Exponential Survival Curves Research Articles

Rationale and design of the multicentric randomized EVAOLD trial: evaluation of a strategy guided by imaging versus routine invasive strategy in elderly patients with ischemia

BackgroundThe management of myocardial infarction without ST segment elevation (NSTEMI) in elderly patients remains challenging, in particular the benefit/risk balance of routine revascularization remains uncertain. Study designEVAOLD is s a multicenter, prospective, open-label trial with 2 parallel arms in NSTEMI patients ≥ 80 years of age. The aim of the trial is to test whether a strategy of selective invasive management guided by ischemia stress imaging (IMG group) will be non-inferior in preventing Major Adverse Cardiac and Cerebrovascular Events (MACCE, ie all-cause death, non-fatal myocardial infarction, non-fatal stroke) rates at 1 year compared with a routine invasive strategy (INV Group). Geriatric assessment and cost- effectiveness analysis will also be performed. A sample size of 1756 patients (assuming a 10% rate of patients lost to follow-up) is needed to show non-inferiority with 80% power. Non-inferiority based on exponential survival curves will be declared if the upper limit of the one-sided 97.5% confidence interval for the hazard ratio is lower than 1.24, corresponding to a non-inferiority margin of 7% in absolute difference and an event rate of 40% in the INV group. ConclusionEVAOLD is a nationwide, prospective, open-label trial testing the non-inferiority of a strategy of selective invasive management guided by ischemia stress imaging versus routine invasive strategy in elderly NSTEMI patients. ClinicalTrials.gov Identifier: NCT03289728

Cost-Effectiveness of Axicabtagene Ciloleucel Versus Mosunetuzumab in Relapsed/Refractory Follicular Lymphoma in the US

Introduction Anti-CD19 chimeric antigen receptor T-cell (CAR-T) therapies, including axicabtagene ciloleucel (axi-cel), and CD20 × CD3 T-cell-engaging bispecific monoclonal antibodies, such as mosunetuzumab (mosun), are novel therapies for 3L+ relapsed/refractory (r/r) follicular lymphoma (FL) that have recently been approved by the US Food and Drug Administration. This analysis assessed the cost-effectiveness of axi-cel compared to mosun in r/r 3L+ FL from a US third-party payer perspective. Methods A three-state (progression-free [PF], progressed disease [PD], and death) partitioned-survival model was used to compare the two treatments over a lifetime horizon in a hypothetical cohort of US adults (age ≥18) receiving 3L+ treatment for r/r FL. ZUMA-5 (NCT03105336) and GO29781 (NCT02500407) trial data were used to inform progression-free survival (PFS) and overall survival (OS) for axi-cel and mosun, respectively. Survival curves for axi-cel were estimated using an exponential distribution for both PFS and OS. In the base case analysis, 40% of axi-cel patients alive at 5 years were assumed to experience long-term remission (i.e., functional cure), and therefore followed general population mortality adjusted by a standardized mortality ratio. This assumption was informed by the literature. Mosun survival was modeled via hazard ratios (HRs) applied to axi-cel exponential survival curves. For PFS, the HR value was estimated via a matching indirect comparison to adjust for differences between the trial populations. As a conservative assumption, a HR of 1.0 was used to model mosun OS due to lack of published results. The mosun arm did not include the cure assumption at 5 years because long-term remission is not expected with monoclonal antibodies in r/r FL. Health state utilities (HSU), healthcare resource use (HCRU), and treatment pattern inputs were obtained from literature. Costs for treatment and administration, adverse event management, monitoring resource use, HCRU, and end-of-life were included in the model. Key model outcomes included discounted (at 3% per year) total and incremental costs, life years (LYs), and quality adjusted life years (QALYs), as well as incremental cost-effectiveness ratios (ICERs). Scenario analyses were conducted on the cure assumption and all input parameters were individually varied by ±20% of their base case values in one-way sensitivity analysis (OWSA) to assess parameter uncertainty. Results Axi-cel use led to increases of 1.51 LY and 1.80 QALY (Table 1) compared to mosun. Progression-free survival for axi-cel patients was 7.11 LY compared to 1.80 LY for mosun, which resulted in a PF state cost increase of $215,045 primarily driven by the one-time cost of axi-cel treatment. Conversely, axi-cel costs were $63,000 less than mosun in the PD state, as patients spent less time with PD and had lower costs for subsequent treatment lines. Total incremental costs for axi-cel were $151,425, resulting in an ICER of $84,016/QALY gained. Analysis of lower cure fractions indicated cost-effectiveness across a wide range of values. Additionally, the OWSA indicated the most impactful inputs for the ICER were mean patient age, the relative dose intensity (RDI) of mosun, PF and PD HSUs, and PD HCRU. Inputs with the largest impact on total incremental costs were RDI, HCRU, and CAR-T infusion hospitalization duration. Conclusions Axi-cel is cost-effective versus mosun in r/r 3L+ FL at an ICER of $84,016/QALY gained, which is far lower than the commonly-cited US willingness-to-pay threshold of $150,000/QALY. This analysis demonstrates the value of using axi-cel, reflecting the aggregate benefits of a one-time therapy, reduction in need for subsequent treatment lines, and population segment experiencing effective cure.

