2  The Life of a Drug: Phases I to IV

A new medicine reaches patients through a sequence of experiments, each larger, longer and more expensive than the last, and each built to answer a different question. The conventional names, Phase I to Phase IV, describe this sequence, and every later chapter of this book sits inside one of them. This chapter is the map. It says what each phase is for, what can go wrong in it, how the traditional design handles it, and where a Bayesian decision maker would act differently. Throughout, a phase is treated as an experiment whose value lies in the decision it informs: whether to proceed to the next phase, at what dose, in which patients.

ImportantRegulatory anchor

The phases have regulatory definitions but need not form a rigid sequence. Chapter 3 describes each document in full and gives its status. Here only the roles matter.

  • 21 CFR 312.21. Describes Phases 1 to 3 of an investigation under an IND and expressly allows them to overlap, so a program is not obliged to complete one phase before starting the next.
  • ICH E8(R1), General Considerations for Clinical Studies (Step 4, October 2021). Classifies studies by objective (human pharmacology, exploratory, confirmatory, postmarketing) and says that the classic phase labels do not fit every program. A program is a set of studies, each with a stated question, organized by objective and not necessarily in a fixed sequence.
  • ICH E9, Statistical Principles for Clinical Trials (1998). Distinguishes exploratory from confirmatory trials. The type I error discipline of this book applies to the confirmatory stage.
  • FDA, Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products (draft guidance, January 2026). A draft, not binding. It is the document that most directly invites Bayesian methods at every stage, including the use of earlier-phase data to inform later ones.

2.1 Before Phase I

A compound enters human testing after discovery, lead optimization, and preclinical studies in cells and animals that establish pharmacology and a safe starting dose. In the United States the sponsor then files an Investigational New Drug application. Some programs run a Phase 0 or microdosing study, giving subtherapeutic doses to a handful of volunteers to check that the drug reaches its target and behaves pharmacokinetically as predicted. The prior for everything that follows is built here, from animal data, from mechanistic models and from the history of similar compounds.

2.2 Phase I: is it safe, and at what dose?

Phase I is the first exposure of humans to the drug. In most therapeutic areas it enrolls 20 to 100 healthy volunteers. In oncology, where the drugs are toxic, it enrolls patients for whom standard therapy has failed. The questions are tolerability, pharmacokinetics (what the body does to the drug), pharmacodynamics (what the drug does to the body), and, in oncology, the maximum tolerated dose.

The traditional oncology design is the 3+3 rule: treat three patients at a dose, escalate if none has a dose-limiting toxicity, add three more if one does, and stop if two or more do. The rule uses toxicity counts at the current dose, including any expansion cohort, without fitting a dose-toxicity curve, so it ignores the shape of that curve and identifies a dose with little precision. Model-based Bayesian designs replace it with a dose-toxicity model, for example

\[ \mathrm{logit}\,\Pr(\text{toxicity}\mid d) = \log a + b\log(d/d^\star),\qquad a,b > 0, \]

the Bayesian logistic regression model of Neuenschwander, Branson, and Gsponer (2008). After each cohort the posterior over \((a,b)\) is updated, and the next dose is the one with the highest posterior probability of a toxicity rate in the target interval, subject to a cap on the posterior probability of overdosing. The continual reassessment method (O’Quigley, Pepe, and Fisher 1990) and escalation with overdose control (Babb, Rogatko, and Zacks 1998) belong to the same family. Section 17.1 simulates the 3+3 and sets it beside these designs on the same scenarios, and Chapter 17 develops them.

NoteTGN1412: a design that could not learn between patients

In March 2006 six healthy volunteers in London received the first human doses of TGN1412, a monoclonal antibody against CD28, and two others received placebo (Suntharalingam et al. 2006). Within hours all six who received the drug developed a cytokine storm with multiple organ failure. The doses were given within minutes of one another, so the first volunteer’s reaction could not inform the decision to dose the others. In the language of this book, the design gave the first observation no chance to update the action for the rest of the cohort. Staggered dosing, in which the first participant is dosed alone and observed before the next, is now standard practice. It is the cheapest possible way to let the posterior after one participant inform the next decision, and a reminder that a sequential design is a safety device before it is an efficiency device.

