Richter Syndrome Presenting as Subcutaneous Nodules and a Dermal Plaque.

ABSTRACT: Richter syndrome (RS) describes a phenomenon in which a patient with chronic lymphocytic leukemia (CLL) develops an aggressive lymphoma, most commonly diffuse large B-cell lymphoma (DLBCL). Reports of cutaneous RS remain exceedingly rare. We report a 61-year-old woman with relapsed/refractory CLL presenting with several subcutaneous nodules on her arms and legs and a single dermal plaque on her abdomen. Skin biopsy revealed a diagnosis of DLBCL, ABC-type, and her clinical status rapidly deteriorated following diagnosis. We review the variety of clinical presentations of cutaneous RS, its association with CLL, risk factors for RS development in CLL patients, and the distinctive histopathologic and immunophenotypic features of DLBCL. We hope to highlight the importance of prompt skin biopsy in patients with CLL presenting with progressive skin lesions and increase awareness of this aggressive clinical syndrome.

Suspected serial killers and unsuspected statistical blunders.

A whole branch of theoretical statistics devotes itself to the analysis of clusters, the aim being to distinguish an apparent cluster arising randomly from one that is more likely to have been produced as a result of some systematic influence. There are many examples in medicine and some that involve both medicine and the legal field; criminal law in particular. Observed clusters or a series of cases in a given setting can set off alarm bells, the recent conviction of Lucy Letby in England being an example. It was an observed cluster, a series of deaths among neonates, that prompted the investigation of Letby. There have been other similar cases in the past and there will be similar cases in the future. Our purpose is not to reconsider any particular trial but, rather, to work with similar, indeed more extreme numbers of cases as a way to underline the statistical mistakes that can be made when attempting to make sense of the data. These notions are illustrated via a made-up case of 10 incidents where the anticipated count was only 2. The most common statistical analysis would associate a probability of less than 0.00005 with this outcome: A very rare event. However, a more careful analysis that avoids common pitfalls results in a probability close to 0.5, indicating that, given the circumstances, we were as likely to see 10 or more as we were to see less than 10.

Making sense of breast cancer risk estimates.

Individual probabilistic assessments on the risk of cancer, primary or secondary, will not be understood by most patients. That is the essence of our arguments in this paper. Greater understanding can be achieved by extensive, intensive, and detailed counseling. But since probability itself is a concept that easily escapes our everyday intuition-consider the famous Monte Hall paradox-then it would also be wise to advise patients and potential patients, to not put undue weight on any probabilistic assessment. Such assessments can be of value to the epidemiologist in the investigation of different potential etiologies describing cancer evolution or to the clinical trialist as a way to maximize design efficiency. But to an ordinary individual we cannot anticipate that these assessments will be correctly interpreted.

Acute hepatic porphyrias: Recommendations for diagnosis and management with real-world examples.

Acute hepatic porphyria (AHP) is a group of four rare inherited diseases, each resulting from a deficiency in a distinct enzyme in the heme biosynthetic pathway. Characterized by acute neurovisceral symptoms that may mimic other medical and psychiatric conditions, lack of recognition of the disease often leads to a delay in diagnosis and initiation of effective treatment. Biochemical testing for pathway intermediates that accumulate when the disease is active forms the basis for screening and establishing a diagnosis. Subsequent genetic analysis identifies the pathogenic variant, supporting screening of family members and genetic counseling. Management of AHP involves avoidance of known exogenous and hormonal triggers, symptomatic treatment, and prevention of recurrent attacks. Here we describe six case studies from our own real-world experience to highlight current recommendations and challenges associated with the diagnosis and long-term management of the disease.

Using Worker Position Data for Human-Driven Decision Support in Labour-Intensive Manufacturing.

This paper provides a novel methodology for human-driven decision support for capacity allocation in labour-intensive manufacturing systems. In such systems (where output depends solely on human labour) it is essential that any changes aimed at improving productivity are informed by the workers' actual working practices, rather than attempting to implement strategies based on an idealised representation of a theoretical production process. This paper reports how worker position data (obtained by localisation sensors) can be used as input to process mining algorithms to generate a data-driven process model to understand how manufacturing tasks are actually performed and how this model can then be used to build a discrete event simulation to investigate the performance of capacity allocation adjustments made to the original working practice observed in the data. The proposed methodology is demonstrated using a real-world dataset generated by a manual assembly line involving six workers performing six manufacturing tasks. It is found that, with small capacity adjustments, one can reduce the completion time by 7% (i.e., without requiring any additional workers), and with an additional worker a 16% reduction in completion time can be achieved by increasing the capacity of the bottleneck tasks which take relatively longer time than others.

