Postgraduate Medical Journal (1985) 61, 133-139

The evaluation of clinical trials

R.R.P. JacksonClinical Operational Research Unit, Department ofStatistical Science, University College London, Gower Street,London WCIE6BT, UK.

Introduction

One of the earliest talking pictures 'Arrowsmith', circa1931, brought the ethical problem of clinical trials tothe attention of the general public. In it, RonaldColman portrayed a gifted doctor, who after the usualtrials and tribulations of general practice in a smallAmerican town eventually succumbed to the call ofresearch and went to work in a prestigious laboratoryin New York, under his old Professor. After muchwork, but still by accident, he discovered a wonderdrug which appeared to obliterate most known germs(in vitro of course). Time passed and eventuallybubonic plague broke out in the West Indies. Ourmedical hero went to see what could be achieved withhis serum. His Professor's words - not to forget sciencefor humanity - were ringing in his ears, with instruc-tions to put alternately, one patient on the serum andone not. Although starting in this vein, his wife's deathof the plague, back at the home base (apparently, hedid not give her his protective serum!), unbalanced ourgood doctor, who in his hour of grief said, 'Give all ofthem the serum,' and this cleared the plague.By current conventions, his initial trial would have

been criticized as being not properly randomized, andtherefore open to bias. His 'treat everybody' be-haviour, despite the evidently excellent results, wouldhave been viewed with caution. Here the problem ispresented as a dilemma, the doctor's ethical considera-tions versus the need for 'scientifically based' trialresults.The real world is seldom so clear cut and evaluating

treatments remains difficult and controversial. Theproblem of evaluation, however, is not one peculiar tomedicine but occurs and has been widely discussed inall fields involving human behaviour, such as educa-tion, social services and health care, and wherevermajor decisions are made. In all of these contexts, it isthe variability of individual behaviour, and a relatedfactor - often referred to as 'system response' - whichmake the task difficult. To illustrate the two effects,consider a clinical trial in which many patients arebeing treated with the same regimen. Considerablevariation in clinical response (i.e. individual be-

haviour) between patients is likely to be observed bythe medical staff, who cannot help but adapt their ownbehaviour to it (i.e. system response). The wholeprocess is complicated further by the fact that theevaluation approach adopted can itself influence theoutcome: different methods may yield different results(e.g. ultra-sound and computerized axial tomographyas ways of measuring tumour burden).A recent review of evaluation methodology (Jack-

son, 1975) contains many points of relevance to theproblem of clinical trials evaluation. In particular,attention is drawn to the distinction between 'Evalua-tion Before' the taking of a decision, and 'EvaluationAfter'. The former asks, on the basis ofwhat is known,whether a particular decision (e.g. whether to employ aparticular experimental treatment regimen) should betaken, and it involves the analysis of existing data (e.g.historical clinical trials data) to establish the likelybenefits. The latter seeks to establish the consequencesof having taken the decision (perhaps through theanalysis of a prospectively planned Phase III clinicaltrial).

Several methods of evaluation are reviewed in thepaper and it is concluded that the development ofappropriate mathematical models (equations whichdescribe the behaviour of those system elements ofinterest) and their manipulation, provide a rationaland effective means of obtaining insights during bothevaluation phases. The approach will be described inmore detail in relation to clinical trials evaluationlater.

Sir Austin Bradford Hill (1962) was the first toattempt a comprehensive discussion of the philosophyand the procedures of controlled clinical experiments.The sound sense and moderate line of his work sets thetenor of good clinical research. For instance: ...personal observations ofa handful of patients, acutelymade and accurately recorded by the masters ofclinical medicine have been, and will continue to be,fundamental to the progress of medicine. Of that,however statistically minded this age may be or maybecome, there can be no doubt whatever'. This istempered by the caution that 'On the other hand, onehas to remember that in many respects the reactions of

C The Fellowship of Postgraduate Medicine, 1985

R.R.P. Jackson, B.Sc.

