.25 1500 21.3% 78.7% safety hypothesis. 0.25 0.25 380 74.3% 25.7% 0.30 0.25 160 99.2% 0.8% DCA-MALA Trial Example 0.20 0.15 140 99.7% 0.3% 0.15 0.10 120 99.9% 0.1% The following text appeared(modified slightly for this paper) in each DCA-MALA DSMB

What safety error rate is the DSMB willing to report following the adoption of the live with. For example from Table 1, if the sequential test called the safety decision DSMB chose =0.05 and =10-7 then we monitoring rule(SDMR) in the DCA-MALA would indicate to the DSMB that they would trial. “After every 20 subjects (one likely “unblind” the trial early 6.3% of the time randomization blocking unit) have completed over theoretical repetitions of the study, and the study the biostatistics coordinating center “unblind” the trial early 97.6% of the time if will “update” the SDMR and recommend to there was a true safety concern. Note that if the DSMB to either remain blinded to the the new treatment was more successful than treatment assignment or to unblind the anticipated the “unblinding rate” goes down treatment assignment due to a significant to 0.5%. If the DSMB wanted a very increase in the mortality rate, beyond stringent rule then they might go with =0.2 random noise, of the DCA group relative to

202 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome the placebo group. In addition to the SDMR, Results for the DCA-MALA Trial mortality data will always be monitored on case-by-case basis, i.e. if a sequential series In this section we illustrate how the SPRT of anomalous deaths occur in any given decision rule worked within the context of the block the DSMB will be notified immediately, DCA-MALA trial through 120 subjects given regardless of the SDMR”. =0.20 and =10-8 corresponding to boundaries of A=9.9999999 and The original trial was designed to enroll B=0.0000111. The trial was terminated due n=1500 subjects if accrual through two to financial circumstances after n=123 interim analysis reached 100%. subjects were enrolled. Hence, the final 3 Unfortunately, the trial was terminated early subject’s data were not included in the safety after only n=123 subjects had completed the monitoring statistic illustrated here. study due to problems stemming from failing ^ ^ to meet accrual milestones set by the Let p1 and p2 denote the estimated sponsors. The low accrual rates were mortality rates in the DCA and placebo directly related to unusual dry spells treatment groups for each block of 20 occurring during the rainy seasons when subjects. As can be seen the value of  i malaria is prevalent. However, there was started to “drift” toward A=9.9999999 as the enough data gathered in order to imbalance in mortality rates favored DCA demonstrate how the SDMR rule works in and then started to “drift” back towards reality. B=0.0000111 as the mortality rates became more balanced. The simplicity of In order to illustrate the new SDMR to the programming this method is illustrated via DCA-MALA DSMB prior to their approval or the SAS program used to carry out the disapproval, the following examples were calculations given in Appendix B. presented to the committee members. The method was illustrated using various “made- Conclusion up” outcomes, which were similar to what we anticipated might possibly occur during the In this note we presented a statistical DCA-MALA trial given decision rule for data safety monitoring H :
= efficacy (p = .19, p = .25), 0 0 1 2 purposes when the primary efficacy and H :
= safety(p = .28, p = .25), 1 1 1 2 primary safety endpoint of a clinical trial is mortality. This rule was designed for ease of The results are presented in Tables 10 – 14. interpretation by DSMB members with little After every N =10+10 subjects completed or no formal statistical training. The goal of i this method is to provide a means of the study
was calculated along with the i controlling the approximate Type I error corresponding recommendation: “Remain control for the efficacy analysis, while Blinded” or “Unblind the Study.” The monitoring safety in a continuous fashion. As example given in Table 14 is the only case was discussed above, the method may be where DCA mortality was consistently lower modified to accommodate more complex than placebo mortality and hence the designs. Future work will involve studying decision was always to “Remain Blinded.” In the probability theory behind the utilization of all other examples the decision to unblind different sequential bounds for efficacy and the study was a function of the true safety such this information can be underlying mortality rates. In our opinion incorporated into the sample size these simple examples provided to the parameters during the design phase of the committee helped illustrate the utility of the trial. SDMR and thus they ultimately endorsed its implementation.

203 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome

Table 10: Treatment trending towards being Table 11: Treatment consistently worse unsafe Sample DCA Placebo DCA Placebo Size No. of No. of Decision Sample No. of No. of deaths deaths Size deaths deaths Decision per 10 per 10 per 10 per 10 20 4 2 Remain Blinded 20 2 2 Remain Blinded 40 4 2 Remain Blinded 40 3 2 Remain Blinded 60 4 2 Remain Blinded 60 4 0 Unblind the study 80 4 2 Unblind the study

Table 12: Treatment consistently worse. Table 13: Spikes in the treatment death rate