2.3 Phase II: does it work, and at what dose?

Phase II is where most drugs fail, and where most of the value of a development program is created or destroyed. Phase IIa is proof of concept: a small randomized or single-arm study asking whether the drug moves a clinical or biomarker endpoint at all. Phase IIb is dose ranging: several doses against placebo, to estimate the dose-response curve and choose the dose for Phase III.

Phase II is where Bayesian methods have the strongest claim, because its purpose is learning rather than confirming, a distinction made central to clinical pharmacology by Sheiner (1997). The natural output of Phase II is not a p-value but a posterior over the dose-response curve and a predictive probability that Phase III will succeed. Chapter 15 builds that predictive probability, beginning from the traditional conditional power of Section 15.1, and Section 9.6.3 shows why a Phase III designed around the Phase II point estimate is usually underpowered. Chapter 17 treats dose finding and dose optimization, and Chapter 16 the allocation rules that adaptive Phase II designs borrow from bandit theory.

NoteASTIN: an early and well-founded no

The ASTIN trial tested a neutrophil inhibitory factor (UK-279,276) in acute ischemic stroke (Krams et al. 2003). Patients were allocated adaptively among many doses and placebo, with a Bayesian dose-response model updated as outcomes accrued and allocation chosen to learn most about the dose giving 95 percent of the maximum effect. The design included rules to stop for futility or efficacy. The trial found no treatment effect and stopped early for futility, at 966 patients according to the published report. A fixed design without interim analyses would have run to completion before learning the same thing, although a conventional group sequential design with a futility rule could also have stopped early. ASTIN is the standard example of a Bayesian adaptive design delivering its most valuable output, a fast and well-founded negative result.

2.4 Phase III: confirming, and the regulatory decision

Phase III trials are large, randomized and usually blinded, designed to confirm efficacy and characterize safety in the population for which the drug will be licensed. They enroll hundreds to tens of thousands of patients and cost from tens to hundreds of millions of dollars. The FDA’s traditional evidentiary standard is two adequate and well-controlled trials, or one large trial with confirmatory evidence. This is the stage at which the type I error rate of Chapter 9 is the contract with the regulator, and at which interim analyses (Chapter 11, Chapter 15) are governed by the strictest rules. Chapter 3 describes the documents that apply.

NoteTorcetrapib: a signal that belonged in the prior

In December 2006 Pfizer stopped ILLUMINATE, a Phase III outcomes trial of torcetrapib, a drug that raised HDL cholesterol, after the data monitoring committee found an excess of deaths on the drug (Barter et al. 2007). The program had cost hundreds of millions of dollars. Torcetrapib had been associated with higher blood pressure in earlier studies, a signal visible before the outcomes trial began. The episode illustrates two themes of this book: information from earlier phases about off-target effects belongs in the prior for Phase III, and the value of an interim analysis lies as much in stopping for harm as for benefit. Chapter 13 develops safety monitoring.

2.5 Phase IV: after approval

Approval is not the end of learning. Phase IV comprises postmarketing studies required or agreed at approval, observational surveillance of adverse events, and confirmatory trials for drugs granted accelerated approval on a surrogate endpoint. Premarketing trials are often too small or too short to characterize rare harms reliably, and such harms become clear only when many more patients are exposed.