DNA Repair Does Not Trigger Genetic Instability of Yeast Cells

The dependence of the delayed formation of colonies on the dose of ionizing radiation (gamma rays of 60Co, dose rate 10 Gy/min) was obtained for six strains of wild-type haploid and diploid yeast, capable of recovering from radiation damage and characterized by sigmoidal survival curves as well as for six haploid and diploid radiosensitive mutants defective in reparation and characterized by exponential survival curves. The delay in the formation of colonies by survival cells after irradiation is considered as a genetic instability display. It was shown that for all diploid strains, genetic instability reached 100% with an increase in the dose of ionizing radiation, regardless of the shape of survival curves and the cell ability to recover from radiation damage. Conversely, for all haploid strains, genetic instability was only close to 20%. In contrast to traditional concepts, these data indicate that the late formation of colonies by surviving yeast cells after irradiation is determined mainly by cell ploidy and does not depend on the shape of the dose-response curves and cell radiosensitivity. This means that DNA repair does not trigger genetic instability in yeast cells.

Multicenter Randomized Controlled Trial of Surveillance Versus Endoscopic Therapy for Barrett’s Esophagus With Low-grade Dysplasia: The SURVENT Trial: Study Rationale, Methodology, Innovation, and Implications

Multicenter Randomized Controlled Trial of Surveillance Versus Endoscopic Therapy for Barrett’s Esophagus With Low-grade Dysplasia: The SURVENT Trial: Study Rationale, Methodology, Innovation, and Implications

Direct ionizing radiation and bystander effect in mouse mesenchymal stem cells

Purpose: This study aimed to evaluate the radiation-induced direct and bystander (BYS) responses of mesenchymal stem cells (MSCs) and to characterize these cells radiobiologically. Methods and materials: MSCs were irradiated (IR) and parameters related to DNA damage and cellular signaling were verified in a dose range from 0.5 to 15 Gy; also a transwell insert co-culture system was used to study medium-mediated BYS effects. Results: The main effects on directly IR cells were seen at doses higher than 6 Gy: induction of cell death, cell cycle arrest, upregulation of p21, and alteration of redox status. Irrespective of a specific dose, induction of micronuclei formation, H2AX phosphorylation, and decreased Akt expression also occurred. Thus, mTOR expression, cell senescence, nitric oxide generation, and calcium levels, in general were not significantly modulated by radiation. Data from the linear-quadratic model showed a high alpha/beta ratio, which is consistent with a more exponential survival curve. BYS effects from the unirradiated MSCs placed into companion wells with the directly IR cells, were not observed. Conclusions: The results can be interpreted as a positive outcome, meaning that the radiation damage is restricted to the directed IR MSCs not leading to off-target cell responses.