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134 R.R.P. JACKSON

human beings to most diseases are, under any circum-stances, extremely variable. They do not all behaveuniformly and decisively. They vary, and that is wherethe trouble begins. 'What the doctor saw' with one,two or three patients may be both acutely noted andaccurately recorded: but what he saw is not necessarilyrelated to what he did. The assumption that it is sorelated, with a handful of patients, perhaps mostlyrecovering, perhaps mostly dying, must, not in-frequently, give credit where no credit is due, orcondemn when condemnation is unjust'.How, then, are we best to proceed?One suggested way, which has become the current

vogue, is by means of the randomized controlled trial(RCT).

Randomized clinical trial

Randomization is advocated so as to remove personalbias from allocation procedures (Hill, 1952), and at thesame time eliminate systematic errors caused byunknown factors (Chatfield, 1975), thus creating asample space which can confidently form the basis fortests of statistical significance (Cornfield, 1976).

'Controlled' implies the use ofconcurrent patients tobe randomized into say two arms ofa clinical trial so asto avoid differences in the composition of patientgroups and the risk of patterns of disease changingover time. Usually, the 'control group' is given thestandard treatment and the other group the ex-perimental treatment being evaluated. A strictprotocol for the administration of each treatment willusually be agreed, and blind or double blind (clinicianand patient) allocation may be used to further avoidsubjective bias.To summarize, an idealized RCT should (Armitage,

1960) avoid changes in diagnostic and patient man-agement procedures over time; should guard againstbias and selectivity when allocating patients to eacharm of the trial, and should avoid subjective bias inmeasuring response variables.The analysis of all RCT focusses on the application

of statistical significance tests to observed treatmentdifferences, and a cautionary discussion of the popularapplication of such tests will be presented later. Thetests do, however, have a bearing on RCT design, sincetheir discrimination is highly dependent on the num-ber of patients in the trial (Mould, 1979). Given thatethical considerations demand little or no suspectedtreatment difference to justify an RCT, calls forrecruitment of large numbers of patients to trials arecommonplace. As an example, statisticians at a con-ference in Oxford (Peto, 1978) were asked to go as faras to sign a declaration supporting the inclusion ofmany more patients into trials with larger numbers ineach arm, for example: 'Stage III breast cancer trials

should be set up annually and recruit at least 1000 girlsto each arm'.

Let us reflect that this is all in the cause of achievingstatistical significance with that level of confidencewhich allows the statistician to pronounce, withoutdue regard to the individual patients. Notwithstandingthe evidence obtained from many thousands ofpatients treated similarly over the years, the messageevery time seems to be 'let us start again'!The RCT was given a great boost by the MRC

espousing its cause, and by the publication of thepapers by Peto et al. (1976-77) on the design andanalysis of clinical trials. This was further carriedforward in a British Medical Journal editorial (1977)in which the doctor's faith in the RCT and theassociated statistical approach was accepted as thebest way forward, with the reminder of several,apparently wrong, decisions made without the benefitof RCTs: 'Let us remember the number of drugs thathave been roman candles, making a bright andbeautiful flash for a short time and then burning out.And how many new drugs (such as lithium for thetreatment ofmanic depression) which were useful havebeen discarded or ignored for many years becausetheir flash was not bright enough?'

This is, no doubt, very poetic, but RCTs havethemselves produced conflicting results, obtainedfrom apparently similar or identical trials, and havecome out in favour of some treatments which havelater been found to be of no benefit such as the use ofimmunotherapy in acute myelogenous leukaemia.There are, in fact, many situations in which, with the

best will in the world, RCTs cannot be used in practice.These are notably where the number of patients beingtreated is too small for such a trial to be conductedover a reasonable time span; where all standardtherapies are known to be ineffective; where treat-ments are believed to be substantially different ineffect and where costs (patient lives, money, lostopportunity) cannot, or will not, be met. Indeed, SirDouglas Black (1979), while describing the RCT ashaving become a 'medico-social belief', expressesreservations 'about its over-riding efficacy'. He givesexamples where clear cut benefits (such as treatmentwith insulin) would not require a trial, and he describessituations where to take account of all possible knownvariations, would require a trial of inordinate length.Nevertheless, he ends, 'In spite of these reservations, Iwould agree that ifa controlled trial is practicable andcan produce a result, it is a most valuable contributionto progress; but it seems to me unrealistic to suggestthat nothing should be done without a controlled trialand that any issue can be settled for all time, even by anRCT'.Another BMJ Editorial (1979) begins to show a

lessening of total commitment to RCTs. Some of theirpractical problems and misuses are given, and atten-

