INTERNATIONAL CONFERENCE ON HARMONISATION OF TECHNICAL
`REQUIREMENTS FOR REGISTRATION OF PHARMACEUTICALS FOR HUMAN
`USE
`
`ICH HARMONISED TRIPARTITE GUIDELINE
`
`DOSE-RESPONSE INFORMATION
`TO SUPPORT DRUG REGISTRATION
`E4
`
`Current Step 4 version
`dated 10 March 1994
`
`
`
`
`
`
`
`
`
`This Guideline has been developed by the appropriate ICH Expert Working Group and
`has been subject to consultation by the regulatory parties, in accordance with the ICH
`Process. At Step 4 of the Process the final draft is recommended for adoption to the
`regulatory bodies of the European Union, Japan and USA.
`
`Page 1 of 14
`
`

`
`E4
`Document History
`
`
`
`
`
`First
`Codification
`
`History
`
`E4
`
`Approval by the Steering Committee under Step 2
`and release for public consultation.
`
`E4
`
`Current Step 4 version
`Approval by the Steering Committee under Step 4 and
`for adoption to the three ICH
`recommendation
`regulatory bodies.
`
`New
`Codification
`November
`2005
`E4
`
`E4
`
`Date
`
`10
` March
`1993
`
`10
`March
`1994
`
`
`
`Page 2 of 14
`
`

`
`
`
`
`
`DOSE-RESPONSE INFORMATION TO SUPPORT DRUG REGISTRATION
`ICH Harmonised Tripartite Guideline
`Having reached Step 4 of the ICH Process at the ICH Steering Committee meeting
`on 10 March 1994, this guideline is recommended for adoption
`to the three regulatory parties to ICH
`
`TABLE OF CONTENTS
`
`I.
`
`INTRODUCTION.....................................................................................................1
`Purpose of Dose-Response Information.........................................................................1
`Use of Dose-Response Information in Choosing Doses.................................................1
`Uses of Concentration-Response Data ..........................................................................2
`Problems with Titration Designs...................................................................................2
`Interactions between Dose-Response and Time ...........................................................3
`II.
`OBTAINING DOSE-RESPONSE INFORMATION ........................................3
`Dose-Response Assessment Should Be an Integral Part of Drug Development .........3
`Studies in Life-Threatening Diseases ...........................................................................3
`Regulatory Considerations When Dose-Response Data Are Imperfect.......................4
`Examining the Entire Database for Dose-Response Information................................4
`III.
`STUDY DESIGNS FOR ASSESSING DOSE-RESPONSE............................5
`General............................................................................................................................5
`Specific Trial Designs.....................................................................................................6
`1. Parallel dose-response............................................................................................6
`2. Cross-over dose-response .......................................................................................7
`3. Forced titration.......................................................................................................7
`4. Optional titration (placebo-controlled titration to end-point)..............................8
`IV. GUIDANCE AND ADVICE.................................................................................9
`
`
`
`i
`
`Page 3 of 14
`
`

`
`Page 4 of 14
`
`Page 4 of 14
`
`

`
`
`
`DOSE-RESPONSE INFORMATION
`TO SUPPORT DRUG REGISTRATION
`
`INTRODUCTION
`I.
`Purpose of Dose-Response Information
`Knowledge of the relationships among dose, drug-concentration in blood, and clinical
`response (effectiveness and undesirable effects) is important for the safe and effective
`use of drugs in individual patients. This information can help identify an appropriate
`starting dose, the best way to adjust dosage to the needs of a particular patient, and a
`dose beyond which increases would be unlikely to provide added benefit or would
`produce unacceptable side effects. Dose-concentration, concentration- and/or dose-
`response information is used to prepare dosage and administration instructions in
`product labeling. In addition, knowledge of dose-response may provide an economical
`approach to global drug development, by enabling multiple regulatory agencies to
`make approval decisions from a common database.
`Historically, drugs have often been initially marketed at what were later recognized
`as excessive doses (i.e., doses well onto the plateau of the dose-response curve for the
`desired effect), sometimes with adverse consequences (e.g. hypokalemia and other
`metabolic disturbances with thiazide-type diuretics in hypertension). This situation
`has been improved by attempts to find the smallest dose with a discernible useful
`effect or a maximum dose beyond which no further beneficial effects is seen, but
`practical study designs do not exist to allow for precise determination of these doses.
