Estimating the grid of time-points for the piecewise exponential model

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Ignoring the presence of dependent censoring in data analysis can lead to biased estimates, for example, not considering the effect of abandonment of the tuberculosis treatment may influence inferences about the cure probability. In order to assess the relationship between cure and abandonment outcomes, we propose a copula Bayesian approach. Therefore, the main objective of this work is to introduce a Bayesian survival regression model, capable of taking into account the dependent censoring in the adjustment. So, this proposed approach is based on Clayton's copula, to provide the relation between survival and dependent censoring times. In addition, the Weibull and the piecewise exponential marginal distributions are considered in order to fit the times. A simulation study is carried out to perform comparisons between different scenarios of dependence, different specifications of prior distributions, and comparisons with the maximum likelihood inference. Finally, we apply the proposed approach to a tuberculosis treatment adherence dataset of an HIV cohort from Alvorada-RS, Brazil. Results show that cure and abandonment outcomes are negatively correlated, that is, as long as the chance of abandoning the treatment increases, the chance of tuberculosis cure decreases.

Which severe COVID-19 patients could benefit from high dose dexamethasone? A Bayesian post-hoc reanalysis of the COVIDICUS randomized clinical trial

BACKGROUND

The respective benefits of high and low doses of dexamethasone (DXM) in patients with severe acute respiratory syndrome coronavirus 2 (SARS-Cov2) and acute respiratory failure (ARF) are controversial, with two large triple-blind RCTs reaching very important difference in the effect-size. In the COVIDICUS trial, no evidence of additional benefit of high-dose dexamethasone (DXM20) was found. We aimed to explore whether some specific patient phenotypes could benefit from DXM20 compared to the standard of care 6 mg dose of DXM (DXMSoC).

METHODS

We performed a post hoc exploratory Bayesian analysis of 473 patients who received either DXMSoc or DXM20 in the COVIDICUS trial. The outcome was the 60 day mortality rate of DXM20 over DXMSoC, with treatment effect measured on the hazard ratio (HR) estimated from Cox model. Bayesian analyses allowed to compute the posterior probability of a more than trivial benefit (HR < 0.95), and that of a potential harm (HR > 1.05). Bayesian measures of interaction then quantified the probability of interaction (Pr Interact) that the HR of death differed across the subsets by 20%. Primary analyses used noninformative priors, centred on HR = 1.00. Sensitivity analyses used sceptical and enthusiastic priors, based on null (HR = 1.00) or benefit (HR = 0.95) effects.

RESULTS

Overall, the posterior probability of a more than trivial benefit and potential harm was 29.0 and 51.1%, respectively. There was some evidence of treatment by subset interaction (i) according to age (Pr Interact, 84%), with a 86.5% probability of benefit in patients aged below 70 compared to 22% in those aged above 70; (ii) according to the time since symptoms onset (Pr Interact, 99%), with a 99.9% probability of a more than trivial benefit when lower than 7 days compared to a < 0.1% probability when delayed by 7 days or more; and (iii) according to use of remdesivir (Pr Interact, 91%), with a 90.1% probability of benefit in patients receiving remdesivir compared to 19.1% in those who did not.

CONCLUSIONS

In this exploratory post hoc Bayesian analysis, compared with standard-of-care DXM, high-dose DXM may benefit patients aged less than 70 years with severe ARF that occurred less than 7 days after symptoms onset. The use of remdesivir may also favour the benefit of DXM20. Further analysis is needed to confirm these findings.

TRIAL REGISTRATION

NCT04344730, date of registration April 14, 2020 ( https://clinicaltrials.gov/ct2/show/NCT04344730?term=NCT04344730&draw=2&rank=1 ); EudraCT: 2020-001457-43 ( https://www.clinicaltrialsregister.eu/ctr-search/search?query=2020-001457-43 ).

On a new piecewise regression model with cure rate: Diagnostics and application to medical data

In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.

Optimality of testing procedures for survival data in the nonproportional hazards setting

Most statistical tests for treatment effects used in randomized clinical trials with survival outcomes are based on the proportional hazards assumption, which often fails in practice. Data from early exploratory studies may provide evidence of nonproportional hazards, which can guide the choice of alternative tests in the design of practice-changing confirmatory trials. We developed a test to detect treatment effects in a late-stage trial, which accounts for the deviations from proportional hazards suggested by early-stage data. Conditional on early-stage data, among all tests that control the frequentist Type I error rate at a fixed α level, our testing procedure maximizes the Bayesian predictive probability that the study will demonstrate the efficacy of the experimental treatment. Hence, the proposed test provides a useful benchmark for other tests commonly used in the presence of nonproportional hazards, for example, weighted log-rank tests. We illustrate this approach in simulations based on data from a published cancer immunotherapy phase III trial.

