A multi-arm multi-stage platform design that allows preplanned addition of arms while still controlling the family-wise error.

There is growing interest in platform trials that allow for adding of new treatment arms as the trial progresses as well as being able to stop treatments part way through the trial for either lack of benefit/futility or for superiority. In some situations, platform trials need to guarantee that error rates are controlled. This paper presents a multi-stage design, that allows additional arms to be added in a platform trial in a preplanned fashion, while still controlling the family-wise error rate, under the assumption of known number and timing of treatments to be added, and no time trends. A method is given to compute the sample size required to achieve a desired level of power and we show how the distribution of the sample size and the expected sample size can be found. We focus on power under the least favorable configuration which is the power of finding the treatment with a clinically relevant effect out of a set of treatments while the rest have an uninteresting treatment effect. A motivating trial is presented which focuses on two settings, with the first being a set number of stages per active treatment arm and the second being a set total number of stages, with treatments that are added later getting fewer stages. Compared to Bonferroni, the savings in the total maximum sample size are modest in a trial with three arms, <1% of the total sample size. However, the savings are more substantial in trials with more arms.

Minimal Residual Disease Status Predicts Outcome in Patients With Previously Untreated Follicular Lymphoma: A Prospective Analysis of the Phase III GALLIUM Study.

PURPOSE: We report an analysis of minimal residual/detectable disease (MRD) as a predictor of outcome in previously untreated patients with follicular lymphoma (FL) from the randomized, multicenter GALLIUM (ClinicalTrials.gov identifier: NCT01332968) trial. PATIENTS AND METHODS: Patients received induction with obinutuzumab (G) or rituximab (R) plus bendamustine, or cyclophosphamide, doxorubicin, vincristine, prednisone (CHOP) or cyclophosphamide, vincristine, prednisone (CVP) chemotherapy, followed by maintenance with the same antibody in responders. MRD status was assessed at predefined time points (mid-induction [MI], end of induction [EOI], and at 4-6 monthly intervals during maintenance and follow-up). Patients with evaluable biomarker data at diagnosis were included in the survival analysis. RESULTS: MRD positivity was associated with inferior progression-free survival (PFS) at MI (hazard ratio [HR], 3.03 [95% CI, 2.07 to 4.45]; P < .0001) and EOI (HR, 2.25 [95% CI, 1.53 to 3.32]; P < .0001). MRD response was higher after G- versus R-chemotherapy at MI (94.2% v 88.9%; P = .013) and at EOI (93.1% v 86.7%; P = .0077). Late responders (MI-positive/EOI-negative) had a significantly poorer PFS than early responders (MI-negative/EOI-negative; HR, 3.11 [95% CI, 1.75 to 5.52]; P = .00011). The smallest proportion of MRD positivity was observed in patients receiving bendamustine at MI (4.8% v 16.0% in those receiving CHOP; P < .0001). G appeared to compensate for less effective chemotherapy regimens, with similar MRD response rates observed across the G-chemo groups. During the maintenance period, more patients treated with R than with G were MRD-positive (R-CHOP, 20.7% v G-CHOP, 7.0%; R-CVP, 21.7% v G-CVP, 9.4%). Throughout maintenance, MRD positivity was associated with clinical relapse. CONCLUSION: MRD status can determine outcome after induction and during maintenance, and MRD negativity is a prerequisite for long-term disease control in FL. The higher MRD responses after G- versus R-based treatment confirm more effective tumor cell clearance.

Updating the probability of study success for combination therapies using related combination study data.

Combination therapies are becoming increasingly used in a range of therapeutic areas such as oncology and infectious diseases, providing potential benefits such as minimising drug resistance and toxicity. Sets of combination studies may be related, for example, if they have at least one treatment in common and are used in the same indication. In this setting, value can be gained by sharing information between related combination studies. We present a framework that allows the study success probabilities of a set of related combination therapies to be updated based on the outcome of a single combination study. This allows us to incorporate both direct and indirect data on a combination therapy in the decision-making process for future studies. We also provide a robustification that accounts for the fact that the prior assumptions on the correlation structure of the set of combination therapies may be incorrect. We show how this framework can be used in practice and highlight the use of the study success probabilities in the planning of clinical studies.

A meta-analytic framework to adjust for bias in external control studies.