`Further, expanding knowledge indicates that the concepts of minimum effective dose
`and maximum useful dose do not adequately account for individual differences and do
`not allow a comparison, at various doses, of both beneficial and undesirable effects.
`Any given dose provides a mixture of desirable and undesirable effects, with no single
`dose necessarily optimal for all patients.
`
`Use of Dose-Response Information in Choosing Doses
`What is most helpful in choosing the starting dose of a drug is knowing the shape and
`location of the population (group) average dose-response curve for both desirable and
`undesirable effects. Selection of dose is best based on that information, together with
`a judgement about the relative importance of desirable and undesirable effects. For
`example, a relatively high starting dose (on or near the plateau of the effectiveness
`dose-response curve) might be recommended for a drug with a large demonstrated
`separation between its useful and undesirable dose ranges or where a rapidly evolving
`disease process demands rapid effective intervention. A high starting dose, however,
`might be a poor choice for a drug with a small demonstrated separation between its
`useful and undesirable dose ranges. In these cases, the recommended starting dose
`might best be a low dose exhibiting a clinically important effect in even a fraction of
`the patient population, with the intent to titrate the dose upwards as long as the drug
`is well-tolerated. Choice of a starting dose might also be affected by potential
`intersubject variability in pharmacodynamic response to a given blood concentration
`level, or by anticipated intersubject pharmacokinetic differences, such as could arise
`from non-linear kinetics, metabolic polymorphism, or a high potential
`for
`pharmacokinetic drug-drug interactions. In these cases, a lower starting dose would
`protect patients who obtain higher blood concentrations. It is entirely possible that
`different physicians and even different regulatory authorities would, looking at the
`same data, make different choices as to the appropriate starting doses, dose titration
`
`1
`
`Page 5 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`steps, and maximum recommended dose, based on different perceptions of risk/benefit
`relationships. Valid dose-response data allow the use of such judgement.
`In adjusting the dose in an individual patient after observing the response to an
`initial dose, what would be most helpful is knowledge of the shape of individual dose-
`response curves, which is usually not the same as the population (group) average
`dose-response curve. Study designs that allow estimation of individual dose-response
`curves could therefore be useful in guiding titration, although experience with such
`designs and their analysis is very limited.
`In utilizing dose-response information, it is important to identify, to the extent
`possible, factors that lead to differences in pharmacokinetics of drugs among
`individuals, including demographic factors (e.g. age, gender, race), other diseases (e.g.
`renal or hepatic failure), diet, concurrent therapies, or individual characteristics (e.g.
`weight, body habitus, other drugs, metabolic differences).
`
`Uses of Concentration-Response Data
`Where a drug can be safely and effectively given only with blood concentration
`monitoring, the value of concentration-response information is obvious. In other
`cases, an established concentration-response relationship is often not needed, but may
`be useful for ascertaining the magnitude of the clinical consequences of 1)
`pharmacokinetic differences, such as those due to drug-disease (e.g. renal failure) or
`drug-drug interactions, or 2) for assessing the effects of the altered pharmacokinetics
`of new dosage forms (e.g. controlled release formulation) or new dosage regimens
`without need for additional clinical data, where such assessment is permitted by
`regional regulations. Prospective randomized concentration-response studies are
`critical to defining concentration monitoring therapeutic “windows” but are also
`useful when pharmacokinetic variability among patients is great; in that case, a
`concentration response relationship may in principle be discerned in a prospective
`study with a smaller number of subjects than could the dose response relationship in
`a standard dose-response study. Note that collection of concentration-response
`information does not imply that therapeutic blood level monitoring will be needed to
`administer the drug properly. Concentration-response relationships can be translated
`into dose-response
`information. Alternatively,
`if
`the relationships between
`concentration and observed effects (e.g., an undesirable or desirable pharmacologic
`effect) are defined, patient response can be titrated without the need for further blood
`level monitoring. Concentration-response information can also allow selection of
`doses (based on the range of concentrations they will achieve) most likely to lead to a
`satisfactory response.