Incomplete Split-Dose Recovery and Induced Radioresistance During Fractionated Irradiation of a Human Glioblastoma Cell Line In Vitro

Fractionated radiotherapy is part of the standard treatment of glioblastoma but radioresistance contributes to local recurrence of these highly malignant tumors. Classical radiobiological models assume complete recovery of surviving cells ascribed to repair of sublethal damage (SLD) between fractions, implying that cell survival after the i’th fraction is determined by the surviving fraction (SF) after a single fraction of dose, d, repeated i times. The purpose was to test this hypothesis in vitro. The radioresistant U251 glioblastoma cell line (p53-mutated) was used. Clonogenic cell survival after irradiation with 6 MV X-rays was determined by the colony formation assay and survival curves were fitted by the linear-quadratic model. In order to test the effect of tumor suppressor protein p53 on survival curve shape and split-dose recovery, early-passage human skin fibroblasts and the human lymphoblastoid cells lines TK6 (p53-wild-type), TK6-E6 (p53-suppressed), and WTK1 (p53-mutated), were included. Mean values ± std.err. are shown and statistical significance was tested by the t-test. Single-dose survival curves of U251 cells showed radioresistance with downward curvature at higher doses (α=0.147±0.021 Gy-1; β=0.039±0.003 Gy-2; n=9). Split-dose recovery between two fractions of 4 Gy each was observed for 15 min to 9h intervals with maximal but incomplete recovery reached at 4h. The survival curve shape for graded second doses at 4h did not recapitulate the curve for single-dose irradiation but was steeper with less downward curvature (a=0.400±0.114 Gy-1, α=0.0005; β=0.020±0.017 Gy-2, p=0.03; n=3). Fractionated irradiation with daily doses of 2 Gy, did not produce the expected exponential decrease of SF(i×d)=SF(d)i. Instead, a downward curvature during the first 2-3 fractions was followed by a reduced slope indicating induced radioresistance. Early-passage fibroblasts with a nearly exponential survival curve showed no split-dose recovery in spite of being proficient for DNA double-strand break (DSB) repair. The association between downward curvature and split-dose recovery was confirmed in the relatively radioresistant WTK1 cell line whereas the sensitive TK6 and TK6-E6 cell lines showed essentially exponential survival curves with little or no split-dose recovery. The reduced recovery after the first few fractions and induced radioresistance after multiple fractions may support the use of highly hypofractionated or single-dose radiotherapy. Whereas SLD repair (detected as split-dose recovery) was associated with downward curvature of cell survival curves, this did not correlate with DSB repair proficiency or lack of functional p53. These results are conflicting with classical radiobiological models and imply that a better understanding of the SLD repair phenotype is needed.

A HYPOTHESIS OF RADIORESISTANCE AND CELL-SURVIVAL CURVE SHAPE BASED ON CELL-CYCLE PROGRESSION AND DAMAGE TOLERANCE.

Exponential survival curves of early-passage human fibroblasts challenge classic biophysical models of cell inactivation. Thus, X-ray doses of 2-4 Gy inactivate normal, human skin fibroblasts in spite of negligible residual double-strand breaks. By contrast, radioresistant p53-mutant U251 glioblastoma cells proliferate in spite of residual damage. Similarly, p53 wildtype TK6 lymphoblastoid cells show exponential survival curves while the related p53-mutant WTK1 cell line continued to proliferate and showed a shouldered survival curve. Here, we propose a model in which the radioresistant shoulder region is due to tolerance to certain types or amounts of residual damage that would otherwise inactivate normal cells. Thus, the steeper initial slope and absence of a shoulder in the survival curve of normal cells may not imply a higher number of residual lesions but rather non-tolerance to these lesions.

Lymphocyte Reproductive Activity Normalized to Numbers of Hematopoietic Stem Cells in Blood and Rate of Death in Fatal Diseases

The numbers of CD133+ and CD31+ lymphocytes and those in the G2-M phases in the total fraction of circulating lymphocytes from patients with fatal liver cirrhosis and advanced lung cancer were investigated by flow cytometry during a long period of conventional treatment with OLT or palliative surgery followed by myelosuppressive chemotherapy. The relationships of specific reproductive activity, sRA (G2-M/CD133+), and the number of committed liver α-fetoprotein-positive (AFP+) cells with the rate of patient deaths, characterized by exponential approximation survival curves for both diseases, were investigated. Subnormal sRA in patients after OLT and excessive sRA in LC patients above a healthy level were associated with higher death rates and lower survival, coinciding with strong immunosuppression caused by anti-rejection and anti-cancer therapies. These findings may be explained by morphogenesis (feeding) activity of circulating lymphocytes targeted toward both normal and malignant tissues rather than in terms of cellular immunity. The sRA changes may be a useful indicator for monitoring the potential for engraftment or tumor growth.

