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.^

Development and evaluation of a video-based modeling strategy for the dissemination phase of a school health tobacco -use prevention program

Even the best school health education programs will be unsuccessful if they are not disseminated effectively in a manner that encourages classroom adoption and implementation. This study involved two components: (1) the development of a videotape intervention to be used in the dissemination phase of a 4-year, NCI-funded diffusion study and (2) the evaluation of that videotape intervention strategy in comparison with a print (information transfer) strategy. Conceptualization has been guided by Social Learning Theory, Diffusion Theory, and communication theory. Additionally, the PRECEDE Framework has been used. Seventh and 8th grade classroom teachers from Spring Branch Independent School District in west Houston participated in the evaluation of the videotape and print interventions using a 57-item preadoption survey instrument developed by the UT Center for Health Promotion Research and Development. Two-way ANOVA was used to study individual score differences for five outcome variables: Total Scale Score (comprised of 57 predisposing, enabling, and reinforcing items), Adoption Characteristics Subscale, Attitude Toward Innovation Subscale, Receptivity Toward Innovation, and Reinforcement Subscale. The aim of the study is to compare the effect upon score differences of video and print interventions alone and in combination. Seventy-three 7th and 8th grade classroom teachers completed the study providing baseline and post-intervention measures on factors related to the adoption and implementation of tobacco-use prevention programs. Two-way ANOVA, in relation to the study questions, found significant scoring differences for those exposed to the videotape intervention alone for both the Attitude Toward Innovation Subscale and the Receptivity to Adopt Subscale. No significant results were found to suggest that print alone influences favorable scoring differences between baseline and post-intervention testing. One interaction effect was found suggesting video and print combined are more effective for influencing favorable scoring differences for the Reinforcement for the Adoption Subscale.^ This research is unique in that it represents a newly emerging field in health promotion communications research with implications for Social Learning Theory, Diffusion Theory, and communication science that are applicable to the development of improved school health interventions. ^

Relative phase shift and oscillation observations at moorings in the Filchner Depression area

Properties of the dense ice shelf water plume emerging from the Filchner Depression in the southwestern Weddell Sea are described, using available current meter records and CTD stations. A mean hydrography, based on more than 300 CTD stations gathered over 25 yr points to a cold, relatively thin and vertically well-defined plume east of the two ridges cross-cutting the continental slope about 60 km from the Filchner sill, whereas the dense bottom layer is warmer, more stratified and much thicker west of these ridges. The data partly confirm the three major pathways suggested earlier and agree with recent theories on topographic steering by submarine ridges. A surprisingly high mesoscale variability in the overflow region is documented and discussed. The variability is to a large extent due to three distinct oscillations (with periods of about 35 h, 3 and 6 d) seen in both temperature and velocity records on the slope. The oscillations are episodic, barotropic and have a horizontal scale of ~20-40 km across the slope. They are partly geographically separated, with the longer period being stronger on the lower part of the slope and the shorter on the upper part of the slope. Energy levels are lower west of the ridges, and in the Filchner Depression. The observations are discussed in relation to existing theories on eddies, commonly generated in plumes, and continental shelf waves.

Solid phase phosphorus geochemistry in surface sediments of sediment cores GeoB3718-4, GeoB3702-2 and GeoB3707-4

In this study we investigate benthic phosphorus cycling in recent continental margin sediments at three sites off the Namibian coastal upwelling area. Examination of the sediments reveals that organic and biogenic phosphorus are the major P-containing phases preserved. High Corg/Porg ratios just at the sediment surface suggest that the preferential regeneration of phosphorus relative to that of organic carbon has either already occurred on the suspension load or that the organic matter deposited at these sites is already rather refractory. Release of phosphate in the course of benthic microbial organic matter degradation cannot be identified as the dominating process within the observed internal benthic phosphorus cycle. Dissolved phosphate and iron in the pore water are closely coupled, showing high concentrations below the oxygenated surface layer of the sediments and low concentrations at the sediment-water interface. The abundant presence of Fe(III)-bound phosphorus in the sediments document the co-precipitation of both constituents as P-containing iron (oxyhydr)oxides. However, highly dissolved phosphate concentrations in pore waters cannot be explained, neither by simple mass balance calculations nor by the application of an established computer model. Under the assumption of steady state conditions, phosphate release rates are too high as to be balanced with a solid phase reservoir. This discrepancy points to an apparent lack of solid phase phosphorus at sediment depth were suboxic conditions prevail. We assume that the known, active, fast and episodic particle mixing by burrowing macrobenthic organisms could repeatedly provide the microbially catalyzed processes of iron reduction with authigenic iron (oxyhydro)oxides from the oxic surface sediments. Accordingly, a multiple internal cycling of phosphate and iron would result before both elements are buried below the iron reduction zone.

