Rare Event Setting Research Articles

Privacy-preserving analysis of time-to-event data under nested case-control sampling.

Analyses of distributed data networks of rare diseases are constrained by legitimate privacy and ethical concerns. Analytical centers (e.g. research institutions) are thus confronted with the challenging task of obtaining data from recruiting sites that are often unable or unwilling to share personal records of participants. For time-to-event data, recently popularized disclosure techniques with privacy guarantees (e.g., Differentially Private Generative Adversarial Networks) are generally computationally expensive or inaccessible to applied researchers. To perform the widely used Cox proportional hazards regression, we propose an easy-to-implement privacy-preserving data analysis technique by pooling (i.e. aggregating) individual records of covariates at recruiting sites under the nested case-control sampling framework before sharing the pooled nested case-control subcohort. We show that the pooled hazard ratio estimators, under the pooled nested case-control subsamples from the contributing sites, are maximum likelihood estimators and provide consistent estimates of the individual level full cohort HRs. Furthermore, a sampling technique for generating pseudo-event times for individual subjects that constitute the pooled nested case-control subsamples is proposed. Our method is demonstrated using extensive simulations and analysis of the National Lung Screening Trial data. The utility of our proposed approach is compared to the gold standard (full cohort) and synthetic data generated using classification and regression trees. The proposed pooling technique performs to near-optimal levels comparable to full cohort analysis or synthetic data; the efficiency improves in rare event settings when more controls are matched on during nested case-control subcohort sampling.

Bayesian estimation and testing in random-effects meta-analysis of rare binary events allowing for flexible group variability.

Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. Based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcers data from 41 studies.

Modeling surrender risk in life insurance: theoretical and experimental insight

Surrender poses one of the major risks to life insurance and a sound modeling of its true probability has direct implication on the risk capital demanded by the Solvency II directive. We add to the existing literature by performing extensive experiments that present highly practical results for various modeling approaches, including XGBoost, random forest, GLM and neural networks. Further, we detect shortcomings of prevalent model assessments, which are in essence based on a confusion matrix. Our results indicate that accurate label predictions and a sound modeling of the true probability can be opposing objectives. We illustrate this with the example of resampling. While resampling is capable of improving label prediction in rare event settings, such as surrender, and thus is commonly applied, we show theoretically and numerically that models trained on resampled data predict significantly biased event probabilities. Following a probabilistic perspective on surrender, we further propose time-dependent confidence bands on predicted mean surrender rates as a complementary assessment and demonstrate its benefit. This evaluation takes a very practical, going concern perspective, which respects that the composition of a portfolio, as well as the nature of underlying risk drivers might change over time.

Assessment of a Modified Sandwich Estimator for Generalized Estimating Equations with Application to Opioid Poisoning in MIMIC-IV ICU Patients

Longitudinal data is encountered frequently in many healthcare research areas to include the critical care environment. Repeated measures from the same subject are expected to correlate with each other. Models with binary outcomes are commonly used in this setting. Regression models for correlated binary outcomes are frequently fit using generalized estimating equations (GEE). The Liang and Zeger sandwich estimator is often used in GEE to produce unbiased standard error estimation for regression coefficients in large sample settings, even when the covariance structure is misspecified. The sandwich estimator performs optimally in balanced designs when the number of participants is large with few repeated measurements. The sandwich estimator’s asymptotic properties do not hold in small sample and rare-event settings. Under these conditions, the sandwich estimator underestimates the variances and is biased downwards. Here, the performance of a modified sandwich estimator is compared to the traditional Liang-Zeger estimator and alternative forms proposed by authors Morel, Pan, and Mancl-DeRouen. Each estimator’s performance was assessed with 95% coverage probabilities for the regression coefficients using simulated data under various combinations of sample sizes and outcome prevalence values with independence and autoregressive correlation structures. This research was motivated by investigations involving rare-event outcomes in intensive care unit settings.

Applications of simple and accessible methods for meta-analysis involving rare events: A simulation study.

