EventPredInCure-package {EventPredInCure}

Event Prediction Including Cured Population

Description

Predicts enrollment and events using assumed enrollment and/or treatment-specific time-to-event models in the existence of the cured population. Calculate test statistics based on the simulated data sets from the assumed enrollment and/or treatment-specific time-to-event models in the existence of the cured population.

Details

Accurately predicting the date at which a target number of subjects or events will be achieved is critical for the planning, monitoring, and execution of clinical trials in the existence of the cured population. The EventPredInCure package provides enrollment and event prediction capabilities using assumed enrollment and treatment-specific time-to-event models and calculate test statistics based on the simulated data sets from the assumed enrollment and/or treatment-specific time-to-event models in the existence of the cured population.

At the design stage, enrollment is often specified using a piecewise Poisson process with a constant enrollment rate during each specified time interval. At the analysis stage, before enrollment completion, the EventPredInCure package considers several models, including the homogeneous Poisson model, the time-decay model with an enrollment rate function lambda(t) = mu/delta*(1 - exp(-delta*t)), the B-spline model with the daily enrollment rate lambda(t) = exp(B(t)*theta), and the piecewise Poisson model. If prior information exists on the model parameters, it can be combined with the likelihood to yield the posterior distribution.

The EventPredInCure package offers several time-to-event models without cured-population,including exponential, Weibull, log-logistic, log-normal, piecewise exponential, model averaging of Weibull and log-normal, and spline. The models including exponential, Weibull, log-logistic, log-normal, piecewise exponential are extended to account cured-population. In the design stage, the models including exponential, Weibull, log-logistic, log-normal, piecewise exponential are also extended for delayed treatment effect setting (only for generating simulated data sets in the design stage). For time to dropout, the same set of model without cured-population and delayed treatment effect options are considered. If enrollment is complete, ongoing subjects who have not had the event of interest or dropped out of the study before the data cut contribute additional events in the future. Their event times are generated from the conditional distribution given that they have survived at the data cut. For new subjects that need to be enrolled, their enrollment time and event time can be generated from the specified enrollment and time-to-event models with parameters drawn from the posterior distribution. Time-to-dropout can be generated in a similar fashion.

The EventPredInCure package displays the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC) and a fitted curve overlaid with observed data to help users select the most appropriate model for enrollment and event prediction. Prediction intervals in the prediction plot can be used to measure prediction uncertainty, and the simulated enrollment and event data can be used for further data exploration.

The most useful function in the EventPredInCure package is getPrediction, which combines model fitting, data simulation, and a summary of simulation results. Other functions perform individual tasks and can be used to select an appropriate prediction model.

The EventPredInCure package implements a model parameterization that enhances the asymptotic normality of parameter estimates. Specifically, the package utilizes the following parameterization to achieve this goal:

• Enrollment models

  • Poisson: theta = log(rate)

  • Time-decay: theta = c(log(mu), log(delta))

  • B-spline: no reparametrization is needed. The knots as considered fixed.

  • Piecewise Poisson: theta = log(rates). The left endpoints of time intervals, denoted as accrualTime, are considered fixed.

• Event or dropout models

  • Exponential: theta = log(rate)

  • Weibull: theta = c(log(scale), -log(shape))

  • Log-logistic: theta = c(log(scale), -log(shape))

  • Log-normal: theta = c(meanlog, log(sdlog))

  • Piecewise exponential: theta = log(rates). The left endpoints of time intervals, denoted as piecewiseSurvivalTime for event model and piecewiseDropoutTime for dropout model, are considered fixed.

  • Model averaging: theta = c(log(weibull$scale), -log(weibull$shape), lnorm$meanlog, log(lnorm$sdlog)). The covariance matrix for theta is structured as a block diagonal matrix, with the upper-left block corresponding to the Weibull component and the lower-right block corresponding to the log-normal component. In other words, the covariance matrix is partitioned into two distinct blocks, with no off-diagonal elements connecting the two components. The weight assigned to the Weibull component, denoted as w1, is considered fixed.

  • Spline: theta corresponds to the coefficients of basis vectors. The knots and scale are considered fixed. The scale can be hazard, odds, or normal, corresponding to extensions of Weibull, log-logistic, and log-normal distributions, respectively.

The EventPredInCure package uses days as its primary time unit. If you need to convert enrollment or event rates per month to rates per day, simply divide by 30.4375.

References

• Chen, Tai-Tsang. "Predicting analysis times in randomized clinical trials with cancer immunotherapy." BMC medical research methodology 16.1 (2016): 1-10.

• Royston, Patrick, and Mahesh KB Parmar. "Flexible parametric proportional‐hazards and proportional‐odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects." Statistics in medicine 21.15 (2002): 2175-2197.

• Bagiella, Emilia, and Daniel F. Heitjan. "Predicting analysis times in randomized clinical trials." Statistics in medicine 20.14 (2001): 2055-2063.

• Ying, Gui‐shuang, and Daniel F. Heitjan. "Weibull prediction of event times in clinical trials." Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry 7.2 (2008): 107-120.

• Zhang, Xiaoxi, and Qi Long. "Stochastic modeling and prediction for accrual in clinical trials." Statistics in Medicine 29.6 (2010): 649-658.