NoteRofecoxib: surveillance as a sequential decision

Rofecoxib (Vioxx) was approved in 1999 and withdrawn on 30 September 2004, after the APPROVe trial, a randomized comparison with placebo in 2,586 patients with a history of colorectal adenoma, showed a higher rate of confirmed thrombotic events on the drug (46 events against 26, rate ratio 1.92, 95% CI 1.19 to 3.11) (Bresalier et al. 2005). Earlier, the VIGOR trial in rheumatoid arthritis had shown fewer gastrointestinal events than with naproxen but more myocardial infarctions (Bombardier et al. 2000). A cumulative meta-analysis found that a statistically clear excess of myocardial infarction was already present at the end of 2000, years before withdrawal (Jüni et al. 2004). Postmarketing surveillance is a sequential decision problem in which the action is to warn, restrict or withdraw, and the cost of waiting is counted in patients harmed. Chapter 13 returns to the case.

Postmarketing surveillance is also where empirical Bayes has had its greatest regulatory success. Spontaneous reporting systems collect millions of reports of drug and adverse-event pairs. The observed count \(n_{ij}\) for drug \(i\) and event \(j\) is compared with the count \(E_{ij}\) expected under independence, and the crude ratio \(\hat\lambda_{ij} = n_{ij}/E_{ij}\) is unstable when counts are small. The gamma-Poisson shrinker of DuMouchel (1999) instead defines a latent relative reporting rate \(\lambda_{ij}\) through the model \(n_{ij}\sim\mathrm{Poisson}(\lambda_{ij}E_{ij})\), with a mixture of gammas for \(\lambda_{ij}\), and reports its posterior estimate, so that an estimate based on three reports is shrunk heavily toward the common distribution and one based on three hundred is not. This is the same kind of partial pooling that Chapter 20 describes for platform trials, applied at the scale of a national database.

2.6 The phases as a sequence of options

Let \(p_{12}\), \(p_{23}\) and \(p_{3A}\) denote the probabilities of moving from Phase I to II, from II to III, and from III to approval, and let \(c_1\), \(c_2\), \(c_3\) be the costs of the phases. Phase \(k\) is paid for only if all earlier phases succeed, so the expected cost per drug started is \(c_1 + p_{12}c_2 + p_{12}p_{23}c_3\). The expected number of approvals per start is \(p_{12}p_{23}p_{3A}\), and the ratio of the two expectations is the long-run cost per approval:

\[ C_{\mathrm{approved}} = \frac{c_1 + p_{12}c_2 + p_{12}p_{23}c_3}{p_{12}\,p_{23}\,p_{3A}}. \tag{2.1}\]

The formula explains why attrition dominates the economics of drug development. Wong, Siah, and Lo (2019) used over 400,000 trial records for more than 21,000 compounds, and estimated that about 13.8 percent of programs entering Phase I eventually reach approval, and 3.4 percent in oncology. Programs that use biomarkers to select patients have higher success probabilities. The sensitivity is easy to see with a stylized example. The probabilities and costs below are illustrative, not estimates from any source: they are chosen only so that the overall success probability is near the published range.

Show the R code 
cost <- function(p12 = 0.5, p23 = 0.3, p3A = 0.6, k = c(25, 60, 250)) {
  (k[1] + p12 * k[2] + p12 * p23 * k[3]) / (p12 * p23 * p3A)
}
base <- cost()
tab <- data.frame(
  Scenario = c("Baseline", "Phase III 20% cheaper", "Phase II success 0.30 to 0.40", "Phase I success 0.50 to 0.60"),
  `Cost per approval` = c(base, cost(k = c(25, 60, 200)), cost(p23 = 0.4), cost(p12 = 0.6)),
  check.names = FALSE
)
tab$`Change (%)` <- 100 * (tab$`Cost per approval` / base - 1)
knitr::kable(tab, digits = c(0, 0, 1))
Table 2.1: Stylized cost per approved drug from Equation 2.1, in millions of dollars. The baseline has p12 = 0.5, p23 = 0.3, p3A = 0.6 and phase costs of 25, 60 and 250 (illustrative values, not data). The rows change one input at a time.
Scenario Cost per approval Change (%)
Baseline 1028 0.0
Phase III 20% cheaper 944 -8.1
Phase II success 0.30 to 0.40 875 -14.9
Phase I success 0.50 to 0.60 981 -4.5

Raising the Phase II to III transition probability from 0.30 to 0.40 lowers the cost per approval by 15 percent, and making Phase III a fifth cheaper lowers it by 8 percent. The ranking of these two savings depends on the perturbations chosen: the first changes Phase II success by a third, the second reduces one cost by a fifth, so the comparison is not a general ranking of inputs. Nor is advancing more compounds in itself better selection; the case for the predictive methods of Chapter 15 is that they advance the right ones.

