Bayesian Adaptive Designs for Early Phase Clinical Trials

My dissertation focuses mainly on Bayesian adaptive designs for phase I and phase II clinical trials. It includes three specific topics: (1) proposing a novel two-dimensional dose-finding algorithm for biological agents, (2) developing Bayesian adaptive screening designs to provide more efficient and ethical clinical trials, and (3) incorporating missing late-onset responses to make an early stopping decision. Treating patients with novel biological agents is becoming a leading trend in oncology. Unlike cytotoxic agents, for which toxicity and efficacy monotonically increase with dose, biological agents may exhibit non-monotonic patterns in their dose-response relationships. Using a trial with two biological agents as an example, we propose a phase I/II trial design to identify the biologically optimal dose combination (BODC), which is defined as the dose combination of the two agents with the highest efficacy and tolerable toxicity. A change-point model is used to reflect the fact that the dose-toxicity surface of the combinational agents may plateau at higher dose levels, and a flexible logistic model is proposed to accommodate the possible non-monotonic pattern for the dose-efficacy relationship. During the trial, we continuously update the posterior estimates of toxicity and efficacy and assign patients to the most appropriate dose combination. We propose a novel dose-finding algorithm to encourage sufficient exploration of untried dose combinations in the two-dimensional space. Extensive simulation studies show that the proposed design has desirable operating characteristics in identifying the BODC under various patterns of dose-toxicity and dose-efficacy relationships. Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Simulation studies show that the proposed design substantially outperforms the conventional multi-arm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while at the same time allocating substantially more patients to efficacious treatments. The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while at the same time providing higher power to identify the best treatment at the end of the trial. Phase II trial studies usually are single-arm trials which are conducted to test the efficacy of experimental agents and decide whether agents are promising to be sent to phase III trials. Interim monitoring is employed to stop the trial early for futility to avoid assigning unacceptable number of patients to inferior treatments. We propose a Bayesian single-arm phase II design with continuous monitoring for estimating the response rate of the experimental drug. To address the issue of late-onset responses, we use a piece-wise exponential model to estimate the hazard function of time to response data and handle the missing responses using the multiple imputation approach. We evaluate the operating characteristics of the proposed method through extensive simulation studies. We show that the proposed method reduces the total length of the trial duration and yields desirable operating characteristics for different physician-specified lower bounds of response rate with different true response rates.

On Bayesian seamless phase I-II designs

Early phase clinical trial designs have long been the focus of interest for clinicians and statisticians working in oncology field. There are several standard phse I and phase II designs that have been widely-implemented in medical practice. For phase I design, the most commonly used methods are 3+3 and CRM. A newly-developed Bayesian model-based mTPI design has now been used by an increasing number of hospitals and pharmaceutical companies. The advantages and disadvantages of these three top phase I designs have been discussed in my work here and their performances were compared using simulated data. It was shown that mTPI design exhibited superior performance in most scenarios in comparison with 3+3 and CRM designs. ^ The next major part of my work is proposing an innovative seamless phase I/II design that allows clinicians to conduct phase I and phase II clinical trials simultaneously. Bayesian framework was implemented throughout the whole design. The phase I portion of the design adopts mTPI method, with the addition of futility rule which monitors the efficacy performance of the tested drugs. Dose graduation rules were proposed in this design to allow doses move forward from phase I portion of the study to phase II portion without interrupting the ongoing phase I dose-finding schema. Once a dose graduated to phase II, adaptive randomization was used to randomly allocated patients into different treatment arms, with the intention of more patients being assigned to receive more promising dose(s). Again simulations were performed to compare the performance of this innovative phase I/II design with a recently published phase I/II design, together with the conventional phase I and phase II designs. The simulation results indicated that the seamless phase I/II design outperform the other two competing methods in most scenarios, with superior trial power and the fact that it requires smaller sample size. It also significantly reduces the overall study time. ^ Similar to other early phase clinical trial designs, the proposed seamless phase I/II design requires that the efficacy and safety outcomes being able to be observed in a short time frame. This limitation can be overcome by using validated surrogate marker for the efficacy and safety endpoints.^

(Table 2) Trace element composition of seleceted clast and matrix materials from ODP Site 125-786

