Inverse probability of treatment weighting with generalized linear outcome models for doubly robust estimation.

There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the g $$ g $$ -formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains 'unbalanced' even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator.

Single-arm studies involving patient-reported outcome data in oncology: a literature review on current practice.

Patient-reported outcomes (PROs) are increasingly used in single-arm cancer studies. We reviewed 60 papers published between 2018 and 2021 of single-arm studies of cancer treatment with PRO data for current practice on design, analysis, reporting, and interpretation. We further examined the studies' handling of potential bias and how they informed decision making. Most studies (58; 97%) analysed PROs without stating a predefined research hypothesis. 13 (22%) of the 60 studies used a PRO as a primary or co-primary endpoint. Definitions of PRO objectives, study population, endpoints, and missing data strategies varied widely. 23 studies (38%) compared the PRO data with external information, most often by using a clinically important difference value; one study used a historical control group. Appropriateness of methods to handle missing data and intercurrent events (including death) were seldom discussed. Most studies (51; 85%) concluded that PRO results supported treatment. Conducting and reporting of PROs in cancer single-arm studies need standards and a critical discussion of statistical methods and possible biases. These findings will guide the Setting International Standards in Analysing Patient-Reported Outcomes and Quality of Life Data in Cancer Clinical Trials-Innovative Medicines Initiative (SISAQOL-IMI) in developing recommendations for the use of PRO-measures in single-arm studies.

Causal inference in survival analysis under deterministic missingness of confounders in register data.

Long-term register data offer unique opportunities to explore causal effects of treatments on time-to-event outcomes, in well-characterized populations with minimum loss of follow-up. However, the structure of the data may pose methodological challenges. Motivated by the Swedish Renal Registry and estimation of survival differences for renal replacement therapies, we focus on the particular case when an important confounder is not recorded in the early period of the register, so that the entry date to the register deterministically predicts confounder missingness. In addition, an evolving composition of the treatment arms populations, and suspected improved survival outcomes in later periods lead to informative administrative censoring, unless the entry date is appropriately accounted for. We investigate different consequences of these issues on causal effect estimation following multiple imputation of the missing covariate data. We analyse the performance of different combinations of imputation models and estimation methods for the population average survival. We further evaluate the sensitivity of our results to the nature of censoring and misspecification of fitted models. We find that an imputation model including the cumulative baseline hazard, event indicator, covariates and interactions between the cumulative baseline hazard and covariates, followed by regression standardization, leads to the best estimation results overall, in simulations. Standardization has two advantages over inverse probability of treatment weighting here: it can directly account for the informative censoring by including the entry date as a covariate in the outcome model, and allows for straightforward variance computation using readily available software.

Trial emulation and survival analysis for disease incidence registers: A case study on the causal effect of pre-emptive kidney transplantation.

When drawing causal inference from observed data, failure time outcomes present additional challenges of censoring often combined with other missing data patterns. In this article, we follow incident cases of end-stage renal disease to examine the effect on all-cause mortality of starting treatment with transplant, so-called pre-emptive kidney transplantation, vs starting with dialysis possibly followed by delayed transplantation. The question is relatively simple: which start-off treatment is expected to bring the best survival for a target population? To address it, we emulate a target trial drawing on the long term Swedish Renal Registry, where a growing common set of baseline covariates was measured nationwide. Several lessons are learned which pertain to long term disease registers more generally. With characteristics of cases and versions of treatment evolving over time, informative censoring is already introduced in unadjusted Kaplan-Meier curves. This leads to misrepresented survival chances in observed treatment groups. The resulting biased treatment association may be aggravated upon implementing IPW for treatment. Aware of additional challenges, we further recall how similar studies to date have selected patients into treatment groups based on events occurring post treatment initiation. Our study reveals the dramatic impact of resulting immortal time bias combined with other typical features of long-term incident disease registers, including missing covariates during the early phases of the register. We discuss feasible ways of accommodating these features when targeting relevant estimands, and demonstrate how more than one causal question can be answered relying on the no unmeasured baseline confounders assumption.