`
`Problems with Titration Designs
`A study design widely used to demonstrate effectiveness utilizes dose titration to
`some effectiveness or safety endpoint. Such titration designs, without careful
`analysis, are usually not informative about dose-response relationships. In many
`studies there is a tendency to spontaneous improvement over time that is not easily
`distinguishable from an increased response to higher doses or cumulative drug
`exposure. This leads to a tendency to choose, as a recommended dose, the highest
`dose used in such studies that was reasonably well-tolerated. Historically, this
`approach has often led to a dose that was well in excess of what was really necessary,
`resulting in increased undesirable effects, e.g. to high dose diuretics used for
`hypertension. In some cases, notably where an early answer is essential, the
`titration-to-highest-tolerable-dose approach is acceptable, because it often requires a
`
`2
`
`Page 6 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`minimum number of patients. For example, the first marketing of zidovudine (AZT)
`for treatment of people with AIDS was based on studies at a high dose; later studies
`showed that lower doses were as effective and far better tolerated. The urgent need
`for the first effective anti-HIV treatment made the absence of dose-response
`information at the time of approval reasonable (with the condition that more data
`were to be obtained after marketing), but in less urgent cases this approach is
`discouraged.
`
`Interactions between Dose-Response and Time
`The choice of the size of an individual dose is often intertwined with the frequency of
`dosing. In general, when the dose interval is long compared to the half-life of the
`drug, attention should be directed to the pharmacodynamic basis for the chosen
`dosing interval. For example, there might be a comparison of the long dose-interval
`regimen with the same dose in a more divided regimen, looking, where this is feasible,
`for persistence of desired effect throughout the dose-interval and for adverse effects
`associated with blood level peaks. Within a single dose-interval, the dose-response
`relationships at peak and through blood levels may differ and the relationship could
`depend on the dose interval chosen.
`Dose-response studies should take time into account in a variety of other ways. The
`study period at a given dose should be long enough for the full effect to be realized,
`whether delay is the result of pharmacokinetic, or pharmacodynamic factors. The
`dose-response may also be different for morning vs evening dosing. Similarly, the
`dose-response relationship during early dosing may not be the same as in the
`subsequent maintenance dosing period. Responses could also be related to
`cumulative dose, rather than daily dose, to duration of exposure (e.g., tachyphylaxis,
`tolerance, or hysteresis) or the relationships of dosing to meals.
`
`II. OBTAINING DOSE-RESPONSE INFORMATION
`Dose-Response Assessment Should Be an Integral Part of Drug Development
`Assessment of dose-response should be an integral component of drug development
`with studies designed to assess dose-response an inherent part of establishing the
`safety and effectiveness of the drug. If development of dose-response information is
`built into the development process it can usually be accomplished with no loss of time
`and minimal extra effort compared to development plans that ignore dose-response.
`
`Studies in Life-Threatening Diseases
`In particular therapeutic areas, different therapeutic and investigational behaviors
`have evolved; these affect the kinds of studies typically carried out. Parallel dose-
`response study designs with placebo or placebo-controlled titration study designs
`(very effective designs typically used in studies of angina, depression, hypertension,
`etc.) would not be acceptable in the study of some conditions, such as life-threatening
`infections or potentially curable tumors, at least if there were effective treatments
`known. Moreover, because in those therapeutic areas considerable toxicity could be
`accepted, relatively high doses of drugs are usually chosen to achieve the greatest
`possible beneficial effect rapidly. This approach may lead to recommended doses that
`deprive some patients of the potential benefit of a drug by inducing toxicity that leads
`to cessation of therapy. On the other hand, use of low, possibly subeffective, doses, or
`of titration to desired effect may be unacceptable, as an initial failure in these cases
`may represent and opportunity for cure forever lost.
`
`3
`
`Page 7 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`Nonetheless, even for life-threatening diseases, drug developers should always be
`weighing the gains and disadvantages of varying regimens and considering how best
`to choose dose, dose-interval and dose-escalation steps. Even in indications involving
`life-threatening diseases, the highest tolerated dose, or the dose with the largest effect
`on a surrogate marker will not always be the optimal dose. Where only single dose is
`studied, blood concentration data, which will almost always show considerable
`individual variability due to pharmacokinetic differences, may retrospectively give
`clues to possible concentration-response relationships.
`Use of just a single dose has been typical of large-scale intervention studies (e.g. post-
`myocardial infarction studies), because of the large sample sizes needed. In planning
`an intervention study, the potential advantages of studying more than a single dose
`should be considered. In some cases it may be possible to simplify the study by
`collecting less information on each patient, allowing study of a larger population
`treated with several doses without significant increase in costs.