While randomized controlled trials (RCTs) are the gold standard for estimating treatment effects in medical research, there is increasing use of and interest in using real-world data for drug development. One such use case is the construction of external control arms for evaluation of efficacy in single-arm trials, particularly in cases where randomization is either infeasible or unethical. However, it is well known that treated patients in non-randomized studies may not be comparable to control patients-on either measured or unmeasured variables-and that the underlying population differences between the two groups may result in biased treatment effect estimates as well as increased variability in estimation. To address these challenges for analyses of time-to-event outcomes, we developed a meta-analytic framework that uses historical reference studies to adjust a log hazard ratio estimate in a new external control study for its additional bias and variability. The set of historical studies is formed by constructing external control arms for historical RCTs, and a meta-analysis compares the trial controls to the external control arms. Importantly, a prospective external control study can be performed independently of the meta-analysis using standard causal inference techniques for observational data. We illustrate our approach with a simulation study and an empirical example based on reference studies for advanced non-small cell lung cancer. In our empirical analysis, external control patients had lower survival than trial controls (hazard ratio: 0.907), but our methodology is able to correct for this bias. An implementation of our approach is available in the R package ecmeta.

Systematic pan-cancer analysis of mutation-treatment interactions using large real-world clinicogenomics data.

Quantifying the effectiveness of different cancer therapies in patients with specific tumor mutations is critical for improving patient outcomes and advancing precision medicine. Here we perform a large-scale computational analysis of 40,903 US patients with cancer who have detailed mutation profiles, treatment sequences and outcomes derived from electronic health records. We systematically identify 458 mutations that predict the survival of patients on specific immunotherapies, chemotherapy agents or targeted therapies across eight common cancer types. We further characterize mutation-mutation interactions that impact the outcomes of targeted therapies. This work demonstrates how computational analysis of large real-world data generates insights, hypotheses and resources to enable precision oncology.

Machine Learning Prediction of Clinical Trial Operational Efficiency.

Clinical trials are the gatekeepers and bottlenecks of progress in medicine. In recent years, they have become increasingly complex and expensive, driven by a growing number of stakeholders requiring more endpoints, more diverse patient populations, and a stringent regulatory environment. Trial designers have historically relied on investigator expertise and legacy norms established within sponsor companies to improve operational efficiency while achieving study goals. As such, data-driven forecasts of operational metrics can be a useful resource for trial design and planning. We develop a machine learning model to predict clinical trial operational efficiency using a novel dataset from Roche containing over 2,000 clinical trials across 20 years and multiple disease areas. The data includes important operational metrics related to patient recruitment and trial duration, as well as a variety of trial features such as the number of procedures, eligibility criteria, and endpoints. Our results demonstrate that operational efficiency can be predicted robustly using trial features, which can provide useful insights to trial designers on the potential impact of their decisions on patient recruitment success and trial duration.

Real-world data prognostic model of overall survival in patients with advanced NSCLC receiving anti-PD-1/PD-L1 immune checkpoint inhibitors as second-line monotherapy.

BACKGROUND AND AIM: The objective of this retrospective, observational, noninterventional cohort study was to investigate prognostic factors of overall survival (OS) in patients with advanced non-small cell lung cancer (aNSCLC) and to develop a novel prognostic model. METHODS: A total of 4049 patients with aNSCLC diagnosed between January 2011 and February 2020 who received atezolizumab, nivolumab, or pembrolizumab as second-line monotherapy were selected from a real-world deidentified database to build the cohort. Patients could not have received first-line treatment with clinical study drug(s) nor immune checkpoint inhibitors including anti-programmed cell death 1 (PD-1)/programmed death-ligand 1 (PD-L1), and anti-cytotoxic T-lymphocyte-associated protein 4 therapies. RESULTS: Patients had a median age of 69 years; 45% were female, 75% White, 70% had stage IV at initial diagnosis, and 70% had nonsquamous histology. A Cox proportional hazards model with lasso regularization was used to build a prognostic model for OS using 18 baseline demographic and clinical factors based on the real-world data cohort. The risk-increasing prognostic factors were abnormally low albumin and chloride levels, Eastern Cooperative Oncology Group performance status score ≥ 2, and abnormally high levels of alkaline phosphatase and white blood cells. The risk-decreasing prognostic factors were PD-L1 positivity, longer time from advanced diagnosis to start of first-line therapy, and higher systolic blood pressure. The performance of the model was validated using data from the OAK trial, and the c-index for the OAK trial validation cohort was 0.65 and 0.67 for the real-world data cohort. CONCLUSIONS: Based on baseline demographic and clinical factors from a real-world setting, this prognostic model was developed to discriminate the risk of death in patients with aNSCLC treated with checkpoint inhibitors as second-line monotherapy, and it performed well in the real-world data and clinical trial cohorts.