Response to Letter Regarding Article, “C-Reactive Protein and the Risk of Stent Thrombosis and Cardiovascular Events After Drug-Eluting Stent Implantation”

On the basis of our previous findings,1 we propose a readily available and simple marker, C-reactive protein, for the prediction of stent thrombosis after implantation of drug-eluting stents.2 A priori sample size was determined by use of the assumption of exponential survival curves for the primary end point (definite or probable stent thrombosis). Using Cox regression of the log hazard ratio on a binary covariate (elevated versus nonelevated C-reactive protein) with a ≥30% prevalence, a sample of 2600 observations achieves 80% power at a 0.05 significance level to detect a regression coefficient equal …

The role of nonhomologous end joining and homologous recombination in the clonogenic bystander effects of mammalian cells after exposure to counted 10 MeV protons and 4.5 MeV α-particles of the PTB microbeam

We have studied the dependence of clonogenic bystander effects on defects in the pathways of DNA double-strand break (DSB) repair and on linear energy transfer (LET). The single-ion microbeam of the Physikalisch-Technische Bundesanstalt (PTB) was used to irradiate parental Chinese hamster ovary cells or derivatives deficient in nonhomologous end joining (NHEJ) or homologous recombination (HR) in the G1-phase of the cell cycle. Cell nuclei were targeted with 10 MeV protons (LET = 4.7 keV/microm) or 4.5 MeV alpha-particles (LET = 100 keV/microm). During exposure, the cells were confluent, allowing signal transfer through both gap junctions and diffusion. When all cell nuclei were targeted with 10 MeV protons, approximately exponential survival curves were obtained for all three cell lines. When only 10% of all cell nuclei were targeted, a significant bystander effect was observed for parental and HR-deficient cells, but not for NHEJ-deficient cells. For all three cell lines, the survival data after exposure of all cell nuclei to 4.5 MeV alpha-particles could be fitted by exponential curves. When only 10% of all cell nuclei were targeted, significant bystander effects were obtained for parental and HR-deficient cells, whereas for NHEJ-deficient cells a small, but significant, bystander effect was observed only at higher doses. The data suggest that bystander cell killing is a consequence of un- or misrejoined DSB which occur in bystander cells during the S-phase as a result of the processing of oxidative bistranded DNA lesions. The relative contributions of NHEJ and HR to the repairing of DSB in the late S/G2-phase may affect clonogenic bystander effects.

Radiation response of primary human skin fibroblasts and their bystander cells after exposure to counted particles at low and high LET

Purpose: To investigate the dependence of bystander effects on linear energy transfer (LET) in the low dose region.Materials and Methods: The single-ion microbeam of the Physikalisch-Technische Bundesanstalt (PTB) was used to irradiate confluent primary human skin fibroblasts. Cells plated on a special irradiation dish were targeted with 10 MeV protons (LET ≈ 4.7 keV/μm) and 4.5 MeV α-particles (LET ≈ 100 keV/μm). During exposure, the cells were confluent allowing signal transfers through both gap junctions and diffusion.Results: For 10 MeV protons the clonogenic capability was significantly higher after exposure to 70 protons (0.31 Gy) compared with unirradiated cells. For higher doses the survival curve was exponential. Exposure of only 10% of all nuclei resulted in a similar radiation response in the low dose region. For higher doses up to 2.2 Gy no cell killing was observed. For 4.5 MeV α-particles an exponential survival curve was obtained. Irradiation of only 10% of all cell nuclei resulted in an survival curve as had been expected in the absence of any bystander effect.Conclusion: The type and extent of bystander effects turned out to be dependent on the particles' LET and are likely to depend also on the cell line used and the techniques applied.