`
`Regulatory Considerations When Dose-Response Data Are Imperfect
`Even well-laid plans are not invariably successful. An otherwise well-designed dose-
`response study may have utilized doses that were too high, or too close together, so
`that all appear equivalent (albeit superior to placebo). In that case, there is the
`possibility that the lowest dose studied is still greater than needed to exert the drug’s
`maximum effect. Nonetheless, an acceptable balance of observed undesired effects
`and beneficial effects might make marketing at one of the doses studied reasonable.
`This decision would be easiest, of course, if the drug had special value, but even if it
`did not, in light of the studies that partly defined the proper dose range, further dose-
`finding might be pursued in the post-marketing period. Similarly, although seeking
`dose-response data should be a goal of every development program, approval based on
`data from studies using a fixed single dose or a defined dose range (but without valid
`dose-response information) might be appropriate where benefit from a new therapy in
`treating or preventing a serious disease is clear.
`
`Examining the Entire Database for Dose-Response Information
`In addition to seeking dose-response information from studies specifically designed to
`provide it, the entire database should be examined intensively for possible dose-
`response effects. The limitations imposed by certain study design feature should of
`course be appreciated. For example, many studies titrate the dose upward for safety
`reasons. As most side effects of drugs occur early and may disappear with continued
`treatment, this can result in a spuriously higher rate of undesirable effects at the
`lower doses. Similarly, in studies where patients are titrated to a desired response,
`those patients relatively unresponsive to the drug are more likely to receive the
`higher dose, giving an apparent, but misleading, inverted “U-shaped” dose-response
`curve. Despite such limitations, clinical data from all sources should be analyzed for
`dose-related covariate effects using multivariate, or other alternative, approaches,
`even if the analyses can yield principally hypotheses, not definitive conclusions. For
`example, an inverse relation of effect to weight or creatinine clearance could reflect a
`dose-related covered relationship. If pharmacokinetics screening (obtaining a small
`number of steady-state blood concentration measurements in most phase 2/3 study
`patients) is carried out, or if other approaches to obtaining drug concentrations during
`trials are used, a relation of effects (desirable or undesirable) to blood concentrations
`may be discerned. The relationship may by itself be a persuasive description of
`concentration response or may suggest further study.
`
`4
`
`Page 8 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`III. STUDY DESIGNS FOR ASSESSING DOSE-RESPONSE
`General
`The choice of study design and study population in dose-response trials will depend on
`the phase of development, therapeutic indication under investigation, and the severity
`of the disease in the patient population of interest. For example, the lack of
`appropriate salvage therapy for life threatening or serious conditions with irreversible
`outcomes may ethically preclude conduct of studies at doses below the maximal
`tolerated dose. A homogeneous patient population will generally allow achievement
`of study objectives with small numbers of subjects given each treatment. On the other
`hand, larger, more diverse populations allow detection of potentially important
`covariate effects.
`In general, useful dose-response information is best obtained from trials specifically
`designed to compare several doses. A comparison of results from two or more
`controlled trials with single fixed doses might sometimes be informative, e.g., if
`control groups were similar, although, even in that case, the many across-study
`differences that occur in separate trials usually make this approach unsatisfactory. It
`is also possible in some cases to derive, retrospectively, blood concentration-response
`relationships from the variable concentrations attained in a fixed dose trial. While
`these analyses are potentially confounded by disease severity or other patient factors,
`the information can be useful and can guide subsequent studies. Conducting dose-
`response studies at an early stage of clinical development may reduce the number of
`failed phase 3 trials, speeding the drug development process and conserving
`development resources.
`Pharmacokinetic information can be used to choose doses that ensure adequate
`spread of attained concentration-response values and diminish or eliminate overlap
`between attained concentrations in dose-response trials. For drugs with high
`pharmacokinetic variability, a greater spread of doses could be chosen. Alternatively,
`the dosing groups could be individualized by adjusting for pharmacokinetic covariates
`(e.g., correction for weight, lean body mass, or renal function) or a concentration-
`controlled study could be carried out.
`As a practical matter, valid dose-response data can be obtained more readily when the
`response is measured by a continuous or categorical variable, is relatively rapidly
`obtained after therapy is started, and is rapidly dissipated after therapy is stopped
`(e.g., blood pressure, analgesia, bronchodilation). In this case, a wider range of study
`designs can be used and relatively small, simple studies can give useful information.
