Pharmaceutical Statistics最新文献

What can be considered an appropriate statistical method for the primary analysis of a randomized clinical trial (RCT) with a time-to-event endpoint when we anticipate non-proportional hazards owing to a delayed effect? This question has been the subject of much recent debate. The standard approach is a log-rank test and/or a Cox proportional hazards model. Alternative methods have been explored in the statistical literature, such as weighted log-rank tests and tests based on the Restricted Mean Survival Time (RMST). While weighted log-rank tests can achieve high power compared to the standard log-rank test, some choices of weights may lead to type-I error inflation under particular conditions. In addition, they are not linked to a mathematically unambiguous summary measure. Test statistics based on the RMST, on the other hand, allow one to investigate the average difference between two survival curves up to a pre-specified time point $\tau$ -a mathematically unambiguous summary measure. However, by emphasizing differences prior to $\tau$ , such test statistics may not fully capture the benefit of a new treatment in terms of long-term survival. In this article, we introduce a graphical approach for direct comparison of weighted log-rank tests and tests based on the RMST. This new perspective allows a more informed choice of the analysis method, going beyond power and type I error comparison.

With the advent of cancer immunotherapy, some special features including delayed treatment effect, cure rate, diminishing treatment effect and crossing survival are often observed in survival analysis. They violate the proportional hazard model assumption and pose a unique challenge for the conventional trial design and analysis strategies. Many methods like cure rate model have been developed based on mixture model to incorporate some of these features. In this work, we extend the mixture model to deal with multiple non-proportional patterns and develop its geometric average hazard ratio (gAHR) to quantify the treatment effect. We further derive a sample size and power formula based on the non-centrality parameter of the log-rank test and conduct a thorough analysis of the impact of each parameter on performance. Simulation studies showed a clear advantage of our new method over the proportional hazard based calculation across different non-proportional hazard scenarios. Moreover, the mixture modeling of two real trials demonstrates how to use the prior information on the survival distribution among patients with different biomarker and early efficacy results in practice. By comparison with a simulation-based design, the new method provided a more efficient way to compute the power and sample size with high accuracy of estimation. Overall, both theoretical derivation and empirical studies demonstrate the promise of the proposed method in powering future innovative trial designs.

The pharmaceutical industry is plagued with long, costly development and high risk. Therefore, a company's effective management and optimisation of a portfolio of projects is critical for success. Project metrics such as the probability of success enable modelling of a company's pipeline accounting for the high uncertainty inherent within the industry. Making portfolio decisions inherently involves managing risk, and statisticians are ideally positioned to champion not only the derivation of metrics for individual projects, but also advocate decision-making at a broader portfolio level. This article aims to examine the existing different portfolio decision-making approaches and to suggest opportunities for statisticians to add value in terms of introducing probabilistic thinking, quantitative decision-making, and increasingly advanced methodologies.

Since the publication of ICH E9 (R1), "Addendum to statistical principles for clinical trials: on choosing appropriate estimands and defining sensitivity analyses in clinical trials," there has been a lot of debate about the hypothetical strategy for handling intercurrent events. Arguments against the hypothetical strategy are twofold: (1) the clinical question has limited clinical/regulatory interest; (2) the estimation may need strong statistical assumptions. In this article, we provide an example of a hypothetical strategy handling use of rescue medications in the acute pain setting. We argue that the treatment effect of a drug that is attributable to the treatment alone is the clinical question of interest and is important to regulators. The hypothetical strategy is important when developing non-opioid treatment as it estimates the treatment effect due to treatment during the pre-specified evaluation period whereas the treatment policy strategy does not. Two widely acceptable and non-controversial clinical inputs are required to construct a reasonable estimator. More importantly, this estimator does not rely on additional strong statistical assumptions and is considered reasonable for regulatory decision making. In this article, we point out examples where estimators for a hypothetical strategy can be constructed without any strong additional statistical assumptions besides acceptable clinical inputs. We also showcase a new way to obtain estimation based on disease specific clinical knowledge instead of strong statistical assumptions. In the example presented, we clearly demonstrate the advantages of the hypothetical strategy compared to alternative strategies including the treatment policy strategy and a composite variable strategy.