Total nitrogen from solid phase in the Jena Experiment (Main Experiment up to 30cm depth, year 2008)

This data set contains measurements of total nitrogen from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Soil sampling and analysis: Stratified soil sampling was performed in April 2008 to a depth of 30 cm. Three independent samples per plot were taken using a split tube sampler with an inner diameter of 4.8 cm (Eijkelkamp Agrisearch Equipment, Giesbeek, the Netherlands). Soil samples were segmented to a depth resolution of 5 cm in the field, giving six depth subsamples per core, and made into composite samples per depth. Sampling locations were less than 30 cm apart from sampling locations in other years. Samples were dried at 40°C. All soil samples were passed through a sieve with a mesh size of 2 mm. Because of much higher proportions of roots in the soil, the samples were further sieved to 1 mm according to common root removal methods. No additional mineral particles were removed by this procedure. Total nitrogen concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany).

Total nitrogen from solid phase in the Jena Experiment (Block 2 Main Experiment up to 100cm depth, year 2002)

This data set contains measurements of total nitrogen from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Soil sampling and analysis: Stratified soil sampling to a depth of 1m was performed before sowing in April 2002. Three independent samples per plot were taken of all plots in block 2 using a motor-driven soil column cylinder (Cobra, Eijkelkamp, 8.3 cm in diameter). Soil samples were dried at 40°C and segmented to a depth resolution of 5 cm giving 20 depth subsamples per core. All samples were analyzed independently. All soil samples were passed through a sieve with a mesh size of 2 mm. Rarely present visible plant remains were removed using tweezers. Total nitrogen concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany).

Total nitrogen from solid phase in the Jena Experiment (Main Experiment up to 30cm depth, year 2004)

This data set contains measurements of total nitrogen from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Soil sampling and analysis: Stratified soil sampling was performed in April 2004 to a depth of 30 cm. Three independent samples per plot were taken using a split tube sampler with an inner diameter of 4.8 cm (Eijkelkamp Agrisearch Equipment, Giesbeek, the Netherlands). Soil samples were segmented to a depth resolution of 5 cm in the field, giving six depth subsamples per core, and made into composite samples per depth. Sampling locations were less than 30 cm apart from sampling locations in other years. Samples were dried at 40°C. All soil samples were passed through a sieve with a mesh size of 2 mm. Because of much higher proportions of roots in the soil, the samples were further sieved to 1 mm according to common root removal methods. No additional mineral particles were removed by this procedure. Total nitrogen concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany).