Meta-analysis of clinical trials targeting rare events face particular challenges when the data lack adequate number of events and are susceptible to high levels of heterogeneity. The standard meta-analysis methods (DerSimonian Laird (DL) and Mantel–Haenszel (MH)) often lead to serious distortions because of such data sparsity. Applications of the methods suited to specific incidence and heterogeneity characteristics are lacking, thus we compared nine available methods in a simulation study. We generated 360 meta-analysis scenarios where each considered different incidences, sample sizes, between-study variance (heterogeneity) and treatment allocation. We include globally recommended methods such as inverse-variance fixed/random-effect (IV-FE/RE), classical-MH, MH-FE, MH-DL, Peto, Peto-DL and the two extensions for MH bootstrapped-DL (bDL) and Peto-bDL. Performance was assessed on mean bias, mean error, coverage and power. In the absence of heterogeneity, the coverage and power when combined revealed small differences in meta-analysis involving rare and very rare events. The Peto-bDL method performed best, but only in smaller sample sizes involving rare events. For medium-to-larger sample sizes, MH-bDL was preferred. For meta-analysis involving very rare events, Peto-bDL was the best performing method which was sustained across all sample sizes. However, in meta-analysis with 20% or more heterogeneity, the coverage and power were insufficient. Performance based on mean bias and mean error was almost identical across methods. To conclude, in meta-analysis of rare binary outcomes, our results suggest that Peto-bDL is better in both rare and very rare event settings in meta-analysis with limited sample sizes. However, when heterogeneity is large, the coverage and power to detect rare events are insufficient. Whilst this study shows that some of the less studied methods appear to have good properties under sparse data scenarios, further work is needed to assess them against the more complex distributional-based methods to understand their overall performances.

Antimicrobial Prophylaxis for Postoperative Urinary Tract Infections in Transurethral Resection of Bladder Tumors: A Systematic Review and Meta-Analysis.

The administration of antimicrobial prophylaxis for postoperative urinary tract infections following transurethral resection of bladder tumors is controversial. We aimed to systematically review evidence on the potential effect of antimicrobial prophylaxis on postoperative urinary tract infections and asymptomatic bacteriuria. We conducted a systematic search in Embase®, Medline® and the Cochrane Central Register of Controlled Trials. Randomized controlled trials and nonrandomized controlled trials assessing the effect of any form of antimicrobial prophylaxis in patients with transurethral resection of bladder tumors on postoperative urinary tract infections or asymptomatic bacteriuria were included. Risk of bias was assessed using RoB 2.0 or the Newcastle-Ottawa Scale. Fixed and random effects meta-analyses were conducted. As a potential basis for a scoping review, we exploratorily searched Medline for risk factors for urinary tract infections after transurethral resection of bladder tumors. The protocol was registered on PROSPERO (CRD42019131733). Of 986 screened publications, 7 studies with 1,725 participants were included; the reported effect sizes varied considerably. We found no significant effect of antimicrobial prophylaxis on urinary tract infections: the pooled odds ratio of the random effects model was 1.55 (95% CI 0.73-3.31). The random effects meta-analysis examining the effect of antimicrobial prophylaxis on asymptomatic bacteriuria showed an OR of 0.43 (0.18-1.04). Risk of bias was moderate. Our exploratory search identified 3 studies reporting age, preoperative pelvic radiation, preoperative hospital stay, duration of operation, tumor size, preoperative asymptomatic bacteriuria and pyuria as risk factors for urinary tract infections following transurethral resection of bladder tumors. We observed insufficient evidence supporting routine antimicrobial prophylaxis in patients undergoing transurethral resection of bladder tumors for the prevention of postoperative urinary tract infections; our findings may inform harmonization of international guidelines.

Meta-analysis of rare adverse events in randomized clinical trials: Bayesian and frequentist methods.