2.7 Bioequivalence: TOST and a posterior summary

A generic or reformulated drug must be shown to deliver the same exposure as the reference product. Exposure is measured by the area under the concentration-time curve, and the parameter of interest is the ratio \(\rho = \mu_T/\mu_R\) of geometric means for test and reference. Bioequivalence is declared when \(\rho\) lies in an equivalence interval, conventionally \((0.80, 1.25)\). The classical analysis is the two one-sided tests (TOST) procedure of Schuirmann (1987), which gives the confidence-interval criterion a test form, on \(\eta = \log\rho\), equivalent to checking that the 90 percent confidence interval lies inside \((\log 0.80, \log 1.25)\); Westlake had proposed a symmetric confidence interval for the same purpose (Westlake 1976), and Hauck and Anderson a different test of equivalence for two-group bioavailability trials (Hauck and Anderson 1984).

The Bayesian version asks the question directly; it goes back to Rodda and Davis (Rodda and Davis 1980), Mandallaz and Mau (Mandallaz and Mau 1981) and Selwyn, Dempster and Hall (Selwyn, Dempster, and Hall 1981), with the Basel worked example of Flühler et al. (1983), a two-stage procedure by Racine-Poon and colleagues (Racine-Poon et al. 1987), and a decision-analytic treatment by Lindley (Lindley 1998). Take a simplified model in which the \(n\) within-subject log differences \(d_i\) are independent and normal with mean \(\eta\), sample mean \(\bar d\) and standard deviation \(s\), and use a reference prior. (A standard two-sequence, two-period crossover analysis also models period and sequence effects and generally has different residual degrees of freedom, so this is a simplification, not the regulatory analysis.) Then the posterior of \(\eta\) is a scaled \(t\) distribution, \(\eta\mid d \sim \bar d + (s/\sqrt n)\,t_{n-1}\), and the reported quantity is

\[ \Pr\bigl(\log 0.80 < \eta < \log 1.25 \mid d\bigr) = F_{t_{n-1}}\!\left(\frac{\log 1.25 - \bar d}{s/\sqrt n}\right) - F_{t_{n-1}}\!\left(\frac{\log 0.80 - \bar d}{s/\sqrt n}\right). \tag{2.2}\]

A rule that concludes bioequivalence when this probability exceeds a threshold such as 0.90 is an alternative to TOST, not the conventional criterion: TOST is the standard in FDA’s final guidance Statistical Approaches to Establishing Bioequivalence (U.S. Food and Drug Administration 2026) (May 2026, Section II.C.1.a), and a posterior-probability rule would need agreement with the regulator and an evaluation of its operating characteristics. The relation to TOST is exact under the reference prior. Each one-sided posterior tail probability equals the corresponding one-sided TOST p-value, so the posterior probability of equivalence is \(1 - p_L - p_U\). If both p-values are below 0.05, the posterior probability exceeds 0.90. The two procedures can therefore disagree only in one direction: TOST at level 0.05 implies a posterior probability above 0.90, and a posterior probability above 0.90 does not imply TOST success. Choosing the threshold 0.95 (and, to match, TOST at 0.025 on each side) changes the comparison. The posterior probability is therefore a supplementary summary of the same data that is easy to read, and it is a weaker rule at 0.90: some data sets pass it and fail TOST (the third row of Table 2.2, with posterior probability 0.9291 and TOST p-value 0.0709). Racine-Poon et al. (1987) made the procedure sequential, using the posterior and its predictive distribution after a first stage to decide whether to stop or how many further subjects to recruit, the template for the interim decision rules of Chapter 15. Average bioequivalence is also not the only approach regulators use: for highly variable drugs some product-specific recommendations use reference-scaled approaches, so the Bayesian rule is one design choice within a family and not a replacement for it.