Shipboard examination of volcanic and sedimentary strata at Site 786 suggested that at least four types of breccias are present: flow-top breccias, associated with cooling and breakup on the upper surface of lava flows; autobreccias, formed by in-situ alteration at the base of flows; fault-gouge breccias; and true sedimentary breccias derived from weathering and erosion of underlying flows. It is virtually impossible to assess the origin of breccia matrix by textural and mineralogical analyses alone. However, it is fundamental for our understanding of breccia provenance to determine the source component of the matrix material. Whether the matrix is uniquely clastderived can be determined by geochemical fingerprinting. Trace elements that are immobile during weathering and alteration do not change their relative abundances. A contribution to the matrix from any source with an immobile trace element signature different from that of the clasts would appear as a perturbation of the trace element signature of the matrix. Trace element analysis of bulk samples from clasts and matrix material in individual breccia units was undertaken in a fashion similar to that used by Brimhall and Dietrich (1987, doi:10.1016/0016-7037(87)90070-6) in analyzing soil provenance: (1) to help distinguish between sedimentary and volcanic breccias, (2) to determine the degree of mixing and depth of erosion in sedimentary breccias, and (3) to analyze the local provenance of the individual breccia components (matrix and clasts). The following elements were analyzed by X-ray fluorescence (XRF): Rb, Sr, Ba, U, Zr, Cu, Zn, Ti, Cr, and V. Of these elements, Zr and Ti probably exhibit truly immobile behavior (Humphris and Thompson, 1978, doi:10.1016/0016-7037(78)90222-3 ). The remaining elements are useful as a reference for the extent of compositional change during the formation of matrix material (Brimhall and Dietrich, 1987, doi:10.1016/0016-7037(87)90070-6).

Nd, Pb, and Be isotopes of ferromanaganese crusts of the Atlantic Ocean

The isotopic composition of Nd in present-day deep waters of the central and northeastern Atlantic Ocean is thought to fingerprint mixing of North Atlantic Deep Water with Antarctic Bottom Water. The central Atlantic Romanche and Vema Fracture Zones are considered the most important pathways for deep water exchange between the western and eastern Atlantic basins today. We present new Nd isotope records of the deepwater evolution in the fracture zones obtained from ferromanganese crusts, which are inconsistent with simple water mass mixing alone prior to 3 Ma and require additional inputs from other sources. The new Pb isotope time series from the fracture zones are inexplicable by simple mixing of North Atlantic Deep Water and Antarctic Bottom Water for the entire past 33 Myr. The distinct and relatively invariable Nd and Pb isotope records of deep waters in the fracture zones appear instead to have been controlled to a large extent by contributions from Saharan dust and the Orinoco/Amazon Rivers. Thus the previously observed similarity of Nd and Pb isotope time series from the western and eastern North Atlantic basins is better explainable by direct supply of Labrador Seawater to the eastern basin via a northern pathway rather than by advection of North Atlantic Deep Water via the Romanche and Vema Fracture Zones.

Radiocarbon, isotope, biogenic, and 230Th measurements for sediment core RC10-196

The subarctic North Pacific Ocean holds a large CO2 reservoir that is currently isolated from the atmosphere by a low-salinity layer. It has recently been hypothesized that the reorganization of these high-CO2 waters may have played a crucial role in the degassing of carbon dioxide to the atmosphere during the last deglaciation. This reorganization would leave some imprint on paleo-productivity records. Here we present 230Th-normalized biogenic fluxes from an intermediate depth sediment core in the Northwest Pacific (RC10-196, 54.7°N, 177.1°E, 1007 m) and place them within the context of a synthesis of previously-published biogenic flux data from 49 deep-sea cores north of 20°N, ranging from 420 to 3968 m water depth. The 230Th-normalized opal, carbonate, and organic carbon fluxes from RC10-196 peak approximately 13,000 calendar years BP during the Bølling/Allerød (B/A) period. Our data synthesis suggests that biogenic fluxes were in general lowest during the last glacial period, increased somewhat in the Northwest Pacific during Heinrich Event 1, and reached a maximum across the entire North Pacific during the B/A period. We evaluate several mechanisms as possible drivers of deglacial change in biogenic fluxes in the North Pacific, including changes in preservation, sediment focusing, sea ice extent, iron inputs, stratification, and circulation shifts initiated in the North Atlantic and North Pacific. Our analysis suggests that while micronutrient sources likely contributed to some of the observed changes, the heterogeneity in timing of glaciogenic retreat and sea level make these mechanisms unlikely causes of region-wide contemporaneous peaks in export production. We argue that paleo-observations are most consistent with ventilation increases in both the North Pacific (during H1) and North Atlantic (during B/A) being the primary drivers of increases in biogenic flux during the deglaciation, as respectively they were likely to bring nutrients to the surface via increased vertical mixing and shoaling of the global thermocline.

Nitrogen isotopic and opal record of sediments in the Gulf of California

High-resolution records of the nitrogen isotopic composition of organic matter (d15Norg), opal content, and opal accumulation rates from the central Gulf of California reveal large and abrupt variations during deglaciation and gradual Holocene changes coincident with climatic changes recorded in the North Atlantic. Homogenous sediments with relatively low d15Norg values and low opal content were deposited at the end of the last glacial period, during the Younger-Dryas event, and during the middle to late Holocene. In contrast, laminated sediments deposited in the two deglacial stages are characterized by very high d15Norg values (>14 per mil) and opal accumulation rates (29-41 mg/cm**2/yr). Abrupt shifts in d15Norg were driven by widespread changes in the extent of suboxic subsurface waters supporting denitrification and were amplified in the central gulf record due to variations in upwelling, vertical mixing, and/or the latitudinal position of the Intertropical Convergence Zone.