`Placebo-controlled individual subject titration designs typical of many early drug
`development studies, for example, properly conducted and analyzed (quantitative
`analysis that models and estimates the population and individual dose-response
`relationships), can give guidance for more definitive parallel, fixed dose, dose-
`response studies or may be definitive on their own.
`In contrast, when the study endpoint or adverse effect is delayed, persistent, or
`irreversible (e.g., stroke or heart attack prevention, asthma prophylaxis, arthritis
`treatments with late onset response, survival in cancer, treatment of depression),
`titration and simultaneous assessment of response is usually not possible, and the
`parallel dose-response study is usually needed. The parallel group, dose-response
`study also offers protection against missing an effective dose because of an inverted
`“U-shaped” (umbrella or bell shaped) dose-response curve, where higher doses are less
`effective than lower doses, a response that can occur, for example, with mixed agonist-
`antagonists.
`
`5
`
`Page 9 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`Trials intended to evaluate dose or concentration response should be well-controlled,
`using randomization and blinding (unless blinding is unnecessary or impossible) to
`assure comparability of treatment groups and to minimize potential patient,
`investigator, and analyst bias, and should be of adequate size.
`It is important to choose as wide a range of doses as is compatible with practicality
`and patient safety to discern clinically meaningful differences. This is especially
`important where there are no pharmacologic or plausible surrogate endpoints to give
`initial guidance as to dose.
`
`Specific Trial Designs
`A number of specific study designs can be used to assess dose-response. The same
`approaches can also be used to measure concentration-response relationships.
`Although not intended to be an exhaustive list, the following approaches have been
`shown to be useful ways of deriving valid dose-response information. Some designs
`outlined in this guidance are better established than others, but all are worthy of
`consideration. These designs can be applied to the study of established clinical
`endpoints or surrogate endpoints.
`
`1. Parallel dose-response
`Randomization to several fixed dose groups (the randomized parallel dose-
`response study) is simple in concept and is a design that has had extensive use
`and considerable success. The fixed dose is the final or maintenance dose;
`patients may be placed immediately on that dose or titrated gradually (in a
`scheduled “forced” titration) to it if that seems safer. In either case, the final dose
`should be maintained for a time adequate to allow the dose-response comparison.
`Although including a placebo group in dose-response studies is desirable, it is not
`theoretically necessary in all cases; a positive slope, even without a placebo group,
`provides evidence of a drug effect. To measure the absolute size of the drug effect,
`however, a placebo or comparator with very limited effect on the endpoint of
`interest is usually needed. Moreover, because a difference between drug groups
`and placebo unequivocally shows effectiveness, inclusion of a placebo group can
`salvage, in part, a study that used doses that were all too high and therefore
`showed no dose-response slope, by showing that all doses were superior to
`placebo. In principle, being able to detect a statistically significant difference in
`pairwise comparisons between doses is not necessary if a statistically significant
`trend (upward slope) across doses can be established using all the data. It should
`be demonstrated, however, that the lowest dose(s) tested, if these are to be
`recommended, have a statistically significant and clinically meaningful effect.
`The parallel dose-response study gives group mean (population-average) dose-
`responses, not the distribution or shape of individual dose-response curves.
`It is all too common to discover, at the end of a parallel dose-response study, that
`all doses were too high (on the plateau of the dose-response curve), or that doses
`did not go high enough. A formally planned interim analysis (or other multi-stage
`design) might detect such a problem and allow study of the proper dose range.
`As with any placebo-controlled trial, it may also be useful to include one or more
`doses of an active drug control. Inclusion of both placebo and active control
`groups allows assessment of “assay sensitivity”, permitting a distinction between
`an ineffective drug and an “ineffective” (null, no test) study. Comparison of dose-
`response curves for test and control drugs, not yet a common design, may also
`
`6
`
`Page 10 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`represent a more valid and informative comparative effectiveness/safety study
`than comparison of single doses of the two agents.
`The factorial trial is a special case of the parallel dose-response study to be
`considered when combination therapy is being evaluated. It is particularly useful
`when both agents are intended to affect the same response variable (a diuretic
`and another anti-hypertensive, for example), or when one drug is intended to
`mitigate the side effects of the other. These studies can show effectiveness (a
`contribution of each component of the combination) and, in addition, provide
`dosing information for the drugs used alone and together.