Show the R code 
be <- function(n, dbar, s, lo = log(0.8), hi = log(1.25)) {
  se <- s / sqrt(n)
  pl <- pt((dbar - lo) / se, n - 1, lower.tail = FALSE)
  pu <- pt((dbar - hi) / se, n - 1)
  c(post = 1 - pl - pu, tost = max(pl, pu))
}
res <- rbind(
  `Centered, n = 24` = be(24, 0.03, 0.30),
  `Centered, n = 12` = be(12, 0.03, 0.30),
  `Shifted to 0.13, n = 24` = be(24, 0.13, 0.30),
  `Shifted to 0.15, n = 24` = be(24, 0.15, 0.30)
)
colnames(res) <- c("Posterior prob. of equivalence", "TOST p-value")
knitr::kable(res, digits = 4)
Table 2.2: Bayesian and TOST bioequivalence for four illustrative crossover scenarios (made-up values): within-subject SD of the log differences 0.30 throughout, and mean log difference 0.03 (n = 24 and n = 12) or 0.13 and 0.15 (n = 24). Posterior probability from the formula above under the reference prior; TOST p-value is the larger of the two one-sided p-values.
Posterior prob. of equivalence TOST p-value
Centered, n = 24 0.9976 0.0022
Centered, n = 12 0.9693 0.0238
Shifted to 0.13, n = 24 0.9291 0.0709
Shifted to 0.15, n = 24 0.8778 0.1222

2.8 Recruitment and the value of speed

Most trials are slow because of accrual, not analysis, and the recruitment rate is the quantity a sponsor can least control. One episode shows both how to estimate a rate and what a recruit is worth. In November 1995 Michael Milken, who had founded CaP CURE (later the Prostate Cancer Foundation) after his own prostate cancer diagnosis, appeared on CNN’s Larry King Live with General Norman Schwarzkopf and the molecular biologist Leroy (Lee) Hood of the University of Washington, and asked families with several men affected by prostate cancer to volunteer for a genetic study (Prostate Cancer Foundation 2025; Daniels 2004). More than 3,000 people called. Within three weeks Hood’s group had a sample of about 300 qualified families, where Johns Hopkins had recruited 90 families over ten years (Daniels 2004); a University of Washington release of 1999 reports 291 families enrolled in the resulting PROGRESS study, many of whom came after seeing the broadcast (University of Washington 1999). The coauthors’ working paper analyzes the episode (Sokolova, Sokolov, and Polson 2026), and the calculations below follow it.

Model enrollment of eligible families as a Poisson process with rate \(\lambda\) per week. With the reference prior \(\mathrm{Gamma}(1/2, 0)\) and \(n\) families observed in \(t\) weeks, the posterior is \(\mathrm{Gamma}(n + 1/2, t)\), the conjugate update of Chapter 6. The conventional pace is not known. “Several years” for 300 families is an assumption, and we bracket it at three to five years, which we treat as fixed scenario rates of \(300/156\) to \(300/260\) families a week, not as data.

The posterior for the broadcast rate has mean 100 families a week and standard deviation 5.8, so the counting error is small. The ratio of the broadcast rate to an assumed fixed conventional rate is 52 (95 percent interval 46 to 58) if the conventional pace was three years, and 87 (77 to 97) if it was five. These are conditional comparisons against assumed conventional rates, rather than estimates from conventional recruitment data. The real uncertainty is the counterfactual pace, not the count. The reported three-week identification of eligible families was much faster than the assumed conventional scenarios, and completed enrollment and specimen-collection rates are not established by this account. This is the Bayesian answer to the planning question of how long accrual will take, and it is the same calculation that, with a prior borrowed from earlier sites, turns a protocol’s accrual assumption into a predictive distribution of the end date.