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EVALUATION OF CLINICAL TRIALS 135

tion is drawn to results in the literature of the effect ofdrug A being greater than B, being greater than C,being greater than A! A most important part of theeditorial is the recognition of Cranberg's (1979)argument that the use of retrospective (as opposed toconcurrent) controls is now worth considering, sincedata is collected more objectively and is more easilyretrievable than in the past. The BMJ editorial finishedwith arguably the quote of the decade that: 'thecontrolled trial has been placed on too high a pedestaland needs to be brought back down to earth'. Thequestion is: How? There is clearly a need for a morerealistic and less restrictive scientific evaluation, bear-ing in mind Cranberg's remarks (1979) '... no onemethod is best in every case - the choice of methodrests on consideration of the options and their con-sequences'.

The modelling approach

The modelling approach to evaluation consists ofconsidering an environment as it is found; ofestablish-ing its important features; ofproducing an idealizationof the relationships between them, and then construct-ing mathematical equations to describe them. Themathematical equations when calibrated on a given setof data, form the basis for predictions of the future, orevaluations of the past or present.The first point to notice is that no longer is a strict

set of design constraints declared, as for the RCT. Itfollows that data emerging from randomized con-trolled trials may themselves be accessible to someform of modelling evaluation, but more significantly,the body of data encompassed by the modellingapproach is much larger than that small subset to befound in RCTs. That is not to say that scientificprinciples need to be discarded. In broadening theclinical trials 'data base' to include retrospective datafor example (and situations have been identified(Gehan Freireich, 1974; Fleming, 1983 personal com-munication), in which the use of historical controls isin fact ethically preferable), care needs to be taken thatcomparability between patient groups is, as far aspossible, maintained, and appropriate methodologiesexist (Kay, 1977), to improve reliability in this respect,by taking account of known prognostic information.In the absence ofknown prognostic factors, modellingresults may actually lead to the identification ofcandidate variables.

Because of the nature of the problem under con-sideration, or the data available, modelling evaluationmay often address slightly different questions to thoseaddressed by the RCT, and may use any of a range ofcomparison methods (other than the statistical test).Where data is scant (as for example in Phase I or IIstudies), formal use of the modelling approach may

establish the most pertinent question(s) to be addres-sed in larger scale prospective studies - which may inturn also be evaluated by means of mathematicalmodels.With the post-war development of the branch of

science known as Operational Research, has come anew theoretical repertoire of techniques which lendthemselves to the evaluation ofsome aspects ofclinicaltrials.A number of mathematical models have been

developed covering various aspects of oncology(Tautu, 1978). However, of those constructed forinvestigating the results of clinical trials (for example,Fix & Neyman, 1951; Le Cam & Neyman, 1982),disappointingly few seem to have been applied inactual clinical studies. A more recent model (Jackson& Aspden, 1979), however, based on an idealization ofpatient progress (Figure 1) has been used for theanalysis of leukaemia trials at St Bartholomew'sHospital, and it will serve to exemplify the modellingapproach. Application of the model leads to a methodof comparing trials which yields hypotheses for moreformal testing, and using clear graphical forms ofpresentation (an important aspect of all analyticalmethods (Altman, 1980; Gore, 1981), it providessequential monitoring of new trials.From the basic schematic (Figure 1) the math-

ematics of the system are written down, calibrated onthe results of a particular trial and then used tomonitor and compare a new ongoing trial (Jackson etal., 1982). An example ofsuch a comparison is given inFigure 2. This represents just one possible form ofanalysis, given the model.The individual graphs correspond to the boxes in