Comparison of thrombotic and clinical outcomes in SARS-CoV-2-pneumonia versus other viral pneumonia in an urban academic medical center.

BACKGROUND: Infection with viral pneumonia (PNA) is known to offset the coagulation cascade. Recent studies assessing novel SARS-CoV-2 infection observed a high frequency of systemic thrombotic events resulting in ambiguity if severity of infection or specific viral strain drive thrombosis and worsen clinical outcomes. Furthermore, limited data exists addressing SARS-CoV-2 in underrepresented patient populations. OBJECTIVES: Assess clinical outcomes events and death in patients diagnosed with SARS-CoV-2 pneumonia compared to patients with other types of viral pneumonia. METHODS: Retrospective cohort study evaluated electronic medical records in adult patients admitted to University of Illinois Hospital and Health Sciences System (UIHHSS) with primary diagnosis of SARS-CoV-2 PNA or other viral (H1N1 or H3N2) PNA between 10/01/2017 and 09/01/2020. Primary composite outcome was the following event incidence rates: death, ICU admission, infection, thrombotic complications, mechanical ventilation, renal replacement therapy, and major bleeding. RESULTS: Of 257 patient records, 199 and 58 patients had SARS-CoV-2 PNA and other viral PNA, respectively. There was no difference in primary composite outcome. Thrombotic events (n = 6, 3%) occurred solely in SARS-CoV-2 PNA patients in the ICU. A significantly higher incidence of renal replacement therapy (8.5% vs 0%, p=0.016) and mortality (15.6% vs 3.4%, p=0.048) occurred in the SARS-CoV-2 PNA group. Multivariable logistic regression analysis revealed age, presence of SARS-CoV-2, and ICU admission, aOR 1.07, 11.37, and 41.95 respectively, was significantly associated with mortality risk during hospitalization; race and ethnicity were not. CONCLUSION: Low overall incidence of thrombotic events occurred only in the SARS-CoV-2 PNA group. SARS-CoV-2 PNA may lead to higher incidence of clinical events than those observed in H3N2/H1N1 viral pneumonia, and that race/ethnicity does not drive mortality outcomes.

Effect of P2Y12 Inhibitors on Organ Support-Free Survival in Critically Ill Patients Hospitalized for COVID-19: A Randomized Clinical Trial.

Importance: Platelet activation is a potential therapeutic target in patients with COVID-19. Objective: To evaluate the effect of P2Y12 inhibition among critically ill patients hospitalized for COVID-19. Design, Setting, and Participants: This international, open-label, adaptive platform, 1:1 randomized clinical trial included critically ill (requiring intensive care-level support) patients hospitalized with COVID-19. Patients were enrolled between February 26, 2021, through June 22, 2022. Enrollment was discontinued on June 22, 2022, by the trial leadership in coordination with the study sponsor given a marked slowing of the enrollment rate of critically ill patients. Intervention: Participants were randomly assigned to receive a P2Y12 inhibitor or no P2Y12 inhibitor (usual care) for 14 days or until hospital discharge, whichever was sooner. Ticagrelor was the preferred P2Y12 inhibitor. Main Outcomes and Measures: The primary outcome was organ support-free days, evaluated on an ordinal scale that combined in-hospital death and, for participants who survived to hospital discharge, the number of days free of cardiovascular or respiratory organ support up to day 21 of the index hospitalization. The primary safety outcome was major bleeding, as defined by the International Society on Thrombosis and Hemostasis. Results: At the time of trial termination, 949 participants (median [IQR] age, 56 [46-65] years; 603 male [63.5%]) had been randomly assigned, 479 to the P2Y12 inhibitor group and 470 to usual care. In the P2Y12 inhibitor group, ticagrelor was used in 372 participants (78.8%) and clopidogrel in 100 participants (21.2%). The estimated adjusted odds ratio (AOR) for the effect of P2Y12 inhibitor on organ support-free days was 1.07 (95% credible interval, 0.85-1.33). The posterior probability of superiority (defined as an OR > 1.0) was 72.9%. Overall, 354 participants (74.5%) in the P2Y12 inhibitor group and 339 participants (72.4%) in the usual care group survived to hospital discharge (median AOR, 1.15; 95% credible interval, 0.84-1.55; posterior probability of superiority, 80.8%). Major bleeding occurred in 13 participants (2.7%) in the P2Y12 inhibitor group and 13 (2.8%) in the usual care group. The estimated mortality rate at 90 days for the P2Y12 inhibitor group was 25.5% and for the usual care group was 27.0% (adjusted hazard ratio, 0.96; 95% CI, 0.76-1.23; P = .77). Conclusions and Relevance: In this randomized clinical trial of critically ill participants hospitalized for COVID-19, treatment with a P2Y12 inhibitor did not improve the number of days alive and free of cardiovascular or respiratory organ support. The use of the P2Y12 inhibitor did not increase major bleeding compared with usual care. These data do not support routine use of a P2Y12 inhibitor in critically ill patients hospitalized for COVID-19. Trial Registration: ClinicalTrials.gov Identifier: NCT04505774.