A rate is not the whole story, because a recruit is worth the evidence it contributes. Linkage studies report a LOD score, the base ten logarithm of the likelihood ratio for linkage against no linkage (Morton 1955). At a fixed recombination fraction and genetic model, a LOD score is a log likelihood ratio. A posterior probability of linkage requires a marginal Bayes factor \(B\) in the sense of Chapter 7, integrating over uncertain linkage parameters, and with prior probability \(\pi\) that a disease gene lies in the region tested it equals \(\pi B / (\pi B + 1 - \pi)\). A maximized LOD of 3 does not automatically imply \(B = 1000\) (Génin, Martinez, and Clerget-Darpoux 1995). If it did, with a prior of one in fifty the posterior probability would be 0.95. Because log likelihood ratios add across independent families, the value of a family is the expected LOD it contributes. A broad appeal brings in families whose clustering reflects screening rather than inheritance (phenocopies) and families whose disease is not linked to the locus under study, and both dilute that expectation. Under a crude working approximation, expected LOD per family is \(e_1 \alpha (1 - \phi)\), with \(e_1\) the expected LOD of a fully informative linked family, \(\alpha\) the fraction of families linked to the locus and \(\phi\) the phenocopy dilution. These are illustrative inputs, not estimates: with \(e_1 = 0.3\), \(\alpha = 0.2\) and \(\phi = 0.3\), a family is worth 0.042 LOD, and under this toy assumption about expected information approximately 71 families would give an expected cumulative LOD of 3, against 29 if \(\alpha = 0.34\) and \(\phi = 0\). These are mean-path calculations, not sample-size requirements: enrollment planning needs a specified probability of reaching the threshold and a model for family heterogeneity, and unlinked families need not contribute zero expected log likelihood ratio. Volume rose by a factor of fifty or more while quality per family may have fallen (a hypothesis, since comparative pedigree and informativeness data would be needed to establish it), so the sensible design takes the volume and then weights families by their posterior probability of carrying the signal, which is what a hierarchical model does automatically (Chapter 19). The same logic applies to a trial: count the information a patient contributes, not the patients.

The value of the acceleration is the part that depends on assumptions, and every one is labeled. Suppose the resulting family resource has probability \(p\) of leading to a clinically useful genetic test (assumed), that the test reduces mortality among hereditary cases by a fraction \(r\) (assumed), and that the broadcast brings that benefit forward by \(y\) years (assumed, and smaller than the years of accrual saved, because genotyping and replication take their own time). Take 37,000 United States prostate cancer deaths a year (late 1990s, as the working paper reports), a hereditary share of 9 percent (an assumption), ten life years lost per death (assumed) and $100,000 per life year (assumed). The expected value is \(V = 37{,}000 \times 0.09 \times r \times 10 \times \$100{,}000 \times y \times p\), which is $67 million at \(p = 0.1\), \(r = 0.1\), \(y = 2\) and $500 million at \(p = 0.25\), \(r = 0.2\), \(y = 3\). If the appeal replaced an assumed $2,000 to $5,000 of conventional outreach expenditure per family and had negligible marginal cost, the modeled gross saving would be $0.6 million to $1.5 million. Under the chosen assumptions, the larger modeled value comes from earlier clinical benefit. The range is wide because the inputs are, and it is an ex ante expectation: the first locus reported, HPC1 on 1q24-25 from 91 high-risk families (Smith et al. 1996), did not become a clinical test, and the actionable variant, HOXB13 G84E, was reported in 2012 (Ewing et al. 2012). An expectation can be the right basis for a decision even when one draw is disappointing. The full treatment of the value of information is in Volume II.