Matching reduces confounding bias in comparing the outcomes of nonrandomized patient populations by removing systematic differences between them. Under very basic assumptions, propensity score (PS) matching can be shown to eliminate bias entirely in estimating the average treatment effect on the treated. In practice, misspecification of the PS model leads to deviations from theory and matching quality is ultimately judged by the observed post-matching balance in baseline covariates. Since covariate balance is the ultimate arbiter of successful matching, we argue for an approach to matching in which the success criterion is explicitly specified and describe an evolutionary algorithm to directly optimize an arbitrary metric of covariate balance. We demonstrate the performance of the proposed method using a simulated dataset of 275,000 patients and 10 matching covariates. We further apply the method to match 250 patients from a recently completed clinical trial to a pool of more than 160,000 patients identified from electronic health records on 101 covariates. In all cases, we find that the proposed method outperforms PS matching as measured by the specified balance criterion. We additionally find that the evolutionary approach can perform comparably to another popular direct optimization technique based on linear integer programming, while having the additional advantage of supporting arbitrary balance metrics. We demonstrate how the chosen balance metric impacts the statistical properties of the resulting matched populations, emphasizing the potential impact of using nonlinear balance functions in constructing an external control arm. We release our implementation of the considered algorithms in Python.

Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross-over designs over conventional parallel designs is increased precision, thanks to within-subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross-over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross-over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed-effects (PLME) model against two commonly cited models-Grizzle's mixed-effects (GME) and Jones & Kenward's mixed-effects (JKME) models-used in the analysis of cross-over trials. Our simulation study tried to mirror real-life situation by deriving true underlying parameters from empirical data. The findings from real-life data confirmed the original hypothesis that high-dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross-over design. The fixed-effects, random-effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance-covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.

We compare the performance of nonparametric estimators for the mean number of recurrent events and provide a systematic overview for different recurrent event settings. The mean number of recurrent events is an easily interpreted marginal feature often used for treatment comparisons in clinical trials. Incomplete observations, dependencies between successive events, terminating events acting as competing risk, or gaps between at risk periods complicate the estimation. We use survival multistate models to represent different complex recurrent event situations, profiting from recent advances in nonparametric estimation for non-Markov multistate models, and explain several estimators by using multistate intensity processes, including the common Nelson-Aalen-type estimators with and without competing mortality. In addition to building on estimation of state occupation probabilities in non-Markov models, we consider a simple extension of the Nelson-Aalen estimator by allowing for dependence on the number of prior recurrent events. We pay particular attention to the assumptions required for the censoring mechanism, one issue being that some settings require the censoring process to be entirely unrelated while others allow for state-dependent or event-driven censoring. We conducted extensive simulation studies to compare the estimators in various complex situations with recurrent events. Our practical example deals with recurrent chronic obstructive pulmonary disease exacerbations in a clinical study, which will also be used to illustrate two-sample-inference using resampling.

There is a growing interest in the use of physical activity data in clinical studies, particularly in diseases that limit mobility in patients. High-frequency data collected with digital sensors are typically summarised into actigraphy features aggregated at epoch level (e.g., by minute). The statistical analysis of such volume of data is not straightforward. The general trend is to derive metrics, capturing specific aspects of physical activity, that condense (say) a week worth of data into a single numerical value. Here we propose to analyse the entire time-series data using Generalised Additive Models (GAMs). GAMs are semi-parametric models that allow inclusion of both parametric and non-parametric terms in the linear predictor. The latter are smooth terms (e.g., splines) and, in the context of actigraphy minute-by-minute data analysis, they can be used to assess daily patterns of physical activity. This in turn can be used to better understand changes over time in longitudinal studies as well as to compare treatment groups. We illustrate the application of GAMs in two clinical studies where actigraphy data was collected: a non-drug, single-arm study in patients with amyotrophic lateral sclerosis, and a physical-activity sub-study included in a phase 2b clinical trial in patients with chronic obstructive pulmonary disease.

We propose a novel frailty model with change points applying random effects to a Cox proportional hazard model to adjust the heterogeneity between clusters. In the specially focused eight Empowered Action Group (EAG) states in India, there are problems with different survival curves for children up to the age of five in different states. Therefore, when analyzing the survival times for the eight EAG states, we need to adjust for the effects among states (clusters). Because the frailty model includes random effects, the parameters are estimated using the expectation-maximization (EM) algorithm. Additionally, our model needs to estimate change points; we thus propose a new algorithm extending the conventional estimation algorithm to the frailty model with change points to solve the problem. We show a practical example to demonstrate how to estimate the change point and the parameters of the distribution of random effect. Our proposed model can be easily analyzed using the existing R package. We conducted simulation studies with three scenarios to confirm the performance of our proposed model. We re-analyzed the survival time data of the eight EAG states in India to show the difference in analysis results with and without random effect. In conclusion, we confirmed that the frailty model with change points has a higher accuracy than the model without a random effect. Our proposed model is useful when heterogeneity needs to be taken into account. Additionally, the absence of heterogeneity did not affect the estimation of the regression parameters.