The use of external controls: To what extent can it currently be recommended?

With more and better clinical data being captured outside of clinical studies and greater data sharing of clinical studies, external controls may become a more attractive alternative to randomized clinical trials (RCTs). Both industry and regulators recognize that in situations where a randomized study cannot be performed, external controls can provide the needed contextualization to allow a better interpretation of studies without a randomized control. It is also agreed that external controls will not fully replace RCTs as the gold standard for formal proof of efficacy in drug development and the yardstick of clinical research. However, it remains unclear in which situations conclusions about efficacy and a positive benefit/risk can reliably be based on the use of an external control. This paper will provide an overview on types of external control, their applications and the different sources of bias their use may incur, and discuss potential mitigation steps. It will also give recommendations on how the use of external controls can be justified.

P38 MAPK and glucocorticoid receptor crosstalk in bronchial epithelial cells.

p38 MAPK inhibition may have additive and synergistic anti-inflammatory effects when used with corticosteroids. We investigated crosstalk between p38 MAPK inhibitors and corticosteroids in bronchial epithelial cells to investigate synergistic effects on cytokine production and the molecular mechanisms involved. Effects of the p38 MAPK inhibitor BIRB-796 and dexamethasone alone and in combination on LPS, polyI:C or TNFα -induced IL-6, CXCL8 and RANTES were assessed in 16HBEs (human epithelial cell line) and on TNFα-induced IL-6 and CXCL8 in primary human epithelial cells from asthma patients and healthy controls. 16HBEs were used to assess effects of BIRB-796 alone and in combination with dexamethasone on glucocorticoid receptor (GR) activity by reporter gene assay, expression of GR target genes and nuclear localisation using Western blot. The effects of BIRB-796 on TNFα stimulated phosphorylation of p38 MAPK and GR at serine (S) 226 by Western blot. Epithelial levels of phosphorylated p38 MAPK and GR S226 were determined by immunohistochemistry in bronchial biopsies from asthma patients and healthy controls. BIRB-796 in combination with dexamethasone increased inhibition of cytokine production in a synergistic manner. Combination treatment significantly increased GR nuclear localisation compared to dexamethasone alone. BIRB-796 inhibited TNFα-induced p38 MAPK and GR S226 phosphorylation. Phosphorylated GR S226 and p38 MAPK levels were increased in bronchial epithelium of more severe asthma patients. Molecular crosstalk exists between p38 MAPK activation and GR function in human bronchial epithelial cells, which alters GR activity. Combining a p38 MAPK inhibitor and a corticosteroid may demonstrate therapeutic potential in severe asthma. KEY MESSAGES: • Combination of corticosteroid and p38 inhibitor in human bronchial epithelial cells • Combination increased cytokine inhibition synergistically and nuclear GR • p38 MAPK inhibition reduced TNFα-induced phosphorylation of GR at S226 but not S211 • Phosphorylated GRS226 and p38 is increased in bronchial epithelium in severe asthma • Combining a p38 inhibitor and a corticosteroid may be effective in asthma treatment.

MRD response in relapsed/refractory FL after obinutuzumab plus bendamustine or bendamustine alone in the GADOLIN trial.

We report assessment of minimal residual disease (MRD) status and its association with outcome in rituximab-refractory follicular lymphoma (FL) in the randomized GADOLIN trial (NCT01059630). Patients received obinutuzumab (G) plus bendamustine (Benda) induction followed by G maintenance, or Benda induction alone. Patients with a clonal marker (t[14;18] translocation and/or immunoglobulin heavy or light chain rearrangement) detected at study screening were assessed for MRD at mid-induction (MI), end of induction (EOI), and every 6-24 months post-EOI/discontinuation by real-time quantitative PCR. At MI, 41/52 (79%) patients receiving G-Benda were MRD-negative vs. 17/36 (47%) patients receiving Benda alone (p = 0.0029). At EOI, 54/63 (86%) patients receiving G-Benda were MRD-negative vs. 30/55 (55%) receiving Benda alone (p = 0.0002). MRD-negative patients at EOI had improved progression-free survival (HR, 0.33, 95% CI, 0.19-0.56, p < 0.0001) and overall survival (HR, 0.39, 95% CI, 0.19-0.78, p = 0.008) vs. MRD-positive patients, and maintained their MRD-negative status for longer if they received G maintenance than if they did not. These results suggest that the addition of G to Benda-based treatment during induction can significantly contribute to the speed and depth of response, and G maintenance in MRD-negative patients potentially delays lymphoma regrowth.

