Comparison of procedures to assess non-linear and time-varying effects in multivariable models for survival data

The focus of many medical applications is to model the impact of several factors on time to an event. A standard approach for such analyses is the Cox proportional hazards model. It assumes that the factors act linearly on the log hazard function (linearity assumption) and that their effects are constant over time (proportional hazards (PH) assumption). Variable selection is often required to specify a more parsimonious model aiming to include only variables with an influence on the outcome. As follow-up increases the effect of a variable often gets weaker, which means that it varies in time. However, spurious time-varying effects may also be introduced by mismodelling other parts of the multivariable model, such as omission of an important covariate or an incorrect functional form of a continuous covariate. These issues interact. To check whether the effect of a variable varies in time several tests for non-PH have been proposed. However, they are not sufficient to derive a model, as appropriate modelling of the shape of time-varying effects is required. In three examples we will compare five recently published strategies to assess whether and how the effects of covariates from a multivariable model vary in time. For practical use we will give some recommendations.     

Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.     

Influence of trial duration on the bias of the estimated treatment effect in clinical trials when individual heterogeneity is ignored

In randomized clinical trials where the times to event of two treatment groups are compared under a proportional hazards assumption, it has been established that omitting prognostic factors from the model entails an underestimation of the hazards ratio. Heterogeneity due to unobserved covariates in cancer patient populations is a concern since genomic investigations have revealed molecular and clinical heterogeneity in these populations. In HIV prevention trials, heterogeneity is unavoidable and has been shown to decrease the treatment effect over time. This article assesses the influence of trial duration on the bias of the estimated hazards ratio resulting from omitting covariates from the Cox analysis. The true model is defined by including an unobserved random frailty term in the individual hazard that reflects the omitted covariate. Three frailty distributions are investigated: gamma, log‐normal, and binary, and the asymptotic bias of the hazards ratio estimator is calculated. We show that the attenuation of the treatment effect resulting from unobserved heterogeneity strongly increases with trial duration, especially for continuous frailties that are likely to reflect omitted covariates, as they are often encountered in practice. The possibility of interpreting the long‐term decrease in treatment effects as a bias induced by heterogeneity and trial duration is illustrated by a trial in oncology where adjuvant chemotherapy in stage 1B NSCLC was investigated.     

Sample size calculation for the combination test under nonproportional hazards

For sample size calculation in clinical trials with survival endpoints, the logrank test, which is the optimal method under the proportional hazard (PH) assumption, is predominantly used. In reality, the PH assumption may not hold. For example, in immuno-oncology trials, delayed treatment effects are often expected. The sample size without considering the potential violation of the PH assumption may lead to an underpowered study. In recent years, combination tests such as the maximum weighted logrank test have received great attention because of their robust performance in various hazards scenarios. In this paper, we propose a flexible simulation-free procedure to calculate the sample size using combination tests. The procedure extends the Lakatos' Markov model and allows for complex situations encountered in a clinical trial, like staggered entry, dropouts, etc. We evaluate the procedure using two maximum weighted logrank tests, one projection-type test, and three other commonly used tests under various hazards scenarios. The simulation studies show that the proposed method can achieve the target power for all compared tests in most scenarios. The combination tests exhibit robust performance under correct specification and misspecification scenarios and are highly recommended when the hazard-changing patterns are unknown beforehand. Finally, we demonstrate our method using two clinical trial examples and provide suggestions about the sample size calculations under nonproportional hazards.     

Joint monitoring and prediction of accrual and event times in clinical trials

In many clinical trials, the primary endpoint is time to an event of interest, for example, time to cardiac attack or tumor progression, and the statistical power of these trials is primarily driven by the number of events observed during the trials. In such trials, the number of events observed is impacted not only by the number of subjects enrolled but also by other factors including the event rate and the follow‐up duration. Consequently, it is important for investigators to be able to monitor and predict accurately patient accrual and event times so as to predict the times of interim and final analyses and enable efficient allocation of research resources, which have long been recognized as important aspects of trial design and conduct. The existing methods for prediction of event times all assume that patient accrual follows a Poisson process with a constant Poisson rate over time; however, it is fairly common in real‐life clinical trials that the Poisson rate changes over time. In this paper, we propose a Bayesian joint modeling approach for monitoring and prediction of accrual and event times in clinical trials. We employ a nonhomogeneous Poisson process to model patient accrual and a parametric or nonparametric model for the event and loss to follow‐up processes. Compared to existing methods, our proposed methods are more flexible and robust in that we model accrual and event/loss‐to‐follow‐up times jointly and allow the underlying accrual rates to change over time. We evaluate the performance of the proposed methods through simulation studies and illustrate the methods using data from a real oncology trial.     