Pollen profiles from three former lakes in the Lake Garda area

1. Late glacial and postglacial sediments from three former lakes in the Lake Garda area (Southern Alps) were investigated. 2. The pollen diagram from Bondone (1550 m) shows an older phase rich in NAP. A younger one corresponds with the Younger Dryas time according to two radiocarbon determinations. In the Preboreal no climatic deterioration could be found. 3. At first plants, which are nowadays typical for snow-ground, pioneer and dwarf shrub associations, immigrated into the surroundings of Bondone. In Alleröd times larch and pine appeared as the first trees. At the beginning of the Preboreal dense forest existed in that region. During the Alleröd timber line was at about 1500 m. 4. In the pollen diagrams from Saltarino (194 m) and Fiavè (654 m) an oldest period rich in NAP is followed by two stadial and two interstadial phases. Tree birches and larches immigrated during the oldest interstadial phase. 5. In the case of Saltarino and Fiavè only a preliminary dating could be made. A correlation seems to be possible with diagrams published by Zoller as well as with the diagram of Bondone. Discrepances in dating, which arise then, are discussed. According to the two possibilities of dating the youngest stadial is synchronous either with the so-called Piottino stadial or the Younger Dryas time. Consequently the oldest interstadial phase of Saltarino corresponds either with the Bölling or with a pre-Bölling interstadial. The last possibility seems to be more probable. 6. In the southern part of the Lake Garda area reforestation was preceded by a long shrub phase mainly with Juniperus. At about 650 m there was a period with Pinus mugo and only with a small amount of Juniperus before reforestation. A phase with Betula nana well known from areas north of the Alps could nowhere be found. 7. In the area under study larch appeared as the first tree. Lateron it has been the most important constituent of the forests near timber line. Birch, which plays an important role as a pioneer tree in Denmark - for instance at the transition of the pollen zones III/IV - as well as in Southern Germany during Bölling time, was of less importance at the southern border of the Alps. In that area the spreading of Pinus occurred very early causing dense forests. 8. During the last stadial phase (probably Younger Dryas time) dense forests with Pinus and Larix existed at 650 m. In the lower part of the Lake Garda area, however, both thermophilous trees as Quercus and herbs frequently occurred. This leads to the conclusion that during this time tree growth was limited by dryness in lower altitudes of the border of the Southern Alps. Pinus and Juniperus, however, do not show higher values in this period, a fact which cannot yet be explained. 9. A list of plants, which were found in the sediments, is compiled. Helodium lanatum, Dictamnus albus, Mercurialis cf. ovata, Buxus, Cerinthe cf. minor, Onosma, Anthericum and Asphodelus albus are findings, which are of special interest for the history of the flora of that region.

Pore water concentrations and solid phase concentrations of sediment cores from the Ligurian continental slope

In October 1979, a period of heavy rainfall along the French Riviera was followed by the collapse of the Ligurian continental slope adjacent to the airport of Nice, France. A body of slope sediments, which was shortly beforehand affected by construction work south of the airport, was mobilized and traveled hundreds of kilometers downslope into the Var submarine canyon and, eventually, into the deep Ligurian basin. As a direct consequence, the construction was destroyed, seafloor cables were torn, and a small tsunami hit Antibes shortly after the failure. Hypotheses regarding the trigger mechanism include (i) vertical loading by construction of an embankment south of the airport, (ii) failure of a layer of sensitive clay within the slope sequence, and (iii) excess pore fluid pressures from charged aquifers in the underground. Over the previous decades, both the sensitive clay layers and the permeable sand and gravel layers were sampled to detect freshened waters. In 2007, the landslide scar and adjacent slopes were revisited for high-resolution seafloor mapping and systematic sampling. Results from half a dozen gravity and push cores in the shallow slope area reveal a limited zone of freshening (i.e. groundwater influence). A 100-250 m wide zone of the margin shows pore water salinities of 5-50% SW concentration and depletion in Cl, SO4, but Cr enrichment, while cores east or west of the landslide scar show regular SW profiles. Most interestingly, the three cores inside the landslide scar hint towards a complex hydrological system with at least two sources for groundwater. The aquifer system also showed strong freshening after a period of several months without significant precipitation. This freshening implies that charged coarse-grained layers represent a permanent threat to the slope's stability, not just after periods of major rainfall such as in October 1979.

Pore water (SO4, CH4, alkalinity, HS-, Ca, Sr, Mg, Ba) and solid phase (Ca, Sr, Mg, Ba) data measured in pockmark sediments of the Northern Congo Fan