A comparison of stochastic programming methods for portfolio level decision-making.

Several methods have been presented in the literature for the management of a pharmaceutical portfolio, i.e. selecting which clinical studies should be conducted. We compare two existing approaches that use stochastic programming techniques and formulate the problem as a mixed integer linear programme (MILP). The first approach will be referred to as the ROV (real option valuation) approach since values are assigned to drug development programmes using methods for real option valuation. The second approach will be referred to as the PS (project scheduling) approach as this approach focusses on the scheduling of clinical studies and is formulated similarly to the resource constrained project scheduling problem. The ROV approach treats the value of a drug development programme as stochastic whereas the PS approach treats the trial outcomes as the stochastic component of the programme. As a consequence, the two approaches may select different portfolios. An advantage of the PS approach is that a schedule for when trials are to be conducted is provided as part of the optimal solution. This advantage comes at a much increased computational burden, however.

Embracing model-based designs for dose-finding trials.

BACKGROUND: Dose-finding trials are essential to drug development as they establish recommended doses for later-phase testing. We aim to motivate wider use of model-based designs for dose finding, such as the continual reassessment method (CRM). METHODS: We carried out a literature review of dose-finding designs and conducted a survey to identify perceived barriers to their implementation. RESULTS: We describe the benefits of model-based designs (flexibility, superior operating characteristics, extended scope), their current uptake, and existing resources. The most prominent barriers to implementation of a model-based design were lack of suitable training, chief investigators' preference for algorithm-based designs (e.g., 3+3), and limited resources for study design before funding. We use a real-world example to illustrate how these barriers can be overcome. CONCLUSIONS: There is overwhelming evidence for the benefits of CRM. Many leading pharmaceutical companies routinely implement model-based designs. Our analysis identified barriers for academic statisticians and clinical academics in mirroring the progress industry has made in trial design. Unified support from funders, regulators, and journal editors could result in more accurate doses for later-phase testing, and increase the efficiency and success of clinical drug development. We give recommendations for increasing the uptake of model-based designs for dose-finding trials in academia.

An adaptive design for updating the threshold value of a continuous biomarker.

Potential predictive biomarkers are often measured on a continuous scale, but in practice, a threshold value to divide the patient population into biomarker 'positive' and 'negative' is desirable. Early phase clinical trials are increasingly using biomarkers for patient selection, but at this stage, it is likely that little will be known about the relationship between the biomarker and the treatment outcome. We describe a single-arm trial design with adaptive enrichment, which can increase power to demonstrate efficacy within a patient subpopulation, the parameters of which are also estimated. Our design enables us to learn about the biomarker and optimally adjust the threshold during the study, using a combination of generalised linear modelling and Bayesian prediction. At the final analysis, a binomial exact test is carried out, allowing the hypothesis that 'no population subset exists in which the novel treatment has a desirable response rate' to be tested. Through extensive simulations, we are able to show increased power over fixed threshold methods in many situations without increasing the type-I error rate. We also show that estimates of the threshold, which defines the population subset, are unbiased and often more precise than those from fixed threshold studies. We provide an example of the method applied (retrospectively) to publically available data from a study of the use of tamoxifen after mastectomy by the German Breast Study Group, where progesterone receptor is the biomarker of interest. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Expression of potential biomarkers associated with homologous recombination repair in patients with ovarian or triple-negative breast cancer.