Regulatory approval of a drug or device involves an assessment of not only the benefits but also the risks of adverse events associated with the therapeutic agent. Although randomized controlled trials (RCTs) are the gold standard for evaluating effectiveness, the number of treated patients in a single RCT may not be enough to detect a rare but serious side effect of the treatment. Meta-analysis plays an important role in the evaluation of the safety of medical products and has advantage over analyzing a single RCT when estimating the rate of adverse events. In this article, we compare 15 widely used meta-analysis models under both Bayesian and frequentist frameworks when outcomes are extremely infrequent or rare. We present extensive simulation study results and then apply these methods to a real meta-analysis that considers RCTs investigating the effect of rosiglitazone on the risks of myocardial infarction and of death from cardiovascular causes. Our simulation studies suggest that the beta hyperprior method modeling treatment group-specific parameters and accounting for heterogeneity performs the best. Most models ignoring between-study heterogeneity give poor coverage probability when such heterogeneity exists. In the data analysis, different methods provide a wide range of log odds ratio estimates between rosiglitazone and control treatments with a mixed conclusion on their statistical significance based on 95% confidence (or credible) intervals. In the rare event setting, treatment effect estimates obtained from traditional meta-analytic methods may be biased and provide poor coverage probability. This trend worsens when the data have large between-study heterogeneity. In general, we recommend methods that first estimate the summaries of treatment-specific risks across studies and then relative treatment effects based on the summaries when appropriate. Furthermore, we recommend fitting various methods, comparing the results and model performance, and investigating any significant discrepancies among them.

Meta-analysis of rare events under the assumption of a homogeneous treatment effect.

We studied the performance of several meta-analysis methods in rare event settings, when the treatment effect is assumed to be homogeneous and baseline prevalences are either homogeneous or heterogeneous. We conducted extensive simulations that included the three most common effect sizes with count data: the odds ratio, the relative risk, and the risk difference. We investigated several important scenarios by varying the level of rareness, the value of the trials' arms unbalance, and the size of the treatment effect. We found that the Mantel-Haenszel method and the Binomial regression model provided the best results across all the scenarios investigated. The Peto method performed satisfactorily only when the true effect size was not too large and the degree of unbalance moderate. Inverse variance was the least reliable method. The use of a continuity correction factor slightly improved the performance of the inverse variance method but deteriorated that of the Peto and Mantel-Haenszel methods. A method based on median unbiased estimators of the probabilities provided similar results to those obtained when using the inverse variance method with a continuity correction. Therefore, when the treatment effect can be assumed to be homogeneous and for either homogeneous or heterogeneous baseline prevalences, we highly recommend using the Mantel-Haenszel method without continuity correction (for all the effect sizes) or the Binomial regression model (for the odds ratio only) to meta-analyze the data.

Efficient Simulation for Dependent Rare Events with Applications to Extremes

We consider the general problem of estimating probabilities which arise as a union of dependent events. We propose a flexible series of estimators for such probabilities, and describe variance reduction schemes applied to the proposed estimators. We derive efficiency results of the estimators in rare-event settings, in particular those associated with extremes. Finally, we examine the performance of our estimators in numerical examples.

Augmented estimation for t-year survival with censored regression models.

Reliable and accurate risk prediction is fundamental for successful management of clinical conditions. Estimating comprehensive risk prediction models precisely, however, is a difficult task, especially when the outcome of interest is time to a rare event and the number of candidate predictors, p, is not very small. Another challenge in developing accurate risk models arises from potential model misspecification. Time-specific generalized linear models estimated with inverse censoring probability weighting are robust to model misspecification, but may be inefficient in the rare event setting. To improve the efficiency of such robust estimation procedures, various augmentation methods have been proposed in the literature. These procedures can also leverage auxiliary variables such as intermediate outcomes that are predictive of event risk. However, most existing methods do not perform well in the rare event setting, especially when p is not small. In this article, we propose a two-step, imputation-based augmentation procedure that can improve estimation efficiency and that is robust to model misspecification. We also develop regularized augmentation procedures for settings where p is not small, along with procedures to improve the estimation of individualized treatment effect in risk reduction. Numerical studies suggest that our proposed methods substantially outperform existing methods in efficiency gains. The proposed methods are applied to an AIDS clinical trial for treating HIV-infected patients.