Cost Effectiveness of Cardiac Resynchronization Therapy in the Comparison of Medical Therapy, Pacing, and Defibrillation in Heart Failure (COMPANION) Trial

The analysis goal was to estimate incremental cost-effectiveness ratios (ICERs) for the Comparison of Medical Therapy, Pacing, and Defibrillation in Heart Failure (COMPANION) trial patients who received cardiac resynchronization therapy (CRT) via pacemaker (CRT-P) or pacemaker-defibrillator (CRT-D) in combination with optimal pharmacological therapy (OPT) relative to patients with OPT alone. In the COMPANION trial, CRT-P and CRT-D reduced the combined risk of all-cause mortality or first hospitalization among patients with advanced heart failure and intraventricular conduction delays, but the cost effectiveness of the therapy remains unknown. In this analysis, intent-to-treat trial data were modeled to estimate the cost effectiveness of CRT-D and CRT-P relative to OPT over a base-case seven-year treatment episode. Exponential survival curves were derived from trial data and adjusted by quality-of-life trial results to yield quality-adjusted life-years (QALYs). For the first two years, follow-up hospitalizations were based on trial data. The model assumed equalized hospitalization rates beyond two years. Initial implantation and follow-up hospitalization costs were estimated using Medicare data. Over two years, follow-up hospitalization costs were reduced by 29% for CRT-D and 37% for CRT-P. Extending the cost-effectiveness analysis to a seven-year base-case time period, the ICER for CRT-P was 19,600 dollars per QALY and the ICER for CRT-D was 43,000 dollars per QALY relative to OPT. For the COMPANION trial patients, the use of CRT-P and CRT-D was associated with a cost-effectiveness ratio below generally accepted benchmarks for therapeutic interventions of 50,000 dollars per QALY to 100,000 dollars per QALY. This suggests that the clinical benefits of CRT-P and CRT-D can be achieved at a reasonable cost.

Platelet production estimation in thrombocytopenic patient: a non-invasive or invasive approach?

Aim: To compare platelet production determined using non-invasive (platelet production index, PI) and invasive method (megakaryocyte number, Mk) in thrombocytopenic patients. Methods: PI was calculated on the basis of autologous 111In platelets T1/2, life span (LS) and Pt blood count determination. Megakaryocyte number (Mk) was described as 1=numerous, 2=present, 3=low productive, 4=rare. Fifty-five persons were investigated: 49 thrombocytopenic (40 chronic immune thrombocytopenic purpuras, ITP; 9 myelodysplastic syndromes, MDS) and six healthy control subjects (C). Results: All C and MDS subjects had linear Pt survival curves and normal platelet LS (mean values 8.9 days in C, and 8.2 days in MDS; P>0.05). Exponential platelet survival curve and shortened Pt LS (1.1 day) were obtained in ITP. A highly significant difference was noticed in Pt LS between ITP and MDS (P<0.001) and between ITP and control group. PI was lower in MDS (0.2) than in ITP (1.2) and C (1.0). Mean value for Mk number was the same in MDS and ITP group (1.0). Conclusion: Platelet production in thrombocytopenic patients is better estimated using a non-invasive than an invasive method.

Altered red cell turnover in diabetic mice

In diabetes, a subpopulation of red cells expose phosphatidylserine, and the size of this subpopulation of cells is related to blood glucose levels. Because phosphatidylserine exposure can lead to the recognition and removal of red cells we hypothesized that red cell survival would be altered. In this study, diabetic female mice (db/db) and heterozygous littermate controls were used to explore relationships between red cell characteristics, phosphatidylserine exposure, and red cell survival. Red cell turnover was assessed using random red cell labeling with biotin. To determine if phosphatidylserine exposure was related to age, red cells were double-labeled and analyzed by flow cytometry. Cellular characteristics were measured by flow cytometry and ektacytometry. While red cell removal was linear for the control mice, for the diabetic mice an exponential survival curve was noted with an extended survival of a subpopulation of cells. The subpopulation of red cells exposing phosphatidylserine was significantly increased in the diabetic mice relative to the control mice (0.9% ± 0.07%, n = 12, and 0.6% ± 0.05 %, n = 22, respectively; P =.007). This subpopulation increased during the life of the red cell, with a higher rate of increase in the diabetic mice. Red cell hemoglobin content and cell volume were abnormal, but no obvious signs of anemia were found in the diabetic animals. A normal hematocrit, low reticulocyte count, and a much reduced spleen in these animals were consistent with a low red cell turnover. The presence of a population of older phosphatidylserine exposing cells indicates altered red cell removal and suggests a role for older red cells in vascular damage. (J Lab Clin Med 2002;140:161-5)

Effects of the combination of thrombopoietin with cytokines on the survival of X-irradiated CD34(+) megakaryocytic progenitor cells from normal human peripheral blood.