`A factorial trial is a parallel group, fixed-dose design that uses a range of doses of
`each separate drug and some or all combinations of these doses. The sample size
`need not be large enough to distinguish single cells from each other in pair-wise
`comparisons because all of the data can be used to derive dose-response
`relationships for the single agents and combinations, i.e., a dose-response surface.
`These trials therefore can be of moderate size. The doses and combinations that
`could be approved for marketing might not be limited to the actual doses studied
`but might include dose and combinations in between those studied. There may be
`some exceptions to the ability to rely entirely on the response surface analysis in
`choosing dose(s). At the low end of the dose range, if the doses used are lower
`than the recognized effective doses of the single agents, it would ordinarily be
`important to have adequate evidence that these can be distinguished from placebo
`in a pair-wise comparison. One way to do this in the factorial study is to have the
`lowest dose combination and placebo groups be somewhat larger than other
`groups; another is to have a separate study of the low-dose combination. Also, at
`the high end of the dose range, it may be necessary to confirm the contribution of
`each component to the overall effect.
`
`2. Cross-over dose-response
`A randomized multiple cross-over study of different doses can be successful if
`drug effect develops rapidly and patients return to baseline conditions quickly
`after cessation of therapy, if responses are not irreversible (cure, death), and if
`patients have reasonably stable disease. This design suffers, however, from the
`potential problems of all cross-over studies: it can have analytic problems if there
`are many treatment withdrawals; it can be quite long in duration for an
`individual patient; and there is often uncertainty about carry-over effects (longer
`treatment periods may minimize this problem), baseline comparability after the
`first period, and period-by-treatment interactions. The length of the trial can be
`reduced by approaches that do not require all patients to receive each dose, such
`as balanced incomplete block designs.
`The advantages of the design are that each individual receives several different
`doses so that the distribution of individual dose-response curves may be
`estimated, as well as the population average curve, and that, compared to a
`parallel group design, fewer patients may be needed. Also, in contrast to titration
`designs, dose and time are not confounded and carry-over effects are better
`assessed.
`
`3. Forced titration
`A forced titration study, where all patients move through a series of rising doses,
`is similar in concept and limitations to a randomized multiple cross-over dose-
`response study, except that assignment to dose levels is ordered, not random. If
`
`7
`
`Page 11 of 14
`
`

`
`Dose-Response Information to Support Drug Registration
`
`most patients complete all doses, and if the study is controlled with a parallel
`placebo-group, the forced titration study allows a series of comparisons of an
`entire randomized group given several doses of drug with a concurrent placebo,
`just as the parallel fixed dose trial does. A critical disadvantage is that by itself,
`this study design cannot distinguish response to increased dose from response to
`increased time on drug therapy or a cumulative drug dosage effect. It is therefore
`an unsatisfactory design when response is delayed, unless treatment at each dose
`is prolonged. Even where the time-until-development of effect is known to be
`short (from other data), this design gives poor information on adverse effects,
`many of which have time-dependent characteristics. A tendency toward
`spontaneous improvement, a very common circumstance, will be revealed by the
`placebo group, but is also a problem for this design, as over time the higher doses
`may find little room to show an increased effect. This design can give a
`reasonable first approximation of both population-average dose-response and the
`distribution of individual dose-response relationships if the cumulative (time-
`dependent) drug effect is minimal and the number of treatment withdrawals is
`not excessive. Compared to a parallel dose-response study, this design may use
`fewer patients, and can, by extending the study duration, be used to investigate a
`wide range of doses, again making it a reasonable first study. With a concurrent
`placebo group this design can provide clear evidence of effectiveness, and may be
`especially valuable in helping choose doses for a parallel dose-response study.
`
`4. Optional titration (placebo-controlled titration to end-point)
`In this design patients are titrated until they reach a well characterized favorable
`or unfavorable response, defined by dosing rules expressed in the protocol. This
`approach is most applicable to conditions where the response is reasonably
`prompt and is not an irreversible event, such as stroke or death. A crude analysis
`of such studies, e.g., comparing the effects in the subgroups of patients titrated to
`various dosages, often gives a misleading inverted “U-shaped” curve, as only poor
`responders are titrated to the highest dose. However, more sophisticated
`statistical analytical approaches that correct for this, by modeling and estimating
`the population and individual dose-response relationships, appear to allow
`calculation of valid dose-response information. Experience in deriving valid dose-
`response information in this fashion is still limited. It is impor