Effect of Thromboprophylaxis on Clinical Outcomes After COVID-19 Hospitalization.

BACKGROUND: Patients hospitalized with COVID-19 have an increased incidence of thromboembolism. The role of extended thromboprophylaxis after hospital discharge is unclear. OBJECTIVE: To determine whether anticoagulation is superior to placebo in reducing death and thromboembolic complications among patients discharged after COVID-19 hospitalization. DESIGN: Prospective, randomized, double-blind, placebo-controlled clinical trial. (ClinicalTrials.gov: NCT04650087). SETTING: Done during 2021 to 2022 among 127 U.S. hospitals. PARTICIPANTS: Adults aged 18 years or older hospitalized with COVID-19 for 48 hours or more and ready for discharge, excluding those with a requirement for, or contraindication to, anticoagulation. INTERVENTION: 2.5 mg of apixaban versus placebo twice daily for 30 days. MEASUREMENTS: The primary efficacy end point was a 30-day composite of death, arterial thromboembolism, and venous thromboembolism. The primary safety end points were 30-day major bleeding and clinically relevant nonmajor bleeding. RESULTS: Enrollment was terminated early, after 1217 participants were randomly assigned, because of a lower than anticipated event rate and a declining rate of COVID-19 hospitalizations. Median age was 54 years, 50.4% were women, 26.5% were Black, and 16.7% were Hispanic; 30.7% had a World Health Organization severity score of 5 or greater, and 11.0% had an International Medical Prevention Registry on Venous Thromboembolism risk prediction score of greater than 4. Incidence of the primary end point was 2.13% (95% CI, 1.14 to 3.62) in the apixaban group and 2.31% (CI, 1.27 to 3.84) in the placebo group. Major bleeding occurred in 2 (0.4%) and 1 (0.2%) and clinically relevant nonmajor bleeding occurred in 3 (0.6%) and 6 (1.1%) apixaban-treated and placebo-treated participants, respectively. By day 30, thirty-six (3.0%) participants were lost to follow-up, and 8.5% of apixaban and 11.9% of placebo participants permanently discontinued the study drug treatment. LIMITATIONS: The introduction of SARS-CoV-2 vaccines decreased the risk for hospitalization and death. Study enrollment spanned the peaks of the Delta and Omicron variants in the United States, which influenced illness severity. CONCLUSION: The incidence of death or thromboembolism was low in this cohort of patients discharged after hospitalization with COVID-19. Because of early enrollment termination, the results were imprecise and the study was inconclusive. PRIMARY FUNDING SOURCE: National Institutes of Health.

Therapeutic trials for long COVID-19: A call to action from the interventions taskforce of the RECOVER initiative.

Although most individuals recover from acute SARS-CoV-2 infection, a significant number continue to suffer from Post-Acute Sequelae of SARS-CoV-2 (PASC), including the unexplained symptoms that are frequently referred to as long COVID, which could last for weeks, months, or even years after the acute phase of illness. The National Institutes of Health is currently funding large multi-center research programs as part of its Researching COVID to Enhance Recover (RECOVER) initiative to understand why some individuals do not recover fully from COVID-19. Several ongoing pathobiology studies have provided clues to potential mechanisms contributing to this condition. These include persistence of SARS-CoV-2 antigen and/or genetic material, immune dysregulation, reactivation of other latent viral infections, microvascular dysfunction, and gut dysbiosis, among others. Although our understanding of the causes of long COVID remains incomplete, these early pathophysiologic studies suggest biological pathways that could be targeted in therapeutic trials that aim to ameliorate symptoms. Repurposed medicines and novel therapeutics deserve formal testing in clinical trial settings prior to adoption. While we endorse clinical trials, especially those that prioritize inclusion of the diverse populations most affected by COVID-19 and long COVID, we discourage off-label experimentation in uncontrolled and/or unsupervised settings. Here, we review ongoing, planned, and potential future therapeutic interventions for long COVID based on the current understanding of the pathobiological processes underlying this condition. We focus on clinical, pharmacological, and feasibility data, with the goal of informing future interventional research studies.