Combinations of thrombopoietin and cytokines that act on megakaryocyte development (stem cell factor, IL3, IL6, IL11, flt3 ligand (now known as FLT3LG), erythropoietin, GM-CSF and G-CSF were evaluated for their ability to enhance clonal growth in vitro of X-irradiated CD34(+) megakaryocytic progenitor cells (CFU-megakaryocytes) purified from normal human peripheral blood. These data were compared with corresponding results described previously for CD34(+) CFU-megakaryocytes from human placental/umbilical cord blood (I. Kashiwakura, Radiat. Res. 153, 144-152, 2000). All cytokines, except IL3, promoted thrombopoietin-induced colony formation, but they resulted in exponential radiation survival curves. No significant differences in the D(0) (46-61 cGy) and extrapolation number n (1.00-1.04) were observed between thrombopoietin alone and in combination with these cytokines. IL3 did not promote colony formation, but marked shoulders were observed on the survival curves (D(0) = 91 cGy, n = 2.83). Flow cytometric analysis of cells harvested from cultures of X-irradiated cells stimulated with thrombopoietin plus IL3 showed no significant differences in the expression of surface antigens and DNA ploidy distribution of megakaryocytes from the control. These findings suggest that IL3 plays a key role in promoting the survival of X-irradiated CD34(+) CFU-megakaryocytes from peripheral blood as well as those from cord blood, though the former are more radiosensitive.

Radiation sensitivity of megakaryocyte colony-forming cells in human placental and umbilical cord blood.

The in vitro radiation sensitivity of CFU-Meg isolated from human placental and umbilical cord blood was evaluated in plasma clot cultures stimulated by recombinant human cytokines, including thrombopoietin, the FLT3 ligand (FLT3LG), interleukin-3, interleukin-11 and stem cell factor. The CD34(+) cells were irradiated with X rays at a dose rate of 73 cGy/ min. The megakaryocyte colonies were identified by using an FITC-conjugated antibody to glycoprotein IIbIIIa and were classified into two groups based on colony size: large colonies (immature CFU-Meg) and small colonies (mature CFU-Meg). Treatment with thrombopoietin alone or in combination with FLT3LG and/or interleukin-11 gave exponential radiation survival curves (D(0) for immature CFU-Meg = 56-77 cGy, D(0) for mature CFU-Meg = 86 cGy-1.12 Gy), while marked shoulders were observed on the survival curves for colonies supported by the combination of thrombopoietin, interleukin-3 and stem cell factor (D(0) for immature CFU-Meg = 89- 98 cGy; D(0) for mature CFU-Meg = 1. 25-1.31 Gy). Our results showed that the immature CFU-Meg were more radiosensitive than the mature CFU-Meg and that the combination of cytokines, including thrombopoietin, interleukin-3 and stem cell factor, affected the radiation sensitivity of CFU-Meg to the same extent as with thrombopoietin alone or in combination with FLT3LG and/or interleukin-11.

Radiotoxicity of Bismuth-213 Bound to Membranes of Monolayer and Spheroid Cultures of Tumor Cells