Estimating a treatment effect with repeated measurements accounting for varying effectiveness duration

To assess treatment efficacy in clinical trials, certain clinicaloutcomes are repeatedly measured over time for the same subject.The difference in their means may characterize a treatment effect.Since treatment effectiveness lag and saturation times may exist,erosion of treatment effect often occurs during the observationperiod. Instead of using models based on ad hoc parametric orpurely nonparametric time-varying coefficients, we model thetreatment effectiveness durations, which are the time intervalsbetween the lag and saturation times. Then we use some meanresponse models to include such treatment effectiveness durations.Our methodology is demonstrated by simulations and analysisof a landmark HIV/AIDS clinical trial of short-course nevirapineagainst mother-to-child HIV vertical transmission during labourand delivery.     

On the COLTON Model for Clinical Trials with Delayed Observations-Dichotomous Responses

In the COLTON model for clinical trials a choice is to be made between two medical treatments where there is a known patient horizon N. In an earlier paper we studied the COLTON model under the additional assumption that there is a time lag between the administration of the treatments and the availability of the responses where the responses are normally distributed. Here we extend the results of the earlier paper to the case where responses are dichotomous. The relative performance of two simple procedures for dealing with the patients who arrive during the waiting period between the end of the administration of treatment in the trial phase and observation of the final trial response is discussed within a BAYESIAN framework.     

Multistate modeling and structure selection for multitype recurrent events and terminal event data

In cardiovascular disease studies, a large number of risk factors are measured but it often remains unknown whether all of them are relevant variables and whether the impact of these variables is changing with time or remains constant. In addition, more than one kind of cardiovascular disease events can be observed in the same patient and events of different types are possibly correlated. It is expected that different kinds of events are associated with different covariates and the forms of covariate effects also vary between event types. To tackle these problems, we proposed a multistate modeling framework for the joint analysis of multitype recurrent events and terminal event. Model structure selection is performed to identify covariates with time-varying coefficients, time-independent coefficients, and null effects. This helps in understanding the disease process as it can detect relevant covariates and identify the temporal dynamics of the covariate effects. It also provides a more parsimonious model to achieve better risk prediction. The performance of the proposed model and selection method is evaluated in numerical studies and illustrated on a real dataset from the Atherosclerosis Risk in Communities study.     

Nonregistration,discontinuation, and nonpublication of randomized trials: A repeated metaresearch analysis

BackgroundWe previously found that 25% of 1,017 randomized clinical trials (RCTs) approved between 2000 and 2003 were discontinued prematurely, and 44% remained unpublished at a median of 12 years follow-up. We aimed to assess a decade later (1) whether rates of completion and publication have increased; (2) the extent to which nonpublished RCTs can be identified in trial registries; and (3) the association between reporting quality of protocols and premature discontinuation or nonpublication of RCTs.Methods and findingsWe included 326 RCT protocols approved in 2012 by research ethics committees in Switzerland, the United Kingdom, Germany, and Canada in this metaresearch study. Pilot, feasibility, and phase 1 studies were excluded. We extracted trial characteristics from each study protocol and systematically searched for corresponding trial registration (if not reported in the protocol) and full text publications until February 2022. For trial registrations, we searched the (i) World Health Organization: International Clinical Trial Registry Platform (ICTRP); (ii) US National Library of Medicine (ClinicalTrials.gov); (iii) European Union Drug Regulating Authorities Clinical Trials Database (EUCTR); (iv) ISRCTN registry; and (v) Google. For full text publications, we searched PubMed, Google Scholar, and Scopus. We recorded whether RCTs were registered, discontinued (including reason for discontinuation), and published. The reporting quality of RCT protocols was assessed with the 33-item SPIRIT checklist. We used multivariable logistic regression to examine the association between the independent variables protocol reporting quality, planned sample size, type of control (placebo versus other), reporting of any recruitment projection, single-center versus multicenter trials, and industry versus investigator sponsoring, with the 2 dependent variables: (1) publication of RCT results; and (2) trial discontinuation due to poor recruitment.Of the 326 included trials, 19 (6%) were unregistered. Ninety-eight trials (30%) were discontinued prematurely, most often due to poor recruitment (37%; 36/98). One in 5 trials (21%; 70/326) remained unpublished at 10 years follow-up, and 21% of unpublished trials (15/70) were unregistered. Twenty-three of 147 investigator-sponsored trials (16%) reported their results in a trial registry in contrast to 150 of 179 industry-sponsored trials (84%).The median proportion of reported SPIRIT items in included RCT protocols was 69% (interquartile range 61% to 77%). We found no variables associated with trial discontinuation; however, lower reporting quality of trial protocols was associated with nonpublication (odds ratio, 0.71 for each 10% increment in the proportion of SPIRIT items met; 95% confidence interval, 0.55 to 0.92; p = 0.009). Study limitations include that the moderate sample size may have limited the ability of our regression models to identify significant associations.ConclusionsWe have observed that rates of premature trial discontinuation have not changed in the past decade. Nonpublication of RCTs has declined but remains common; 21% of unpublished trials could not be identified in registries. Only 16% of investigator-sponsored trials reported results in a trial registry. Higher reporting quality of RCT protocols was associated with publication of results. Further efforts from all stakeholders are needed to improve efficiency and transparency of clinical research.