BACKGROUND: Poly(ADP)-ribose polymerase (PARP) inhibitors such as olaparib can induce cell death in cancer cells with homologous recombination (HR) DNA repair deficiencies, such as BRCA1/2 mutations. AIM: To identify prognostic biomarkers of long-term outcomes in cancer patients. METHODS: Immunohistochemistry was used to analyse expression of key HR pathway proteins (ATM, ATR, BRCA1, MDC1, MRE11) and PARP-1 in 100 serous ovarian cancer (SOC) and 100 triple-negative breast cancer (TNBC) tumour samples from Japanese patients. RECIST assessment was used. RESULTS: Patient demographic data and BRCA1/2 mutation status were unavailable. Most proteins listed previously were detected in > 80% of tissue samples, with BRCA1 expression detected in 60-65%. A potential link between BRCA1 expression and overall survival (M stage adjusted) in SOC patients was observed, but was not statistically significant after multiple testing adjustment. Correlations between other biomarker expression and survival were not observed. In TNBC patients, MDC1 staining was associated with progressive disease, but this was not statistically significant; the analysis did not identify significant correlations between biomarker expression and disease control. Limited event numbers prevented assessment of the prognostic value of BRCA1 in TNBC. CONCLUSION: BRCA1 expression may be a candidate for a prognostic biomarker in SOC. Further studies are warranted.

Evaluating Robustness and Sensitivity of the NanoString Technologies nCounter Platform to Enable Multiplexed Gene Expression Analysis of Clinical Samples.

Analysis of clinical trial specimens such as formalin-fixed paraffin-embedded (FFPE) tissue for molecular mechanisms of disease progression or drug response is often challenging and limited to a few markers at a time. This has led to the increasing importance of highly multiplexed assays that enable profiling of many biomarkers within a single assay. Methods for gene expression analysis have undergone major advances in biomedical research, but obtaining a robust dataset from low-quality RNA samples, such as those isolated from FFPE tissue, remains a challenge. Here, we provide a detailed evaluation of the NanoString Technologies nCounter platform, which provides a direct digital readout of up to 800 mRNA targets simultaneously. We tested this system by examining a broad set of human clinical tissues for a range of technical variables, including sensitivity and limit of detection to varying RNA quantity and quality, reagent performance over time, variability between instruments, the impact of the number of fields of view sampled, and differences between probe sequence locations and overlapping genes across CodeSets. This study demonstrates that Nanostring offers several key advantages, including sensitivity, reproducibility, technical robustness, and utility for clinical application.

Experimental designs for detecting synergy and antagonism between two drugs in a pre-clinical study.

The identification of synergistic interactions between combinations of drugs is an important area within drug discovery and development. Pre-clinically, large numbers of screening studies to identify synergistic pairs of compounds can often be ran, necessitating efficient and robust experimental designs. We consider experimental designs for detecting interaction between two drugs in a pre-clinical in vitro assay in the presence of uncertainty of the monotherapy response. The monotherapies are assumed to follow the Hill equation with common lower and upper asymptotes, and a common variance. The optimality criterion used is the variance of the interaction parameter. We focus on ray designs and investigate two algorithms for selecting the optimum set of dose combinations. The first is a forward algorithm in which design points are added sequentially. This is found to give useful solutions in simple cases but can lack robustness when knowledge about the monotherapy parameters is insufficient. The second algorithm is a more pragmatic approach where the design points are constrained to be distributed log-normally along the rays and monotherapy doses. We find that the pragmatic algorithm is more stable than the forward algorithm, and even when the forward algorithm has converged, the pragmatic algorithm can still out-perform it. Practically, we find that good designs for detecting an interaction have equal numbers of points on monotherapies and combination therapies, with those points typically placed in positions where a 50% response is expected. More uncertainty in monotherapy parameters leads to an optimal design with design points that are more spread out.

Reproducible, Quantitative, and Flexible Molecular Subtyping of Clinical DLBCL Samples Using the NanoString nCounter System.