Evaluating the prognostic performance of a polygenic risk score for breast cancer risk stratification.

BACKGROUND: Polygenic risk scores (PRS) could potentially improve breast cancer screening recommendations. Before a PRS can be considered for implementation, it needs rigorous evaluation, using performance measures that can inform about its future clinical value. OBJECTIVES: To evaluate the prognostic performance of a regression model with a previously developed, prevalence-based PRS and age as predictors for breast cancer incidence in women from the Estonian biobank (EstBB) cohort; to compare it to the performance of a model including age only. METHODS: We analyzed data on 30,312 women from the EstBB cohort. They entered the cohort between 2002 and 2011, were between 20 and 89 years, without a history of breast cancer, and with full 5-year follow-up by 2015. We examined PRS and other potential risk factors as possible predictors in Cox regression models for breast cancer incidence. With 10-fold cross-validation we estimated 3- and 5-year breast cancer incidence predicted by age alone and by PRS plus age, fitting models on 90% of the data. Calibration, discrimination, and reclassification were calculated on the left-out folds to express prognostic performance. RESULTS: A total of 101 (3.33‰) and 185 (6.1‰) incident breast cancers were observed within 3 and 5 years, respectively. For women in a defined screening age of 50-62 years, the ratio of observed vs PRS-age modelled 3-year incidence was 0.86 for women in the 75-85% PRS-group, 1.34 for the 85-95% PRS-group, and 1.41 for the top 5% PRS-group. For 5-year incidence, this was respectively 0.94, 1.15, and 1.08. Yet the number of breast cancer events was relatively low in each PRS-subgroup. For all women, the model's AUC was 0.720 (95% CI: 0.675-0.765) for 3-year and 0.704 (95% CI: 0.670-0.737) for 5-year follow-up, respectively, just 0.022 and 0.023 higher than for the model with age alone. Using a 1% risk prediction threshold, the 3-year NRI for the PRS-age model was 0.09, and 0.05 for 5 years. CONCLUSION: The model including PRS had modest incremental performance over one based on age only. A larger, independent study is needed to assess whether and how the PRS can meaningfully contribute to age, for developing more efficient screening strategies.

Checkpoint inhibition in combination with an immunoboost of external beam radiotherapy in solid tumors (CHEERS): study protocol for a phase 2, open-label, randomized controlled trial.

BACKGROUND: While the introduction of checkpoint inhibitors (CPIs) as standard of care treatment for various tumor types has led to considerable improvements in clinical outcome, the majority of patients still fail to respond. Preclinical data suggest that stereotactic body radiotherapy (SBRT) could work synergistically with CPIs by acting as an in situ cancer vaccine, thus potentially increasing response rates and prolonging disease control. Though SBRT administered concurrently with CPIs has been shown to be safe, evidence of its efficacy from large randomized trials is still lacking. The aim of this multicenter randomized phase II trial is to assess whether SBRT administered concurrently with CPIs could prolong progression-free survival as compared to standard of care in patients with advanced solid tumors. METHODS/DESIGN: Ninety-eight patients with locally advanced or metastatic disease will be randomized in a 1:1 fashion to receive CPI treatment combined with SBRT (Arm A) or CPI monotherapy (Arm B). Randomization will be stratified according to tumor histology (melanoma, renal, urothelial, head and neck squamous cell or non-small cell lung carcinoma) and disease burden (≤ or > 3 cancer lesions). The recommended SBRT dose is 24Gy in 3 fractions, which will be administered to a maximum of 3 lesions and is to be completed prior to the second or third CPI cycle (depending on CPI treatment schedule). The study's primary endpoint is progression-free survival as per iRECIST. Secondary endpoints include overall survival, objective response, local control, quality of life and toxicity. Translational analyses will be performed using blood, fecal and tissue samples. DISCUSSION: The CHEERS trial will provide further insights into the clinical and immunological impact of SBRT when combined with CPIs in patients with advanced solid tumors. Furthermore, study results will inform the design of future immuno-radiotherapy trials. TRIAL REGISTRATION: Clinicaltrials.gov identifier: NCT03511391 . Registered 17 April 2018.