Benjamin Speich and colleagues investigate whether rates of trial completion and publication have increased over the past decade, the extent to which non-published trials can be identified in registries, and the association between reporting quality of protocols and premature discontinuation or non-publication of trials.     

Long-term dietary intervention trials: critical issues and challenges

ABSTRACT: BACKGROUND: There are many challenges involved in running randomised controlled dietary intervention trials that investigate health outcomes. The aim of this paper was to evaluate the recruitment process, retention of participants and challenges faced in our dairy intervention trial, and to provide strategies to combat the difficulties of running long-term dietary intervention trials. METHODS: A 12-month, randomised, two-way crossover study in overweight adults with habitually low dairy food consumption designed to assess the effects of a high dairy intake (HD; 4 serves of reduced fat dairy per day) compared to a low dairy intake (LD; 1 serve of reduced fat dairy per day) on measures of cardiometabolic and cognitive health was conducted. On completion of the HD phase, each participant was interviewed about their experience in the trial and responses were used to evaluate the key issues for study participants. RESULTS: Although the recruitment target was achieved, high rates of attrition (49.3%) and difficulties maintaining participant compliance (reported by 37.8% of participants) were major threats to the viability of the study. Factors that contributed to the high attrition included inability to comply with the dietary requirements of the study protocol (27.0%), health problems or medication changes (24.3%) and time commitment (10.8%). CONCLUSIONS: Attrition and adherence to study requirements present challenges to trials requiring longer-term dietary change. Including a run-in period to further assess the motivation, commitment and availability of participants, maintaining regular contact with participants during control phases, minimising time commitment, providing flexibility with dietary requirements, facilitating positive experiences, and stringent monitoring of diet are some key recommendations for future dietary intervention trials.     

Wolf population dynamics in the U.S. Northern Rocky Mountains are affected by recruitment and human-caused mortality

Reliable analyses can help wildlife managers make good decisions, which are particularly critical for controversial decisions such as wolf (Canis lupus) harvest. Creel and Rotella (2010) recently predicted substantial population declines in Montana wolf populations due to harvest, in contrast to predictions made by Montana Fish, Wildlife and Parks (MFWP). We replicated their analyses considering only those years in which field monitoring was consistent, and we considered the effect of annual variation in recruitment on wolf population growth. Rather than assuming constant rates, we used model selection methods to evaluate and incorporate models of factors driving recruitment and human-caused mortality rates in wolf populations in the Northern Rocky Mountains. Using data from 27 area-years of intensive wolf monitoring, we show that variation in both recruitment and human-caused mortality affect annual wolf population growth rates and that human-caused mortality rates have increased with the sizes of wolf populations. We document that recruitment rates have decreased over time, and we speculate that rates have decreased with increasing population sizes and/or that the ability of current field resources to document recruitment rates has recently become less successful as the number of wolves in the region has increased. Estimates of positive wolf population growth in Montana from our top models are consistent with field observations and estimates previously made by MFWP for 2008–2010, whereas the predictions for declining wolf populations of Creel and Rotella (2010) are not. Familiarity with limitations of raw data, obtained first-hand or through consultation with scientists who collected the data, helps generate more reliable inferences and conclusions in analyses of publicly available datasets. Additionally, development of efficient monitoring methods for wolves is a pressing need, so that analyses such as ours will be possible in future years when fewer resources will be available for monitoring. © 2011 The Wildlife Society.     