Monoclonal antibody 13A to murine CD44 was used to bind the alpha-particle emitter 213Bi to cell surfaces of cultured EMT-6 or Line 1 tumor cells. Data on kinetics and saturation of binding, cell shape and nuclear size were used to calculate the absorbed dose to the nuclei. Treatment of monolayer cells with [213Bi]MAb 13A produced a classical exponential survival curve with no apparent shoulder. Microdosimetry analyses indicated that 1.4-1.7 Gy produced a 37% surviving fraction (D0). Multicellular spheroids were shown to bind [213Bi]MAb 13A mainly on the outer cell layer. Relatively small amounts of activity added to the spheroids resulted in relatively large absorbed doses. The result was that 3-6-fold less added radioisotope was necessary to kill similar fractions of cells in spheroids than in monolayer cells. These data are consistent with the interpretation that the alpha particles from a single 213Bi atom bound to one cell can penetrate and kill adjacent cells. Flow cytometry was used to sort cells originating from the periphery or from the interior of spheroids. Cells from the outside of the [213Bi]MAb 13A exposed spheroids had a lower surviving fraction per administered activity than cells from the interior. Cells were killed efficiently in spheroids up to 20-30 cells in diameter. The data support the hypothesis that alpha-particle emitters should be very efficient at killing cells in micrometastases of solid tumors.

Generalization of exponential survival statistics for microorganisms in radiation field

Abstract For a comprehensive description of the fraction, SF , of species surviving irradiation dose, D , we use the generalized exponential SF =exp[−( D / D 0 ) α ], where D 0 denotes the effective dose, and α >0 is the dispersion parameter. The generalized exponential reduces to an exponential survival curve for α =1, reproduces the concave or tailed survival curves for 0 α α >1. The differences among these common types of survival curves are phenomenologically interpreted solely in terms of the distributions of radiation sensitivity of species under the given experimental conditions. As an example the survival statistics for five strains of yeast Saccharomyces cerevisine are shown.

Approximate confidence intervals after a sequential clinical trial comparing two exponential survival curves with censoring

A sequential test is considered for comparing two exponential survival curves with unknown failure rates θ 1, θ 2 > 0. The survival times are censored by both real time and an independent censoring variable. It is shown how very weak expansions for the bivariate version of the signed root transformation may be used to construct an approximate confidence interval for δ = log( θ 1 θ 2 ) following the test. The accuracy of the method is illustrated by simulation results for several sequential tests and data-dependent allocation rules.

Radiotoxic effect and dosimetry of 67Ga in multicellular spheroids as compared to single cells of the lymphoma cell line U715

Purpose : The purpose of the present study was to investigate if there were differences between U715 spheroids and single cells in the radiotoxic effect of 67Ga on cell growth and clonogenic capacity in vitro and to generate dosimetric approaches for the multicellular tumor model. Methods and Materials : Human lymphoma U715 cells were cultured in vitro as single cells and multicellular spheroids, grown with the use of a combination of fibrin clot technique, spinner flasks, and liquid-overlay culture. Cells were incubated with 2.96–8.88 MBq/ml 67Gallium for 4 days. Spheroids were dispersed to single cells by treatment with plasmin. Residual proliferative and clonogenic capacity after 67Ga incubation were assayed using the MTT-test and clonogenic test, respectively. Autoradiography was performed with 1 μm sections and Ilford L4 liquid photographic emulsion. Dosimetric approaches were made, based on the MIRD-approach. Results : During 67Ga incubation proliferation was inhibited. The residual proliferative or clonogenic capacity was inhibited by 8.88 MBq/ml for 39 and 88%, respectively. For single cells with 6.66 MBq/ml these inhibitions were 64 and 96%, respectively. Autoradiography showed an homogeneous distribution of 67Ga in spheroids and single cells. In single cells a 2.1–3.5 times higher 67Ga uptake/cell than in spheroids produced an equitoxic effect. The uptake parameters were implemented in new dosimetric approaches and showed that the efficacy of intracellular 67Ga was two times higher in spheroid clusters than in single cells due to energy deposition of internal conversion electrons within the cell clusters with a mean diameter size of nine cells. Both for proliferative and clonogenic capacity the exponential survival curves were superimposed. Conclusions : With the new approaches made in our dosimetric model the discrepancy found between 67Ga accumulation and radiotoxic effect in spheroids as compared to single cells can be explained by additional effects of the crossfire of internal conversion electrons within clusters of about nine cells in diameter in spheroids. Only twice as much 67Ga was needed to reach equitoxic absorbed doses in spheroids than was needed in single cells. Such might be important for the use of 67Ga treatment of small metastasis of malignant lymphoma.