Formulating causal questions and principled statistical answers.

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline ("point exposure") and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a "simulation learner," that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org, where SAS and Stata code for analysis is also provided.

The genetic structure of the Belgian population.

BACKGROUND: National and international efforts like the 1000 Genomes Project are leading to increasing insights in the genetic structure of populations worldwide. Variation between different populations necessitates access to population-based genetic reference datasets. These data, which are important not only in clinical settings but also to potentiate future transitions towards a more personalized public health approach, are currently not available for the Belgian population. RESULTS: To obtain a representative genetic dataset of the Belgian population, participants in the 2013 National Health Interview Survey (NHIS) were invited to donate saliva samples for DNA analysis. DNA was isolated and single nucleotide polymorphisms (SNPs) were determined using a genome-wide SNP array of around 300,000 sites, resulting in a high-quality dataset of 189 samples that was used for further analysis. A principal component analysis demonstrated the typical European genetic constitution of the Belgian population, as compared to other continents. Within Europe, the Belgian population could be clearly distinguished from other European populations. Furthermore, obvious signs from recent migration were found, mainly from Southern Europe and Africa, corresponding with migration trends from the past decades. Within Belgium, a small north-west to south-east gradient in genetic variability was noted, with differences between Flanders and Wallonia. CONCLUSIONS: This is the first study on the genetic structure of the Belgian population and its regional variation. The Belgian genetic structure mirrors its geographic location in Europe with regional differences and clear signs of recent migration.

Cure of cancer for seven cancer sites in the Flemish Region.

Cumulative relative survival curves for many cancers reach a plateau several years after diagnosis, indicating that the cancer survivor group has reached "statistical" cure. Parametric mixture cure model analysis on grouped relative survival curves provide an interesting way to determine the proportion of statistically cured cases and the mean survival time of the fatal cases in particular for population-based cancer registries. Based on the relative survival data from the Belgian Cancer Registry, parametric cure models were applied to seven cancer sites (cervix, colon, corpus uteri, skin melanoma, pancreas, stomach and oesophagus), at the Flemish Regional level for the incidence period 1999-2011. Statistical cure was observed for the examined cancer sites except for oesophageal cancer. The estimated cured proportion ranged from 5.9% [5.7, 6.1] for pancreatic cancer to 80.8% [80.5, 81.2] for skin melanoma. Cure results were further stratified by gender or age group. Stratified cured proportions were higher for females compared to males in colon cancer, stomach cancer, pancreas cancer and skin melanoma, which can mainly be attributed to differences in stage and age distribution between both sexes. This study demonstrates the applicability of cure rate models for the selected cancer sites after 14 years of follow-up and presents the first population-based results on the cure of cancer in Belgium.

Model-Based Classification for Digital PCR: Your Umbrella for Rain.

Standard data analysis pipelines for digital PCR estimate the concentration of a target nucleic acid by digitizing the end-point fluorescence of the parallel micro-PCR reactions, using an automated hard threshold. While it is known that misclassification has a major impact on the concentration estimate and substantially reduces accuracy, the uncertainty of this classification is typically ignored. We introduce a model-based clustering method to estimate the probability that the target is present (absent) in a partition conditional on its observed fluorescence and the distributional shape in no-template control samples. This methodology acknowledges the inherent uncertainty of the classification and provides a natural measure of precision, both at individual partition level and at the level of the global concentration. We illustrate our method on genetically modified organism, inhibition, dynamic range, and mutation detection experiments. We show that our method provides concentration estimates of similar accuracy or better than the current standard, along with a more realistic measure of precision. The individual partition probabilities and diagnostic density plots further allow for some quality control. An R implementation of our method, called Umbrella, is available, providing a more objective and automated data analysis procedure for absolute dPCR quantification.