An alternative metric for evaluating the potential patient benefit of response-adaptive randomization procedures

When planning a two-arm group sequential clinical trial with a binary primary outcome that has severe implications for quality of life (e.g., mortality), investigators may strive to find the design that maximizes in-trial patient benefit. In such cases, Bayesian response-adaptive randomization (BRAR) is often considered because it can alter the allocation ratio throughout the trial in favor of the treatment that is currently performing better. Although previous studies have recommended using fixed randomization over BRAR based on patient benefit metrics calculated from the realized trial sample size, these previous comparisons have been limited by failures to hold type I and II error rates constant across designs or consider the impacts on all individuals directly affected by the design choice. In this paper, we propose a metric for comparing designs with the same type I and II error rates that reflects expected outcomes among individuals who would participate in the trial if enrollment is open when they become eligible. We demonstrate how to use the proposed metric to guide the choice of design in the context of two recent trials in persons suffering out of hospital cardiac arrest. Using computer simulation, we demonstrate that various implementations of group sequential BRAR offer modest improvements with respect to the proposed metric relative to conventional group sequential monitoring alone.     

Predicting the growth of the amphibian chytrid fungus in varying temperature environments

Environmental temperature is a crucial abiotic factor that influences the success of ectothermic organisms, including hosts and pathogens in disease systems. One example is the amphibian chytrid fungus, Batrachochytrium dendrobatidis (Bd), which has led to widespread amphibian population declines. Understanding its thermal ecology is essential to effectively predict outbreaks. Studies that examine the impact of temperature on hosts and pathogens often do so in controlled constant temperatures. Although varying temperature experiments are becoming increasingly common, it is unrealistic to test every temperature scenario. Thus, reliable methods that use constant temperature data to predict performance in varying temperatures are needed. In this study, we tested whether we could accurately predict Bd growth in three varying temperature regimes, using a Bayesian hierarchical model fit with constant temperature Bd growth data. We fit the Bayesian hierarchical model five times, each time changing the thermal performance curve (TPC) used to constrain the logistic growth rate to determine how TPCs influence the predictions. We then validated the model predictions using Bd growth data collected from the three tested varying temperature regimes. Although all TPCs overpredicted Bd growth in the varying temperature regimes, some functional forms performed better than others. Varying temperature impacts on disease systems are still not well understood and improving our understanding and methodologies to predict these effects could provide insights into disease systems and help conservation efforts.     

Multifactorial day hospital intervention to reduce falls in high risk older people in primary care: a multi-centre randomised controlled trial [ISRCTN46584556]

Background

There are many barriers to patient participation in randomised controlled trials of cancer treatments. To increase participation in trials, strategies need to be identified to overcome these barriers. Our aim was to assess the effectiveness of interventions to overcome barriers to patient participation in randomised controlled trials (RCTs) of cancer treatments.

Methods

A systematic review was conducted. Published and unpublished studies in any language were searched for in fifteen electronic databases, including MEDLINE, EMBASE, CINAHL and PsycINFO, from inception to the end of 2004. Studies of any interventions to improve cancer patient participation in RCTs, which reported the change in recruitment rates, were eligible for inclusion. RCTs and non-randomised controlled trials as well as before and after studies reporting baseline rates specific to the population being investigated were included. Data were extracted by one reviewer into structured summary tables and checked for accuracy by a second reviewer. Each included study was assessed against a checklist for methodological quality by one reviewer and checked by a second reviewer. A narrative synthesis was conducted.

Results

Eight studies were identified that met the inclusion criteria: three RCTs, two non-randomised controlled trials and three observational studies. Six of the studies had an intervention that had some relevance to the UK. There was no robust evidence that any of the interventions investigated led to an increase in cancer patient participation in RCTs, though one good quality RCT found that urologists and nurses were equally effective at recruiting participants to a treatment trial for prostate cancer. Although there was no evidence of an effect in any of the studies, the evidence was not of sufficient quality to be able to conclude that these interventions therefore do not work.

Conclusion

There is not a strong evidence-base for interventions that increase cancer patient participation in randomised trials. Further research is required to evaluate the effectiveness of strategies to increase participation in cancer treatment trials.     

PA-CRM: A continuous reassessment method for pediatric phase I oncology trials with concurrent adult trials

Pediatric phase I trials are usually carried out after the adult trial testing the same agent has started, but not completed yet. As the pediatric trial progresses, in light of the accrued interim data from the concurrent adult trial, the pediatric protocol often is amended to modify the original pediatric dose escalation design. In practice, this is done frequently in an ad hoc way, interrupting patient accrual and slowing down the trial. We developed a pediatric-continuous reassessment method (PA-CRM) to streamline this process, providing a more efficient and rigorous method to find the maximum tolerated dose for pediatric phase I oncology trials. We use a discounted joint likelihood of the adult and pediatric data, with a discount parameter controlling information borrowing between pediatric and adult trials. According to the interim adult and pediatric data, the discount parameter is adaptively updated using the Bayesian model averaging method. Numerical study shows that the PA-CRM improves the efficiency and accuracy of the pediatric trial and is robust to various model assumptions.     