the schematic. Each one shows the number of patientsin the vertical axis, against time from the start of thenew trial along the horizontal. The solid central line oneach graph is the prediction of the numbers of patientsin the new trial expected to be there at particular times,given patients in both trials behave in the same way.The dotted lines on either side represent the upper andlower limits between which numbers are likely to occuron 90% of occasions, and represent some measure ofconfidence in the predictions obtained from the math-ematical model. From these graphs two very impor-tant hypotheses can be drawn. First, by consideringthe dead non-remitters graph, it is seen that from thevery start ofthe new trial there are more patients dyingwithout remission than would be expected, all aster-isks lying on or above the prediction curve. This couldbe due to the remission proportion being substantiallylower than in the previous trial, and/or the time todeath for non-remitters being shorter. The secondimportant inference was at that time really no morethan speculation, but it was noted that none of thepatients lucky enough to remit had relapsed.Was this then a kill or cure treatment? The detailed,

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136 R.R.P. JACKSON

Input Induction ~~Patients in PatientsInputeInductio completeireastherapy ~~~remission i eas

Dead (non- Deadremitters) (remitters)

Figure 1 Schematic of acute myelogenous leukaemia.

up-dated analysis is presented elsewhere (Jackson etal., 1982), and all the above inferences were confirmedwith further follow-up.

These types of models have been used to analysedata from a number of trials in Hodgkin's disease(Aspden et al., 1981), Wilms' tumour (Jackson et al.,1981), small cell bronchogenic cancer (Hughes, 1981)and early breast cancer (Metasa Ltd, 1979). An

important feature of such models is that they 'provideilluminating analyses ofdata that cannot be studied byconventional statistical methods, either because thedata are too heterogeneous or because it is not clearwhich are the alternative hypotheses between whichthe statistical analysis is to adjudicate' (Beale, 1979personal communication).The form ofthe graphs allows comparisons between

*atS, / aK0;*}t,"';2,s;.4 \\, . : '.'tI..'j.'J.tY-'.'c * '.*N/_ .-o- .;! ..; .

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Figure 2 Use of calibrated model to monitor an ongoing trial (for explanation see text).

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EVALUATION OF CLINICAL TRIALS 137

the results at any time (K.D. Tocher, 1981, personalcommunication). Indeed, if in the hypothesis testingphase, likelihood methods (Edwards, 1972) are used, itis possible to overcome the problems normallyassociated with sequential testing (Armitage, 1975).The carefully elicited structure of the model allows forthe presentation ofresults in a form consistent with theclinicians' understanding of the course of trials whilsthighlighting the effects of different phases.One phase of patient progress (box in Figure 1),

namely the 'in-remission' box, has been modelled inmore detail (Birkhead, 1984), to try to account for theshape of observed remission duration curves. Themodel was based on a priori assumptions about cellgrowth and the effects of treatment, and developedfrom application and discussion of the more generalmodel.Models oftumour response to chemotherapy (Birk-

head & Gregory, 1984) and of the effects of drugresistance (Birkhead, 1984) have also recently beenconstructed with the aim of helping the more rationaldesign of cancer treatment strategies. They exemplifyanother aspect of the 'Evaluation before' approach asit applies to clinical trials, which is featuring increasin-gly in the medical research literature (Goldie &Coldman, 1979; Goldie et al., 1982).

Routine statistical analysis - a word of warning

It is unlikely that any clinician will have the resourcesavailable for him to develop models for his ownparticular problem. At the present time none of thetype of models discussed above in the references isavailable in sufficiently clear form for him to usealone. Generally, they are developed by operationalresearchers in close collaboration with clinicians -which is one of the strengths of the approach.What the clinician often does currently, and proba-

bly will continue to do for the foreseeable future, is toanalyse clinical trials survival times using either thelog-rank test (Peto & Peto, 1972) or, more popular inAmerica, the generalized Wilcoxon statistic (Gehan,1965). Often small trials are effected by randomizingonly 40 or 50 patients to two or more treatments, butanalysis proceeds regardless of design faults, viasurvival curves, and P-values are reported. 'P-valuesor no publication' seems to be the current editorialdictum, when the question 'why P-values?' might beusefully asked. Research clinicians however, are goingto continue to analyse data on small trials addressingquestions which are not always well-defined. One ortwo notes ofcaution about life-table analysis thereforeneed to be sounded.