A phase I/II trial of fixed-dose stereotactic body radiotherapy with sequential or concurrent pembrolizumab in metastatic urothelial carcinoma: evaluation of safety and clinical and immunologic response.

BACKGROUND: Current first-line standard of therapy for metastatic urothelial carcinoma is platinum-based combination chemotherapy. Pembrolizumab in phase III has demonstrated a promising overall response rate of 21.1% in patients with progression or recurrence after platinum-based chemotherapy. Preclinical and clinical evidence suggests that radiotherapy has a systemic anti-cancer immune effect and can increase the level of PD-L1 and tumor infiltrating lymphocytes in the tumor microenvironment. These findings gave rise to the hypothesis that the combination of radiotherapy with anti-PD1 treatment could lead to a synergistic effect, hereby enhancing response rates. METHODS: The phase I part will assess the dose limiting toxicity of the combination treatment of stereotactic body radiotherapy (SBRT) with four cycles of pembrolizumab (200 mg intravenously, every 3 weeks) in patients with metastatic urothelial carcinoma. The dose of both pembrolizumab and SBRT will be fixed, yet the patients will be randomized to receive SBRT either before the first cycle of pembrolizumab or before the third cycle of pembrolizumab. SBRT will be delivered (24 Gy in 3 fractions every other day) to the largest metastatic lesion. Secondary objectives include response rate according to RECIST v1.1 and immune related response criteria, progression-free survival and overall survival. The systemic immune effect triggered by the combination therapy will be monitored on various time points during the trial. The PD-L1/TIL status of the tumors will be analyzed via immunohistochemistry and response rates in the subgroups will be analyzed separately. A Simon's two-stage optimum design is used to select the treatment arm associated with the best response rate and with acceptable toxicity to proceed to the phase II trial. In this phase, 13 additional patients will be accrued to receive study treatment. DISCUSSION: The progress made in the field of immunotherapy has lead to promising breakthroughs in various solid malignancies. Unfortunately, the majority of patients do not respond. The current trial will shed light on the toxicity and potential anti-tumor activity of the combination of radiotherapy with anti-PD1 treatment and may identify potential new markers for response and resistance to therapy. Trial registration this trial is registered on clinicaltrials.gov (NCT02826564).

Effect of Neoadjuvant Radiation Dose and Schedule on Nodal Count and Its Prognostic Impact in Stage II-III Rectal Cancer.

BACKGROUND: It is unknown how neoadjuvant treatment schedule affects lymph node count (LNC) and lymph node ratio (LNR) and how these correlate with overall survival (OS) in rectal cancer (RC). METHODS: Data were used from the Belgian PROCARE rectal cancer registry on RC patients treated with surgery alone, short-term radiotherapy with immediate surgery (SRT), or chemoradiation with deferred surgery (CRT). The effect of neoadjuvant therapy on LNC was examined using Poisson log-linear analysis. The association of LNC and LNR with overall survival (OS) was studied using Cox proportional hazards models. RESULTS: Data from 4037 patients were available. Compared with surgery alone, LNC was reduced by 12.3 % after SRT and by 31.3 % after CRT (p < 0.001). In patients with surgery alone, the probability of finding node-positive disease increased with LNC, while after SRT and CRT no increase was noted for more than 12 and 18 examined nodes, respectively. Per node examined, we found a decrease in hazard of death of 2.7 % after surgery alone and 1.5 % after SRT, but no effect after CRT. In stage III patients, the LNR but not (y)pN stage was significantly correlated with OS regardless of neoadjuvant therapy. Specifically, a LNR > 0.4 was associated with a significantly worse outcome. CONCLUSIONS: Nodal counts are reduced in a schedule-dependent manner by neoadjuvant treatment in RC. After chemoradiation, the LNC does not confer any prognostic information. A LNR of >0.4 is associated with a significantly worse outcome in stage III disease, regardless of neoadjuvant therapy type.