Prohibition of Palestine Arab Return to Israel as a Crime Against Humanity.

A displaced population of Palestine Arabs, numbering over seven million, is dispersed around the world, with major concentrations in Lebanon, Jordan, Syria, and Palestine itself. This population is prohibited from entry for renewed residence in home areas situated in Israel. In international law a right of return to one's country is guaranteed as a matter of fundamental rights. Severe deprivation of internationally defined rights victimizing a civilian population based on ethnicity or nationality constitutes the crime of persecution, a sub-category of crimes against humanity, prosecutable at the International Criminal Court. With respect to a major portion of the displaced Palestine Arabs, jurisdictional prerequisites obtain for the opening of an investigation that might lead to charges against Israeli officials responsible for denying return to the Palestine Arabs.

Dynamin-2 deficiency causes age- and sex-dependent neutropenia and myelodysplasia in mice.

The dynamins are a family of ubiquitously expressed GTPase proteins, best known for their role in membrane remodeling. Their contribution to hematopoiesis is incompletely recognized. Individuals with Charcot-Marie-Tooth disease with dynamin-2 (DNM2) mutations often develop neutropenia. We previously reported that dynamin (DNM) inhibition impairs SDF1a-mediated migration in megakaryocytes. Here, we report on conditionally Dnm2 deleted mice in hematopoietic tissues using the Vav-Cre murine strain. Homozygous Dnm2 deletion in blood tissues is embryonic lethal. Dnm2het male mice only developed a slightly decreased hemoglobin level. Dnm2het female mice developed leukopenia by 40 weeks of age and neutropenia by 65 weeks of age. Flow cytometry revealed decreased lineage-negative cells and granulocyte-monocyte progenitors in Dnm2het female mice. Immunohistochemical staining of bone marrow (BM) for mature neutrophils with Ly6G was decreased and myelodysplastic features were present in the BM of Dnm2het female mice. A linear distribution of Ly6G+ BM cells along blood vessels was observed in fewer Dnm2het mice than in controls, suggesting that the migration pattern in the marrow is altered. Marrow neutrophils treated with dynamin inhibitor, dynasore, showed increased cell surface CXCR4, suggesting that abnormal migration results in marrow neutrophil retention. Dnm2het female mice also developed splenomegaly secondary to germinal center hyperplasia at younger ages, suggesting perturbed immunity. In summary, female mice with BM Dnm2 haploinsufficiency developed neutropenia as they aged with decreased granulocyte progenitor production and migration defects. Our studies indicate a potential mechanism for the development of chronic idiopathic neutropenia, a disease that predominantly presents in middle-aged women.

Controlled amplification in oncology dose-finding trials.

In oncology clinical trials the guiding principle of model-based dose-finding designs for cytotoxic agents is to progress as fast as possible towards, and identify, the dose level most likely to be the MTD. Recent developments with non-cytotoxic agents have broadened the scope of early phase trials to include multiple objectives. The ultimate goal of dose-finding designs in our modern era is to collect the relevant information in the study for final RP2D determination. While some information is collected on dose levels below and in the vicinity of the MTD during the escalation (using conventional tools such as the Continual Reassessment Method for example), designs that include expansion cohorts or backfill patients effectively amplify the information collected on the lower dose levels. This is achieved by allocating patients to dose levels slightly differently during the study in order to take into account the possibility that "less (dose) might be more". The objective of this paper is to study the concept of amplification. Under the heading of controlled amplification we can include dose expansion cohorts and backfill patients among others. We make some general observations by defining these concepts more precisely and study a specific design that exploits the concept of controlled amplification.

Deconstructing the Kaplan-Meier curve: Quantification of treatment effect using the treatment effect process.

In studies of survival and its association with treatment and other prognostic variables, elapsed time alone will often show itself to be among the strongest, if not the strongest, of the predictor variables. Kaplan-Meier curves will show the overall survival of each group and the general differences between groups due to treatment. However, the time-dependent nature of treatment effects is not always immediately transparent from these curves. More sophisticated tools are needed to spotlight the treatment effects. An important tool in this context is the treatment effect process. This tool can be potent in revealing the complex myriad of ways in which treatment can affect survival time. We look at a recently published study in which the outcome was relapse-free survival, and we illustrate how the use of the treatment effect process can provide a much deeper understanding of the relationship between time and treatment in this trial.