Satisfaction of the uncertainty principle in cancer clinical trials: retrospective cohort analysis

Objective To assess whether publicly funded adult cancer trials satisfy the uncertainty principle, which states that physicians should enrol a patient in a trial only if they are substantially uncertain which of the treatments in the trial is most appropriate for the patient. This principle is violated if trials systematically favour either the experimental or the standard treatment.Design Retrospective cohort study of completed cancer trials, with randomisation as the unit of analysis.Setting Two cooperative research groups in the United States.Studies included 93 phase III randomised trials (103 randomisations) that completed recruitment of patients between 1981 and 1995.Main outcome measures Whether the randomisation favoured the experimental treatment, the standard treatment, or neither treatment; effect size (outcome of the experimental treatment compared with outcome of the standard treatment) for each randomisation.Results Three randomisations (3%) favoured the standard treatment, 70 (68%) found no significant difference between treatments, and 30 (29%) favoured the experimental treatment. The average effect size was 1.20 (95% confidence interval 1.13 to 1.28), reflecting a slight advantage for the experimental treatment.Conclusions In cooperative group trials in adults with cancer, there is a measurable average improvement in disease control associated with assignment to the experimental rather than the standard arm. However, the heterogeneity of outcomes and the small magnitude of the advantage suggest that, as a group, these trials satisfy the uncertainty principle.     

The placebo response in clinical trials: more questions than answers

Meta-analyses and re-analyses of trial data have not been able to answer some of the essential questions that would allow prediction of placebo responses in clinical trials. We will confront these questions with current empirical evidence. The most important question asks whether the placebo response rates in the drug arm and in the placebo arm are equal. This 'additive model' is a general assumption in almost all placebo-controlled drug trials but has rarely been tested. Secondly, we would like to address whether the placebo response is a function of the likelihood of receiving drug/placebo. Evidence suggests that the number of study arms in a trial may determine the size of the placebo and the drug response. Thirdly, we ask what the size of the placebo response is in 'comparator' studies with a direct comparison of a (novel) drug against another drug. Meta-analytic and experimental evidence suggests that comparator studies may produce higher placebo response rates when compared with placebo-controlled trials. Finally, we address the placebo response rate outside the laboratory and outside of trials in clinical routine. This question poses a serious challenge whether the drug response in trials can be taken as evidence of drug effects in clinical routine.     

Modeling nonhomogeneous Markov processes via time transformation

Summary .   Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.     

Lung cancer rate predictions using generalized additive models

Predictions of lung cancer incidence and mortality are necessary for planning public health programs and clinical services. It is proposed that generalized additive models (GAMs) are practical for cancer rate prediction. Smooth equivalents for classical age-period, age-cohort, and age-period-cohort models are available using one-dimensional smoothing splines. We also propose using two-dimensional smoothing splines for age and period. Variance estimation can be based on the bootstrap. To assess predictive performance, we compared the models with a Bayesian age-period-cohort model. Model comparison used cross-validation and measures of predictive performance for recent predictions. The models were applied to data from the World Health Organization Mortality Database for females in five countries. Model choice between the age-period-cohort models and the two-dimensional models was equivocal with respect to cross-validation, while the two-dimensional GAMs had very good predictive performance. The Bayesian model performed poorly due to imprecise predictions and the assumption of linearity outside of observed data. In summary, the two-dimensional GAM performed well. The GAMs make the important prediction that female lung cancer rates in these countries will be stable or begin to decline in the future.     

Seed predation and seedling recruitment in plants: the effect of the distance between parents

We present a graphic model that explores the effect of distance between parent plants on seed predation and seedling recruitment. Based on the assumption that distance between parents may affect the shape of the seed shadow, the model predicts that seed predators may affect seedling recruitment curves under isolated plants but they are unable to affect these curves under close parent plants. The predictions of the model are tested experimentally in Cryptocarya alba (Lauraceae), a common tree of the Mediterranean forest, Central Chile. Results show that predictions are not met under isolated parent plants. Although seed density decreases significantly away from parent plants, this effect is not relevant for seed predation and seedling recruitment. The biotic/abiotic contrast existing under the canopy vs outside the canopy, plus the shade-tolerance of this tree, better explains the seedling recruitment observed under isolated parent plants. Nevertheless, the predictions of the model are corroborated under close parent plants. Seed shadows overlap to the extent that they generate a homogeneous seed distribution, homogeneous seed predation and homogeneous seedling recruitment as well. We discuss the implications of the model in terms of the spatial pattern of seedlings and the benefits of dispersal from isolated and close parent plants.