On the practice of ignoring center-patient interactions in evaluating hospital performance.

We evaluate the performance of medical centers based on a continuous or binary patient outcome (e.g., 30-day mortality). Common practice adjusts for differences in patient mix through outcome regression models, which include patient-specific baseline covariates (e.g., age and disease stage) besides center effects. Because a large number of centers may need to be evaluated, the typical model postulates that the effect of a center on outcome is constant over patient characteristics. This may be violated, for example, when some centers are specialized in children or geriatric patients. Including interactions between certain patient characteristics and the many fixed center effects in the model increases the risk for overfitting, however, and could imply a loss of power for detecting centers with deviating mortality. Therefore, we assess how the common practice of ignoring such interactions impacts the bias and precision of directly and indirectly standardized risks. The reassuring conclusion is that the common practice of working with the main effects of a center has minor impact on hospital evaluation, unless some centers actually perform substantially better on a specific group of patients and there is strong confounding through the corresponding patient characteristic. The bias is then driven by an interplay of the relative center size, the overlap between covariate distributions, and the magnitude of the interaction effect. Interestingly, the bias on indirectly standardized risks is smaller than on directly standardized risks. We illustrate our findings by simulation and in an analysis of 30-day mortality on Riksstroke.

On shrinkage and model extrapolation in the evaluation of clinical center performance.

We consider statistical methods for benchmarking clinical centers based on a dichotomous outcome indicator. Borrowing ideas from the causal inference literature, we aim to reveal how the entire study population would have fared under the current care level of each center. To this end, we evaluate direct standardization based on fixed versus random center effects outcome models that incorporate patient-specific baseline covariates to adjust for differential case-mix. We explore fixed effects (FE) regression with Firth correction and normal mixed effects (ME) regression to maintain convergence in the presence of very small centers. Moreover, we study doubly robust FE regression to avoid outcome model extrapolation. Simulation studies show that shrinkage following standard ME modeling can result in substantial power loss relative to the considered alternatives, especially for small centers. Results are consistent with findings in the analysis of 30-day mortality risk following acute stroke across 90 centers in the Swedish Stroke Register.

Evaluating hospital performance based on excess cause-specific incidence.

Formal evaluation of hospital performance in specific types of care is becoming an indispensable tool for quality assurance in the health care system. When the prime concern lies in reducing the risk of a cause-specific event, we propose to evaluate performance in terms of an average excess cumulative incidence, referring to the center's observed patient mix. Its intuitive interpretation helps give meaning to the evaluation results and facilitates the determination of important benchmarks for hospital performance. We apply it to the evaluation of cerebrovascular deaths after stroke in Swedish stroke centers, using data from Riksstroke, the Swedish stroke registry.

Impact of variance components on reliability of absolute quantification using digital PCR.

BACKGROUND: Digital polymerase chain reaction (dPCR) is an increasingly popular technology for detecting and quantifying target nucleic acids. Its advertised strength is high precision absolute quantification without needing reference curves. The standard data analytic approach follows a seemingly straightforward theoretical framework but ignores sources of variation in the data generating process. These stem from both technical and biological factors, where we distinguish features that are 1) hard-wired in the equipment, 2) user-dependent and 3) provided by manufacturers but may be adapted by the user. The impact of the corresponding variance components on the accuracy and precision of target concentration estimators presented in the literature is studied through simulation. RESULTS: We reveal how system-specific technical factors influence accuracy as well as precision of concentration estimates. We find that a well-chosen sample dilution level and modifiable settings such as the fluorescence cut-off for target copy detection have a substantial impact on reliability and can be adapted to the sample analysed in ways that matter. User-dependent technical variation, including pipette inaccuracy and specific sources of sample heterogeneity, leads to a steep increase in uncertainty of estimated concentrations. Users can discover this through replicate experiments and derived variance estimation. Finally, the detection performance can be improved by optimizing the fluorescence intensity cut point as suboptimal thresholds reduce the accuracy of concentration estimates considerably. CONCLUSIONS: Like any other technology, dPCR is subject to variation induced by natural perturbations, systematic settings as well as user-dependent protocols. Corresponding uncertainty may be controlled with an adapted experimental design. Our findings point to modifiable key sources of uncertainty that form an important starting point for the development of guidelines on dPCR design and data analysis with correct precision bounds. Besides clever choices of sample dilution levels, experiment-specific tuning of machine settings can greatly improve results. Well-chosen data-driven fluorescence intensity thresholds in particular result in major improvements in target presence detection. We call on manufacturers to provide sufficiently detailed output data that allows users to maximize the potential of the method in their setting and obtain high precision and accuracy for their experiments.