Evidence-based consensus guidelines for the diagnosis and management of erythropoietic protoporphyria and X-linked protoporphyria.

Erythropoietic protoporphyria and X-linked protoporphyria are rare genetic photodermatoses. Limited expertise with these disorders among physicians leads to diagnostic delays. Here, we present evidence-based consensus guidelines for the diagnosis, monitoring, and management of erythropoietic protoporphyria and X-linked protoporphyria. A systematic literature review was conducted, and reviewed among subcommittees of experts, divided by topic. Consensus on guidelines was reached within each subcommittee and then among all members of the committee. The appropriate biochemical and genetic testing to establish the diagnosis is reviewed in addition to the interpretation of results. Prevention of symptoms, management of acute phototoxicity, and pharmacologic and nonpharmacologic treatment options are discussed. The importance of ongoing monitoring for liver disease, iron deficiency, and vitamin D deficiency is discussed with management guidance. Finally, management of pregnancy and surgery and the safety of other therapies are summarized. We emphasize that these are multisystemic disorders that require longitudinal monitoring. These guidelines provide a structure for evidence-based diagnosis and management for practicing physicians. Early diagnosis and management of these disorders are essential, particularly given the availability of new and emerging therapies.

Testing for Differences in Survival When Treatment Effects Are Persistent, Decaying, or Delayed.

A statistical test for the presence of treatment effects on survival will be based on a null hypothesis (absence of effects) and an alternative (presence of effects). The null is very simply expressed. The most common alternative, also simply expressed, is that of proportional hazards. For this situation, not only do we have a very powerful test in the log-rank test but also the outcome is readily interpreted. However, many modern treatments fall outside this relatively straightforward paradigm and, as such, have attracted attention from statisticians eager to do their best to avoid losing power as well as to maintain interpretability when the alternative hypothesis is less simple. Examples include trials where the treatment effect decays with time, immunotherapy trials where treatment effects may be slow to manifest themselves as well as the so-called crossing hazards problem. We review some of the solutions that have been proposed to deal with these issues. We pay particular attention to the integrated log-rank test and how it can be combined with the log-rank test itself to obtain powerful tests for these more complex situations.

Structural racism is a mediator of disparities in acute myeloid leukemia outcomes.

Non-Hispanic Black (NHB) and Hispanic patients with acute myeloid leukemia (AML) have higher mortality rates than non-Hispanic White (NHW) patients despite more favorable genetics and younger age. A discrete survival analysis was performed on 822 adult patients with AML from 6 urban cancer centers and revealed inferior survival among NHB (hazard ratio [HR] = 1.59; 95% confidence interval [CI]: 1.15, 2.22) and Hispanic (HR = 1.25; 95% CI: 0.88, 1.79) patients compared with NHW patients. A multilevel analysis of disparities was then conducted to investigate the contribution of neighborhood measures of structural racism on racial/ethnic differences in survival. Census tract disadvantage and affluence scores were individually calculated. Mediation analysis of hazard of leukemia death between groups was examined across 6 composite variables: structural racism (census tract disadvantage, affluence, and segregation), tumor biology (European Leukemia Network risk and secondary leukemia), health care access (insurance and clinical trial enrollment), comorbidities, treatment patterns (induction intensity and transplant utilization), and intensive care unit (ICU) admission during induction chemotherapy. Strikingly, census tract measures accounted for nearly all of the NHB-NHW and Hispanic-NHW disparity in leukemia death. Treatment patterns, including induction intensity and allogeneic transplant, and treatment complications, as assessed by ICU admission during induction chemotherapy, were additional mediators of survival disparities in AML. This is the first study to formally test mediators for observed disparities in AML survival and highlights the need to investigate the mechanisms by which structural racism interacts with known prognostic and treatment factors to influence leukemia outcomes.

Effect of P2Y12 Inhibitors on Survival Free of Organ Support Among Non-Critically Ill Hospitalized Patients With COVID-19: A Randomized Clinical Trial.