This study focuses on the vertical distribution of authigenic carbonates (aragonite and high Mg-calcite) in the form of finely disseminated precipitates as well as massive carbonate concretions present in and above gas hydrate bearing sediments of the Northern Congo Fan. Analyses of Ca, Mg, Sr and Ba in pore water, bulk sediments and authigenic carbonates were carried out on gravity cores taken from three pockmark structures (Hydrate Hole, Black Hole and Worm Hole). In addition, a background core was retrieved from an area not influenced by fluid seepage. Pore water Sr/Ca and Mg/Ca ratios are used to reveal the current depths of carbonate formation as well as the mineralogy of the authigenic precipitates. The Sr/Ca and Mg/Ca ratios of bulk sediments and massive carbonate concretions were applied to infer the presence and depth distribution of authigenic aragonite and high Mg-calcite, based on the approach presented by Bayon et al. [Bayon et al. (2007). Sr/Ca and Mg/Ca ratios in Niger Delta sediments: Implications for authigenic carbonate genesis in cold seep environments. Marine Geology 241(1-4), 93-109, doi:10.1016/j.margeo.2007.03.007]. We show that the approach developed by Bayon et al. (2007) for sediments of cold seeps of the Niger Delta is also suitable to identify the mineralogy of authigenic carbonates in pockmark sediments of the Congo Deep-Sea Fan. We expand this approach by combining interstitial with solid phase Sr/Ca and Mg/Ca ratios, which demonstrate that high Mg-calcite is the predominant authigenic carbonate that currently forms at the sulfate/methane reaction zone (SMRZ). This is the first study which investigates both solid phase and pore water signatures typical for either aragonite or high Mg-calcite precipitation for the same sediment cores and thus is able to identify active and fossil carbonate precipitation events. At all investigated pockmark sites fossil horizons of the SMRZ were deduced from high Mg-calcite located above and below the current depths of the SMRZ. Additionally, aragonite enrichments typical for high seepage rates were detected close to the sediment surface at these sites. However, active precipitation of aragonite as indicated by pore water characteristics only occurs at the Black Hole site. Dissolved and solid phase Ba concentrations were used to estimate the time the SMRZ was fixed at the current depths of the diagenetic barite fronts. The combined pore water and solid phase elemental ratios (Mg/Ca, Sr/Ca) and Ba concentrations allow the reconstruction of past changes in methane seepage at the investigated pockmark sites. At the Hydrate Hole and Worm Hole sites the time of high methane seepage was estimated to have ceased at least 600 yr BP. In contrast, a more recent change from a high flux to a more dormant stage must have occurred at the Black Hole site as evidenced by active aragonite precipitation at the sediment surface and a lack of diagenetic Ba enrichments.

Age determination and stable isotope ratios of three sediment cores from the Great Belt

The marine transgression Into the Baltic Sea through the Great Belt took place around 9,370 calibrated C-14-years B.P. The sedimentary sequence from the early brackish phase and the change to marine conditions has been investigated in detail through C-14-datings, and oxygen and carbon isotope measurements, and is interpreted by comparison with modern analogs. The oldest brackish sediments are the strongly laminated clays and silts rich in organic carbon followed by non-laminated heavily bioturbated silts. The bedding and textural characteristics and stable isotope analyses on Ammonia beccarii (dextral) and A. beccarii (sinistral) show that the deposltlonal conditions respond to a change at about 9,100 cal. a B.P. from an unstratified brackish water environment in the initial stage of the Littorina Transgression to a thermohaline layered milieu in the upper unit. The oxygen isotope results indicate that the bottom waters of this latter period had salinities and temperatures comparable to the present day Kiel Bay waters. The isotopic composition of the total organic carbon and the d13C-values of A. beccarii reveal a gradual change from an initially lacustrine/terrestrial provenance toward a brackish/marine dominated depositional environment. A stagnation of the sea level at around 9,100 to 9,400 B.P. is indicated.

Pore water and solid phase sulfur, carbon and iron data from samples collected in the Argentine Basin during expedition M78

Sulfur phases in the Argentine Basin.

Porewater and solid-phase phosphorus geochemistry in surface sediments of sediment core GeoB9510-3, GeoB9518-4 and GeoB9519-6

Despite intensive research on the different domains of the marine phosphorus (P) cycle during the last decades, frequently discussed open questions still exist especially on controlling factors for the benthic behaviour of P and its general distribution in sediment-pore water systems. Steady state or the internal balance of all relevant physical and (bio)geochemical processes are amongst the key issues. In this study we present and discuss an extended data set from surface sediments recovered from three locations on the NW African continental slope. Pore water data and results from sequential sediment extractions give clear evidence to the well-known close relationship between the benthic cycles of P and iron. Accordingly, most of the dissolved phosphate must have been released by microbially catalyzed reductive dissolution of iron (oxhydr)oxides. However, rates of release and association of P and iron, respectively, are not directly represented in profiles of element specific sediment compositions. Results from steady-state based transport-reaction modelling suggest that particle mixing due to active bioturbation, or rather a physical net downward transport of P associated to iron (oxyhydr)oxides, is an essential process for the balance of the inspected benthic cycles. This study emphasizes the importance of balancing analytical data for a comprehensive understanding of all processes involved in biogeochemical cycles.