Splitting sequential Monte Carlo for efficient unreliability estimation of highly reliable networks

Assessing the reliability of complex technological systems such as communication networks, transportation grids, and bridge networks is a difficult task. From a mathematical point of view, the problem of estimating network reliability belongs to the #P complexity class. As a consequence, no analytical solution for solving this problem in a reasonable time is known to exist and one has to rely on approximation techniques. In this paper we focus on a well-known sequential Monte Carlo algorithm — Lomonosov’s turnip method. Despite the fact that this method was shown to be efficient under some mild conditions, it is known to be inadequate for a stable estimation of the network reliability in a rare-event setting. To overcome this obstacle, we suggest a quite general combination of sequential Monte Carlo and multilevel splitting. The proposed method is shown to bring a significant variance reduction as compared to the turnip algorithm, is easy to implement and parallelize, and has a proven performance guarantee for certain network topologies.

Exact Meta-Analysis Approach for Discrete Data and its Application to 2 × 2 Tables With Rare Events

This article proposes a general exact meta-analysis approach for synthesizing inferences from multiple studies of discrete data. The approach combines the p-value functions (also known as significance functions) associated with the exact tests from individual studies. It encompasses a broad class of exact meta-analysis methods, as it permits broad choices for the combining elements, such as tests used in individual studies, and any parameter of interest. The approach yields statements that explicitly account for the impact of individual studies on the overall inference, in terms of efficiency/power and the Type I error rate. Those statements also give rises to empirical methods for further enhancing the combined inference. Although the proposed approach is for general discrete settings, for convenience, it is illustrated throughout using the setting of meta-analysis of multiple 2 × 2 tables. In the context of rare events data, such as observing few, zero, or zero total (i.e., zero events in both arms) outcomes in binomial trials or 2 × 2 tables, most existing meta-analysis methods rely on the large-sample approximations which may yield invalid inference. The commonly used corrections to zero outcomes in rare events data, aiming to improve numerical performance can also incur undesirable consequences. The proposed approach applies readily to any rare event setting, including even the zero total event studies without any artificial correction. While debates continue on whether or how zero total event studies should be incorporated in meta-analysis, the proposed approach has the advantage of automatically including those studies and thus making use of all available data. Through numerical studies in rare events settings, the proposed exact approach is shown to be efficient and, generally, outperform commonly used meta-analysis methods, including Mantel-Haenszel and Peto methods.

Improving the Asmussen–Kroese-Type Simulation Estimators

The Asmussen–Kroese Monte Carlo estimators of P(S n > u) and P(S N > u) are known to work well in rare event settings, where S N is the sum of independent, identically distributed heavy-tailed random variables X 1,…,X N and N is a nonnegative, integer-valued random variable independent of the X i . In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the X i are nonnegative. We also apply our ideas to estimate the quantity E[(S N -u)+].

Improving the Asmussen–Kroese-Type Simulation Estimators

The Asmussen–Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,…,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta‐analysis with zero cells

For clinical trials with binary endpoints there are a variety of effect measures, for example risk difference, risk ratio and odds ratio (OR). The choice of metric is not always straightforward and should reflect the clinical question. Additional issues arise if the event of interest is rare. In systematic reviews, trials with zero events in both arms are encountered and often excluded from the meta-analysis.The arcsine difference (AS) is a measure which is rarely considered in the medical literature. It appears to have considerable promise, because it handles zeros naturally, and its asymptotic variance does not depend on the event probability.This paper investigates the pros and cons of using the AS as a measure of intervention effect. We give a pictorial representation of its meaning and explore its properties in relation to other measures. Based on analytical calculation of the variance of the arcsine transformation, a more conservative variance estimate for the rare event setting is proposed. Motivated by a published meta-analysis in cardiac surgery, we examine the statistical properties of the various metrics in the rare event setting.We find the variance estimate of the AS to be more stable than that of the log-OR, even if events are rare. However, parameter estimation is biased if the groups are markedly unbalanced. Though, from a theoretical viewpoint, the AS is a natural choice, its practical use is likely to continue to be limited by its less direct interpretation.