Importance: Platelets represent a potential therapeutic target for improved clinical outcomes in patients with COVID-19. Objective: To evaluate the benefits and risks of adding a P2Y12 inhibitor to anticoagulant therapy among non-critically ill patients hospitalized for COVID-19. Design, Setting, and Participants: An open-label, bayesian, adaptive randomized clinical trial including 562 non-critically ill patients hospitalized for COVID-19 was conducted between February 2021 and June 2021 at 60 hospitals in Brazil, Italy, Spain, and the US. The date of final 90-day follow-up was September 15, 2021. Interventions: Patients were randomized to a therapeutic dose of heparin plus a P2Y12 inhibitor (n = 293) or a therapeutic dose of heparin only (usual care) (n = 269) in a 1:1 ratio for 14 days or until hospital discharge, whichever was sooner. Ticagrelor was the preferred P2Y12 inhibitor. Main Outcomes and Measures: The composite primary outcome was organ support-free days evaluated on an ordinal scale that combined in-hospital death (assigned a value of -1) and, for those who survived to hospital discharge, the number of days free of respiratory or cardiovascular organ support up to day 21 of the index hospitalization (range, -1 to 21 days; higher scores indicate less organ support and better outcomes). The primary safety outcome was major bleeding by 28 days as defined by the International Society on Thrombosis and Hemostasis. Results: Enrollment of non-critically ill patients was discontinued when the prespecified criterion for futility was met. All 562 patients who were randomized (mean age, 52.7 [SD, 13.5] years; 41.5% women) completed the trial and 87% received a therapeutic dose of heparin by the end of study day 1. In the P2Y12 inhibitor group, ticagrelor was used in 63% of patients and clopidogrel in 37%. The median number of organ support-free days was 21 days (IQR, 20-21 days) among patients in the P2Y12 inhibitor group and was 21 days (IQR, 21-21 days) in the usual care group (adjusted odds ratio, 0.83 [95% credible interval, 0.55-1.25]; posterior probability of futility [defined as an odds ratio <1.2], 96%). Major bleeding occurred in 6 patients (2.0%) in the P2Y12 inhibitor group and in 2 patients (0.7%) in the usual care group (adjusted odds ratio, 3.31 [95% CI, 0.64-17.2]; P = .15). Conclusions and Relevance: Among non-critically ill patients hospitalized for COVID-19, the use of a P2Y12 inhibitor in addition to a therapeutic dose of heparin, compared with a therapeutic dose of heparin only, did not result in an increased odds of improvement in organ support-free days within 21 days during hospitalization. Trial Registration: ClinicalTrials.gov Identifier: NCT04505774.

Stopping rules for phase I clinical trials with dose expansion cohorts.

Many clinical trials incorporate stopping rules to terminate early if the clinical question under study can be answered with a high degree of confidence. While common in later-stage trials, these rules are rarely implemented in dose escalation studies, due in part to the relatively smaller sample size of these designs. However, even with a small sample size, this paper shows that easily implementable stopping rules can terminate dose-escalation early with minimal loss to the accuracy of maximum tolerated dose estimation. These stopping rules are developed when the goal is to identify one or two dose levels, as the maximum tolerated dose and co-maximum tolerated dose. In oncology, this latter goal is frequently considered when the study includes dose-expansion cohorts, which are used to further estimate and compare the safety and efficacy of one or two dose levels. As study protocols do not typically halt accrual between escalation and expansion, early termination is of clinical importance as it either allows for additional patients to be treated as part of the dose expansion cohort to obtain more precise estimates of the study endpoints or allows for an overall reduction in the total sample size.

SEMIPARAMETRIC DOSE FINDING METHODS FOR PARTIALLY ORDERED DRUG COMBINATIONS.

We investigate a statistical framework for Phase I clinical trials that test the safety of two or more agents in combination. For such studies, the traditional assumption of a simple monotonic relation between dose and the probability of an adverse event no longer holds. Nonetheless, the dose toxicity (adverse event) relationship will obey an assumption of partial ordering in that there will be pairs of combinations for which the ordering of the toxicity probabilities is known. Some authors have considered how to best estimate the maximum tolerated dose (a dose providing a rate of toxicity as close as possible to some target rate) in this setting. A related, and equally interesting, problem is to partition the 2-dimensional dose space into two sub-regions: doses with probabilities of toxicity lower and greater than the target. We carry out a detailed investigation of this problem. The theoretical framework for this is the recently presented semiparametric dose finding method. This results in a number of proposals one of which can be viewed as an extension of the Product of Independent beta Priors Escalation method (PIPE). We derive useful asymptotic properties which also apply to the PIPE method when seen as a special case of the more general method given here. Simulation studies provide added confidence concerning the good behaviour of the operating characteristics.