Sample DCA Placebo Sample DCA Placebo Size No. of No. of Decision Size No. of No. of Decision deaths deaths deaths deaths per 10 per 10 per 10 per 10 20 3 2 Remain Blinded 20 1 2 Remain Blinded 40 3 2 Remain Blinded 40 1 2 Remain Blinded 60 3 2 Remain Blinded 60 1 2 Remain Blinded 80 3 2 Remain Blinded 80 8 2 Remain Blinded 100 3 2 Remain Blinded 100 1 2 Remain Blinded 120 3 2 Unblind the Study 120 8 2 Unblind the study

Table 14: Treatment consistently better Table 15: Results from the DCA-MALA Study

Sample DCA Placebo ^ ^ Size No. of No. of Decision i
Decision p p deaths deaths i 1 2 per 10 per 10 1 1.40995 remain blinded 0.2 0.1 20 1 2 Remain Blinded 2 2.91669 remain blinded 0.1 0.0 40 1 2 Remain Blinded 3 3.89147 remain blinded 0.3 0.2 60 1 2 Remain Blinded 4 2.04235 remain blinded 0.0 0.1 80 1 2 Remain Blinded 5 2.12806 remain blinded 0.2 0.2 100 1 2 Remain Blinded 6 1.11686 remain blinded 0.0 0.1 120 1 2 Remain Blinded 140 1 2 Remain Blinded 160 1 2 Remain Blinded 180 1 2 Remain Blinded 200 1 2 Remain Blinded 220 1 2 Remain Blinded

Acknowledgements Appendix A: SPRT Statistical Details

Let p and p denote the true underlying mortality rates Special thanks to David Harrington for 1 2 in the DCA and placebo treatment groups, respectively. suggesting developing many of the ideas For our application we have developed a modified included in this manuscript and for Sandy SPRT statistical decision rule which will test the Zientek in the manuscript preparation. Dr. following simple hypotheses after every 20 subjects Hutson’s work is partially supported by a have been enrolled, namely,

NYSTAR Faculty Development Grant. H0 :
0 = arcsin p1 - arcsin p2 ,

204 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome

H :
= arcsin - arcsin . 1 1 p1 p2 Appendix B: SDMR SAS Program The values for p and p were chosen based upon the 1 2 proc format; original study design. value dform 0=’nblind’ ^ 1='recalculate' Test Statistic. Let p1 = (≠ mortalities in the DCA 2='remain blinded'; ^ data simul; arm/n ) and p = (≠ mortalities in the placebo input d1 d2 n1 n2; 1i 2 n1=10; arm/n ), where n denotes the number of subjects per 2i 1i n2=10; block i on DCA and n denotes the number of subjects cards; 2i per block i on placebo, i=1, 2,‡‡‡, 75. In most instances 2 1 n =n =10. Even though the sample size per block is 1 0 1i 2i 3 2 relatively small, the following asymptotic distributional 0 1 results will serve the purpose for the SPRT decision 2 2 rule, 0 1 ; ^ ≈ 1 ’ arcsin p1i ~ AN ∆arcsin p1, ÷ , data check;set simul; « 4n1i ◊ retain f0 f1; label p1='DCA death rate' (A.1) p2='placebo death rate'; ^ ≈ 1 ’ p1=d1/n1; and arcsin p2i ~ AN ∆arcsin p2, ÷ . p2=d2/n2; « 4n2i ◊ /***********Set Parameters****************/ (A.2) hp1=.19; /*active under null*/ Next we define the SPRT test statistic hp11=.28; /*active under alternative*/

hp2=.25; /*placebo*/ ^ ^ mu0=arsin(sqrt(hp1))-arsin(sqrt(hp2)); arcsin p1i − arcsin p2i − θj mu1=arsin(sqrt(hp11))-arsin(sqrt(hp2)); z = , (A.3) alpha=.1; i 1 1 beta=.00001; + /*****************************************/ 4n1i 4n1i if _n_=1 then do; which will be monitored continuously in time as defined f0=1;f1=1; by block i. It is easily shown that z ~ AN(
j,1), where end; i the distribution of z will be denoted θj i , under Hj, /*calculate test statistic */ i f (z ) z0=(arsin(sqrt(p1))-arsin(sqrt(p2))- j=0,1, respectively. Based upon fθj(zi) the SPRT mu0)/sqrt(1/(4*n1)+1/(4*n2)); test decision rule now follows straightforward from the z1=(arsin(sqrt(p1))-arsin(sqrt(p2))- classical methods. Calculate mu1)/sqrt(1/(4*n1)+1/(4*n2)); pi=2*arcos(0); fθi(z) f0=f0*exp(-z0*z0/2)/sqrt(2 *pi*(1/(4*n1)+1/(4*n2))); i (A.4) λ = f1=f1*exp(-z1*z1/2)/sqrt(2 *pi*(1/(4*n1)+1/(4*n2))); fθo z ( ) lambda=f1/f0; m a=(1-beta)/alpha;b=beta/(1-alpha); where fθj z = fθj(zi) and m = 1,2···, ( ) ∏i=1 dec=2; denotes the current block. If
> A then stop and reject if lambda>a then dec=0; i if lambda

205 Trop J Pharm Res, December 2003; 2 (2) Hutson, 2003 Safety and efficacy outcome

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