Nd and Sr isotopic composition of Cretaceous MORB

Chemical and isotopic (Nd and Sr) compositions have been determined for 12 Cretaceous basaltic samples (108 Ma old) from Holes 417D and 418A of Legs 51,52 and 53. We have found that: (1) The chemical compositions are typical of MORB. They do not vary systematically with the stratigraphic positions of the analyzed samples; thus, the chemical evolution is independent of the eruption sequence that occurred at this Cretaceous ridge. (2) REE patterns for all rocks are characterized by a strong LREE depletion with (La/Sm)N = 0.38-0.50; no significant Eu anomalies are found; HREE are nearly flat or slightly depleted towards Yb-Lu and have 12-18 * chondritic abundances. Combining the results of previous studies, it suggests that no significant temporal and spatial variation in magma chemistry (especially for LIL elements) has occurred in the 'normal' ridge segments over the last 150 Ma. (3) lsotopically, 143Nd/144Nd ratios vary from 0.513026 to 0.513154, corresponding to epsilon-Nd(0) = +7.5 to +10, and they fall in the typical range of MORB. However, these rocks have unexpectedly high 87Sr/86Sr ratios (0.70355-0.70470) which are attributed to the result of seawater-rock interaction. (4) The Nd model ages (Tin), ranging from 1.53 to 2.47 (average 2.06) AE, suggest that the upper mantle source(s) underwent a large scale chemical differentiation leading to LREE and other LIL element depletion about 2 AE ago, assuming a simple two-stage model. More realistically, the variation in Tm(Nd) or epsilon-Nd could be derived from mixing of heterogeneous mantle sources that were a consequence of continuous mantle differentiation and continental formation. (5) Because of the low mg values (0.52-0.63), the analyzed basaltic rocks do not represent primary liquids of mantle melting. The variation in La/Sm ratios and TiO2 are not compatible with a model in which all rocks are genetically related by a simple fractional crystallization. Rather, it is proposed that the basaltic rocks might have been derived from some heterogeneous upper mantle source with or without later magmatic mixing, and followed by some shallow-level fraetionations.

Petrology and geochemistry of oceanic intraplate sheet-flow basalts at DSDP Hole 89-462A

Reentry of Hole 462A during Leg 89 resulted in the penetration of a further 140 m of basalt sheet-flows similar to those found during Leg 61 at the same site. Twelve volcanic units (45 to 56) were recognized, comprising a series of rapidly extruded, interlayered aphyric and poorly clinopyroxene-plagioclase-olivine phyric, nonvesicular basalts. All exhibit variable, mild hydration and oxidation, relative to fresh oceanic basalts, produced under reducing, low-CO2-activity conditions within the zeolite facies. Secondary assemblages are dominated by smectites, zeolites, and pyrite, produced by low-temperature reaction with poorly oxygenated seawater. No systematic mineralogical or chemical changes are observed with depth, although thin quenched units and more massive hypocrystalline units exhibit slightly different alteration parageneses. Chemically, the basalts are olivine- and quartz-normative tholeiites, characterized by low incompatible-element abundances, similar to mildly enriched MORB (approaching T-type), with moderate, chrondite-normalized, large-ionlithophile- element depletion patterns and generally lower or near-chrondritic ratios for many low-distribution-coefficient (KD) element pairs. In general, relative to cyclic MORB chemical variation, they are uniform throughout, although 3 chemical megagroups and 22 subgroups are recognized. It is considered that the megagroups represent separate low-pressure-fractionated systems (olivine + Plagioclase ± clinopyroxene), whereas minor variations within them (subgroups) indicate magma mixing and generation of near-steady-state conditions. Overall, relatively minor fractionation coupled with magma mixing produced a series of compositionally uniform lavas. Parental melts were produced by similar degrees of partial melting, although the source may have varied slightly in LIL-element content.

Stable carbon and nitrogen isotopic ratios of cores from the Bering Sea

Stable carbon and nitrogen isotopic ratios (d13C and d15N) of organic matter were measured in three sediment cores from deep basins of the Bering Sea to investigate past changes in surface nutrient conditions. For surface water reconstructions, hemipelagic layers in the cores were distinguished from turbidite layers (on the basis of their sedimentary structures and 14C ages) and analyzed for isotopic studies. Although d13C profiles may have been affected by diagenesis, both d15N and d13C values showed common positive anomalies during the last deglaciation. We explain these anomalies as reflecting suppressed vertical mixing and low nutrient concentrations in surface waters caused by injection of meltwater from alpine glaciers around the Bering Sea.