Simultaneous alleviation of verification and reference standard biases in a community-based tuberculosis screening study using Bayesian latent class analysis.

BACKGROUND: Estimation of prevalence and diagnostic test accuracy in tuberculosis (TB) prevalence surveys suffer from reference standard and verification biases. The former is attributed to the imperfect reference test used to bacteriologically confirm TB disease. The latter occurs when only the participants screening positive for any TB-compatible symptom or chest X-ray abnormality are selected for bacteriological testing (verification). Bayesian latent class analysis (LCA) alleviates the reference standard bias but suffers verification bias in TB prevalence surveys. This work aims to identify best-practice approaches to simultaneously alleviate the reference standard and verification biases in the estimates of pulmonary TB prevalence and diagnostic test performance in TB prevalence surveys. METHODS: We performed a secondary analysis of 9869 participants aged ≥15 years from a community-based multimorbidity screening study in a rural district of KwaZulu-Natal, South Africa (Vukuzazi study). Participants were eligible for bacteriological testing using Xpert Ultra and culture if they reported any cardinal TB symptom or had an abnormal chest X-ray finding. We conducted Bayesian LCA in five ways to handle the unverified individuals: (i) complete-case analysis, (ii) analysis assuming the unverified individuals would be negative if bacteriologically tested, (iii) analysis of multiply-imputed datasets with imputation of the missing bacteriological test results for the unverified individuals using multivariate imputation via chained equations (MICE), and simultaneous imputation of the missing bacteriological test results in the analysis model assuming the missing bacteriological test results were (iv) missing at random (MAR), and (v) missing not at random (MNAR). We compared the results of (i)-(iii) to the analysis based on a composite reference standard (CRS) of Xpert Ultra and culture. Through simulation with an overall true prevalence of 2.0%, we evaluated the ability of the models to alleviate both biases simultaneously. RESULTS: Based on simulation, Bayesian LCA with simultaneous imputation of the missing bacteriological test results under the assumption that the missing data are MAR and MNAR alleviate the reference standard and verification biases. CRS-based analysis and Bayesian LCA assuming the unverified are negative for TB alleviate the biases only when the true overall prevalence is <3.0%. Complete-case analysis produced biased estimates. In the Vukuzazi study, Bayesian LCA with simultaneous imputation of the missing bacteriological test results under the MAR and MNAR assumptions produced overall PTB prevalence of 0.9% (95% Credible Interval (CrI): 0.6-1.9) and 0.7% (95% CrI: 0.5-1.1) respectively alongside realistic estimates of overall diagnostic test sensitivity and specificity with substantially overlapping 95% CrI. The CRS-based analysis and Bayesian LCA assuming the unverified were negative for TB produced 0.7% (95% CrI: 0.5-0.9) and 0.7% (95% CrI: 0.5-1.2) overall PTB prevalence respectively with realistic estimates of overall diagnostic test sensitivity and specificity. Unlike CRS-based analysis, Bayesian LCA of multiply-imputed data using MICE mitigates both biases. CONCLUSION: The findings demonstrate the efficacy of these advanced techniques in alleviating the reference standard and verification biases, enhancing the robustness of community-based screening programs. Imputing missing values as negative for bacteriological tests is plausible under realistic assumptions.