PURPOSE: Diffuse large B-cell lymphoma (DLBCL) is a heterogeneous disease with distinct molecular subtypes. The most established subtyping approach, the "Cell of Origin" (COO) algorithm, categorizes DLBCL into activated B-cell (ABC) and germinal center B-cell (GCB)-like subgroups through gene expression profiling. Recently developed immunohistochemical (IHC) techniques and other established methodologies can deliver discordant results and have various technical limitations. We evaluated the NanoString nCounter gene expression system to address issues with current platforms. EXPERIMENTAL DESIGN: We devised a scoring system using 145 genes from published datasets to categorize DLBCL samples. After cell line validation, clinical tissue segmentation was tested using commercially available diagnostic DLBCL samples. Finally, we profiled biopsies from patients with relapsed/refractory DLBCL enrolled in the fostamatinib phase IIb clinical trial using three independent RNA expression platforms: NanoString, Affymetrix, and qNPA. RESULTS: Diagnostic samples showed a typical spread of subtypes with consistent gene expression profiles across matched fresh, frozen, and formalin-fixed paraffin-embedded tissues. Results from biopsy samples across platforms were remarkably consistent, in contrast to published IHC data. Interestingly, COO segmentation of longitudinal fostamatinib biopsies taken at initial diagnosis and then again at primary relapse showed 88% concordance (15/17), suggesting that COO designation remains stable over the course of disease progression. CONCLUSIONS: DLBCL segmentation of patient tumor samples is possible using a number of expression platforms. However, we found that NanoString offers the most flexibility and fewest limitations in regards to robust clinical tissue subtype characterization. These subtype distinctions should help guide disease prognosis and treatment options within DLBCL clinical practice.

Corticosteroid insensitive alveolar macrophages from asthma patients; synergistic interaction with a p38 mitogen-activated protein kinase (MAPK) inhibitor.

AIMS: Some asthma patients remain symptomatic despite using high doses of inhaled corticosteroids (ICS). We used alveolar macrophages to identify individual patients with insensitivity to corticosteroids and to evaluate the anti-inflammatory effects of a p38 mitogen-activated protein kinase (MAPK) inhibitor combined with a corticosteroid on these cells. METHODS: Alveolar macrophages from 27 asthma patients (classified according to the Global Initiative for Asthma (GINA) treatment stage. Six GINA1, 10 GINA2 and 11 GINA3/4) were stimulated with lipoploysaccharide (LPS) (1 µg ml(-1)). The effects of dexamethasone (dex 1-1000 nm), the p38 MAPK inhibitor 1-(5-tert-butyl-2-p-tolyl-2Hpyrazol-3-yl)-3(4-(2-morpholin-4-yl-ethoxy)naphthalen-1-yl)urea (BIRB-796 1-1000 nm) and both drugs combined at all concentrations on supernatant TNFα, IL-6 and CXCL-8 concentrations were analyzed by ELISA. Dose-sparing and efficacy enhancing effects of combination treatment were determined. RESULTS: Dexamethasone reduced LPS-induced TNFα, IL-6 and CXCL-8 in all groups, but maximum inhibition was significantly reduced for GINA3/4 compared with GINA2 and GINA1 (P < 0.01). A subgroup of corticosteroid insensitive patients with a reduced effect of dexamethasone on cytokine secretion were identified. BIRB-796 in combination with dexamethasone significantly increased cytokine inhibition compared with either drug alone (P < 0.001) in all groups. This effect was greater in corticosteroid insensitive compared with sensitive patients. There were significant synergistic dose-sparing effects (P < 0.05) for the combination treatment on inhibition of TNFα, IL-6 and CXCL-8 in all groups. There was also significant efficacy enhancing benefits (P < 0.05) on TNFα and IL-6. CONCLUSIONS: p38 MAPK inhibitors synergistically enhance efficacy of corticosteroids in macrophages from asthma patients. This effect is greater in corticosteroid insensitive asthma patients, suggesting that this class of drug should be targeted to this patient phenotype.

Investigation of the robustness of two models for assessing synergy in pre-clinical drug combination studies.

Pre-clinical studies may be used to screen for synergistic combinations of drugs. The types of in vitro assays used for this purpose will depend upon the disease area of interest. In oncology, one frequently used study measures cell line viability: cells placed into wells on a plate are treated with doses of two compounds, and cell viability is assessed from an optical density measurement corrected for blank well values. These measurements are often transformed and analysed as cell survival relative to untreated wells. The monotherapies are assumed to follow the Hill equation with lower and upper asymptotes at 0 and 1, respectively. Additionally, a common variance about the dose-response curve may be assumed. In this paper, we consider two models for incorporating synergy parameters. We investigate the effect of different models of biological variation on the assessment of synergy from both of these models. We show that estimates of the synergy parameters appear to be robust, even when estimates of the other model parameters are biased. Using untransformed measurements provides better coverage of the 95% confidence intervals for the synergy parameters than using transformed measurements, and the requirement to fit the upper asymptote does not cause difficulties. Assuming homoscedastic variances appears to be robust. The added complexity of determining and fitting an appropriate heteroscedastic model does not seem to be justified.