Clinicians often misunderstand the meaning of P-values, assuming that a number less than 0.05 issufficient. Interim analyses are often performed (and

are sometimes necessary on ethical grounds), yet manyclinical analysts fail to appreciate that a small P-valueobtained at any one of a series of interim analyses isnot as strong as one obtained at a single pre-deter-mined point. Frequent testing at the 0.05 level will leadto many false positive results in early tests (Armitage etal., 1969). Instructive examples have been constructedto demonstrate precisely this (Fleming et al., 1981,unpublished).

In addition to the danger of false positives, there is aprobability with every test procedure of obtainingfalse negative results. That is, of failing to identify asignificant difference between survival distributionswhen one actually does exist. A statistical analysis(Freiman, 1978) of 71 published RCTs whichproduced non-significant treatment differences, in-dicated that half of these trials which were otherwisewell-conducted had a 40% chance of missing even a50% reduction in mortality! As has been remarkedearlier, to increase the power of such tests and thus thesensitivity of the trials, the number of patients must beincreased.

Finally, it is often not realized that the log-rank andsimilar tests as described in layman's language by Petoet al. (1976-77), are based on sets of assumptions,which are almost never checked but which in manycases may be violated.

Despite the many pitfalls awaiting them, clinicianswill continue to undertake analysis of small trials usingtheir limited understanding of conventional statistics.Such analysis, therefore, should be made available tothem in as comprehensible and comprehensive a wayas possible, but should contain the necessary stricturesto avoid the common errors. Similar precautions willeventually be necessary with interactive mathematicalmodelling methods as they become available on desk-top computers.

Clinical information systems

One of the great advances of recent years has been thedevelopment and use of computerized clinical databases. The more recent discipline for clinicians ofhelping in the designing of data sheets has beenextremely beneficial (Gregory et al., 1981). Earlysystems were developed for use on large (main-frame)computers which required central staff to operate andoften technical help at the clinicians' end. However, asthe enthusiasm of the clinician increased it becamevery clear that a system which he could use, on hisdesk, was wanted. This meant that a new concept of'User Friendliness' had to be developed. An exampleof this work is seen in PEDRO (Patient EndoscopyData Records Organiser), a micro-computer basedsystem on which patients' data are recorded on a visit-by-visit basis by staff in the medical unit.

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138 R.R.P. JACKSON

This kind of development will eventually lead todata base, analysis and graphics all being available forclinicians, in an entirely understandable form on amicro-computer.The need for safeguards against wrong analysis and

inference is recognized and must be built into anysystems to be used by non-professional analysts.However, the importance of this computing develop-ment lies in the future availability of accurate data,which can then be used with confidence for trialsevaluation.

Discussion

RCTs concentrate on detecting differences in patientresponse due to, say, two different treatments. Toachieve this aim an idealized trial is conceived and theanalysis follows to the satisfaction of the medicalstatistician. However, inherent in the trials is theassumption that it is possible, over a long period, tocreate comparable patient groups and treat patientswithin such groups, identically. Some of the limita-tions and short-comings of the approach have been

discussed. In particular, the use of historical data isnearly always excluded. But the recent development ofcomputerized clinical data bases makes this prohibi-tion redundant in some cases and makes it possible toobtain useful information from a large body ofpreviously discarded trials data. Advances in thetheories of evaluation point to a need for otherapproaches (such as mathematical modelling) whichcould greatly enhance the design and analysis ofclinical trials.

Acknowledgements

The views in this paper (which are the author's own) weredeveloped in the Operational Research Service, DepartmentofHealth and Social Security and the Research Centre for theMathematical Modelling of Clinical Trials, University ofWarwick, and latterly, at the Clinical Operational ResearchUnit, Department of Statistical Science, University CollegeLondon.

I am very grateful to Mr B. Birkhead for his comments,suggestions, and references.The Clinical Operational Research Unit is grateful for

financial aid given to this study by the Department of Healthand Social Security.

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