Penalized estimation of complex, non-linear exposure-lag-response associations

We propose a novel approach for the flexible modeling of complex exposure-lag-response associations in time-to-event data, where multiple past exposures within a defined time window are cumulatively associated with the hazard. Our method allows for the estimation of a wide variety of effects, including potentially smooth and smoothly time-varying effects as well as cumulative effects with leads and lags, taking advantage of the inference methods that have recently been developed for generalized additive mixed models. We apply our method to data from a large observational study of intensive care patients in order to analyze the association of both the timing and the amount of artificial nutrition with the short term survival of critically ill patients. We evaluate the properties of the proposed method by performing extensive simulation studies and provide a systematic comparison with related approaches.

A generalized additive model approach to time-to-event analysis

Abstract:

This tutorial article demonstrates how time-to-event data can be modelled in a very flexible way by taking advantage of advanced inference methods that have recently been developed for generalized additive mixed models. In particular, we describe the necessary pre-processing steps for transforming such data into a suitable format and show how a variety of effects, including a smooth nonlinear baseline hazard, and potentially nonlinear and nonlinearly time-varying effects, can be estimated and interpreted. We also present useful graphical tools for model evaluation and interpretation of the estimated effects. Throughout, we demonstrate this approach using various application examples. The article is accompanied by a new R -package called pammtools implementing all of the tools described here.

Robust treatment comparison based on utilities of semi-competing risks in non-small-cell lung cancer

A design is presented for a randomized clinical trial comparing two second-line treatments, chemotherapy versus chemotherapy plus reirradiation, for treatment of recurrent non-small-cell lung cancer. The central research question is whether the potential efficacy benefit that adding reirradiation to chemotherapy may provide justifies its potential for increasing the risk of toxicity. The design uses two co-primary outcomes: time to disease progression or death, and time to severe toxicity. Because patients may be given an active third-line treatment at disease progression that confounds second-line treatment effects on toxicity and survival following disease progression, for the purpose of this comparative study follow-up ends at disease progression or death. In contrast, follow-up for disease progression or death continues after severe toxicity, so these are semi-competing risks. A conditionally conjugate Bayesian model that is robust to misspecification is formulated using piecewise exponential distributions. A numerical utility function is elicited from the physicians that characterizes desirabilities of the possible co-primary outcome realizations. A comparative test based on posterior mean utilities is proposed. A simulation study is presented to evaluate test performance for a variety of treatment differences, and a sensitivity assessment to the elicited utility function is performed. General guidelines are given for constructing a design in similar settings, and a computer program for simulation and trial conduct is provided.

Influenza vaccine efficacy trials: a simulation approach to understand failures from the past

The success of a seasonal influenza vaccine efficacy trial depends not only upon the design but also upon the annual epidemic characteristics. In this context, simulation methods are an essential tool in evaluating the performances of study designs under various circumstances. However, traditional methods for simulating time-to-event data are not suitable for the simulation of influenza vaccine efficacy trials because of the seasonality and heterogeneity of influenza epidemics. Instead, we propose a mathematical model parameterized with historical surveillance data, heterogeneous frailty among the subjects, survey-based heterogeneous number of daily contact, and a mixed vaccine protection mechanism. We illustrate our methodology by generating multiple-trial data similar to a large phase III trial that failed to show additional relative vaccine efficacy of an experimental adjuvanted vaccine compared with the reference vaccine. We show that small departures from the designing assumptions, such as a smaller range of strain protection for the experimental vaccine or the chosen endpoint, could lead to smaller probabilities of success in showing significant relative vaccine efficacy.

Improved survival modeling in cancer research using a reduced piecewise exponential approach

Statistical models for survival data are typically nonparametric, for example, the Kaplan-Meier curve. Parametric survival modeling, such as exponential modeling, however, can reveal additional insights and be more efficient than nonparametric alternatives. A major constraint of the existing exponential models is the lack of flexibility due to distribution assumptions. A flexible and parsimonious piecewise exponential model is presented to best use the exponential models for arbitrary survival data. This model identifies shifts in the failure rate over time based on an exact likelihood ratio test, a backward elimination procedure, and an optional presumed order restriction on the hazard rate. Such modeling provides a descriptive tool in understanding the patient survival in addition to the Kaplan-Meier curve. This approach is compared with alternative survival models in simulation examples and illustrated in clinical studies.