Contents of rare earth and other chemical elements in Fe-Mn micronodules, nodules, and bottom sediments from the Clarion-Clipperton ore province in the Pacific Ocean

Processes governing the formation of rare earth element (REE) composition are under consideration for ferromanganese deposits (nodules, separate parts of nodules, and micronodules of different size fractions) within the Clarion-Clipperton ore province in the Pacific Ocean. It is shown that ferromanganese oxyhydroxide deposits with different chemical compositions can be produced in sediments under similar sedimentation conditions. In areas with high bioproductivity size of micronodules has positive correlation with Mn content and Mn/Fe and P/Fe ratios and negative correlation with Fe, P, REE, and Ce anomaly. Behavior of REE in micronodules from sediments within bioproductive zones is related to increase of influence of diagenetic processes in sediments as a response to the growth of size of micronodules. Distinctions in chemical composition of micronodules and nodules are related to their interaction with associated sediments. Micronodules grow in sediments using hydrogenous ferromanganese oxyhydroxides. As they grow, micronodules are enriched in labile fraction of sediments reworked during diagenesis. Sources of material of ferromanganese nodules are governed by their formation at the water bottom interface. Their upper part is formed by direct settling of iron oxyhydroxides from bottom water, whereas the lower part is accumulated due to diagenetic processes in sediments. Differences of REE compositions in ferromanganese deposits are caused by the reduction of manganese during diagenesis and its separation from iron. Iron oxyhydroxides form a sorption complex due to sorption of phosphate-ion from bottom and pore waters. Sorption of phosphate-ion results in additional sorption of REE.

Isotopic and chemical compositions of rocks and minerals from the TAG hydrothermal mound, ODP Site 957

Strontium- and oxygen-isotopic measurements of samples recovered from the Trans-Atlantic Geotraverse (TAG) hydrothermal mound during Leg 158 of the Ocean Drilling Program provide important constraints on the nature of fluid-rock interactions during basalt alteration and mineralization within an active hydrothermal deposit. Fresh Mid-Ocean Ridge Basalt (MORB), with a 87Sr/86Sr of 0.7026, from the basement beneath the TAG mound was altered at both low and high temperatures by seawater and altered at high temperature by near end-member black smoker fluids. Pillow breccias occurring beneath the margins of the mound are locally recrystallized to chlorite by interaction with large volumes of conductively heated seawater (>200°C). The development of a silicified, sulfide-mineralized stockwork within the basaltic basement follows a simple paragenetic sequence of chloritization followed by mineralization and the development of a quartz+pyrite+paragonite stockwork cut by quartz-pyrite veins. Initial alteration involved the development of chloritic alteration halos around basalt clasts by reaction with a Mg-bearing mixture of upwelling, high-temperature (>300°C), black smoker-type fluid with a minor (<10%) proportion of seawater. Continued high-temperature (>300°C) interaction between the wallrock and these Mg-bearing fluids results in the complete recrystallization of the wallrock to chlorite+quartz+pyrite. The quartz+pyrite+paragonite assemblage replaces the chloritized basalts, and developed by reaction at 250-360°C with end-member hydrothermal fluids having 87Sr/86Sr ~0.7038, similar to present-day vent fluids. The uniformity of the 87Sr/86Sr ratios of hydrothermal assemblages throughout the mound and stockwork requires that the 87Sr/86Sr ratio of end-member hydrothermal fluids has remained relatively constant for a time period longer than that required to change the interior thermal structure and plumbing network of the mound and underlying stockwork. Precipitation of anhydrite in breccias and as late-stage veins throughout most of the mound and stockwork, down to at least 125 mbsf, records extensive entrainment of seawater into the hydrothermal deposit. 87Sr/86Sr ratios indicate that most of the anhydrite formed from ~2:1 mixture of seawater and black smoker fluids (65%±15% seawater). Oxygen-isotopic compositions imply that anhydrite precipitated at temperatures between 147°C and 270°C and require that seawater was conductively heated to between 100°C and 180°C before mixing and precipitation occurred. Anhydrite from the TAG mound has a Sr-Ca partition coefficient Kd ~0.60±0.28 (2 sigma). This value is in agreement with the range of experimentally determined partition coefficients (Kd ~0.27-0.73) and is similar to those calculated for anhydrite from active black smoker chimneys from 21°N on the East Pacific Rise. The d18O (for SO4) of TAG anhydrite brackets the value of seawater sulfate oxygen (~9.5?). Dissolution of anhydrite back into the oceans during episodes of hydrothermal quiescence provides a mechanism of buffering seawater sulfate oxygen to an isotopically light composition, in addition to the precipitation and dissolution of anhydrite within the oceanic basement during hydrothermal recharge at the mid-ocean ridges.