2.9 A Bayesian reading of the phases

Each phase updates a posterior and hands it to the next. Phase I produces a posterior over the dose-toxicity curve and the pharmacokinetic parameters, which becomes the prior for dose selection in Phase II. Phase II produces a posterior over the dose-response curve, and its predictive distribution gives the probability that Phase III will succeed. Phase III produces the evidence on which approval is decided. Phase IV keeps updating after approval. Traditional development also passes information forward: estimates and their uncertainty, dose-response and pharmacokinetic models, and safety findings all inform the next phase, and the confirmatory phase is where formal hypothesis tests carry the decision. The distinction is not that the traditional path passes verdicts and the Bayesian path passes distributions. It is that a Bayesian development program specifies one probability model across the phases, so that what one phase learns propagates into the predictive probabilities and decisions of the next, whereas the traditional path links phases through estimates and judgment. The rest of the book is about what this buys, and about the conditions (calibration, pre-specification, simulation) under which a regulator will accept the alternative. Table 2.3 is the map from phase to chapter.

Table 2.3: Phases, the questions they answer, and where this book treats each.
Phase Question Traditional design Bayesian method Chapter
I Safe? Which dose? 3+3 Model-based escalation (BLRM, CRM, EWOC) Chapter 17
II Works? Which dose? Fixed-dose arms, single-arm response test Dose-response models, predictive probability, adaptive allocation Chapter 17, Chapter 15, Chapter 16
III Confirmed? Fixed or group sequential, type I error 0.025 Posterior success criteria calibrated to error control, borrowing Chapter 11, Chapter 9, Chapter 19
IV Harm after approval? Spontaneous reports, observational studies Empirical Bayes shrinkage, sequential monitoring Chapter 13

Key points

  • The phases are experiments in which each hands the next a decision. Traditional development passes estimates, models and safety findings forward; a Bayesian program additionally propagates one probability model into predictive decisions.
  • Phase I is a safety problem first: TGN1412 shows the cost of a design that cannot update between patients. Model-based escalation fits a dose-toxicity curve to all accumulated toxicity data, where the 3+3 uses only the counts at the current dose.
  • Phase II is where most programs fail and where Bayesian learning pays most: a posterior over the dose-response curve and a predictive probability of Phase III success replace a p-value.
  • Phase III is confirmatory, and a Bayesian criterion there is judged by its operating characteristics under a pre-specified design.
  • Phase IV is a sequential decision problem. The rofecoxib record shows that evidence of harm can be in hand years before action.
  • Cost per approval, Equation 2.1, falls with each transition probability and each phase cost. In the stylized example a one-third rise in Phase II success saves more than a one-fifth cut in Phase III cost, but that ranking depends on the perturbations chosen, and advancing more compounds is not itself better selection.
  • Bayesian bioequivalence is a familiar posterior probability. Under a reference prior, TOST success at 0.05 implies a posterior probability above 0.90, but not conversely, so the posterior rule is a supplementary summary or an alternative needing regulatory agreement, while TOST remains the conventional criterion.
  • Recruitment is usually the slowest step, and a recruit is worth the evidence it adds. A gamma-Poisson posterior turns an enrollment count into a rate with an interval, and a LOD score, a log likelihood ratio at a fixed model, shows why more participants can mean less information per participant when a broad appeal dilutes the signal.
NoteDiscussion questions
  1. For each of Phases I to IV, state in one sentence the decision the phase informs and the kind of error that matters most in it. Where does a type I error rate become the contract with the regulator?
  2. The stylized cost-per-approval example changes one input at a time. What does it establish, and what does it not? Why can a ranking of two savings depend on the size of the perturbations chosen?
  3. Why might advancing more compounds from Phase II to Phase III be a worse decision, even though it raises the Phase II transition probability?
  4. Under a reference prior, TOST success at level 0.05 implies a posterior probability of equivalence above 0.90, but not the reverse. Explain why, and say what a sponsor would have to show a regulator before using the posterior rule as the primary criterion.
  5. TGN1412 and ASTIN are both sequential designs. What did each show about the value of letting early data change later actions?
  6. In the Larry King episode the enrollment rate rose fiftyfold or more while the expected LOD per family probably fell. How should a trial team decide whether a faster, broader recruitment channel is worth using, and what would it need to measure?