Latency function estimation under the mixture cure model when the cure status is available

This paper addresses the problem of estimating the conditional survival function of the lifetime of the subjects experiencing the event (latency) in the mixture cure model when the cure status information is partially available. The approach of past work relies on the assumption that long-term survivors are unidentifiable because of right censoring. However, in some cases this assumption is invalid since some subjects are known to be cured, e.g., when a medical test ascertains that a disease has entirely disappeared after treatment. We propose a latency estimator that extends the nonparametric estimator studied in López-Cheda et al. (TEST 26(2):353-376, 2017b) to the case when the cure status is partially available. We establish the asymptotic normality distribution of the estimator, and illustrate its performance in a simulation study. Finally, the estimator is applied to a medical dataset to study the length of hospital stay of COVID-19 patients requiring intensive care.

Prognostic Factors Analysis of Metastatic Recurrence in Cervical Carcinoma Patients Treated with Definitive Radiotherapy: A Retrospective Study Using Mixture Cure Model

OBJECTIVES

This study aims to identify prognostic factors associated with metastatic recurrence-free survival of cervical carcinoma (CC) patients treated with radical radiotherapy and assess the cure probability of radical radiotherapy from metastatic recurrence.

METHODS

Data were from 446 cervical carcinoma patients with radical radiotherapy for an average follow up of 3.96 years. We applied a mixture cure model to investigate the association between metastatic recurrence and prognostic factors and the association between noncure probability and factors, respectively. A nonparametric test of cure probability under the framework of a mixture cure model was used to examine the significance of cure probability of the definitive radiotherapy treatment. Propensity-score-matched (PSM) pairs were generated to reduce bias in subgroup analysis.

RESULTS

Patients in advanced stages (p = 0.005) and those with worse treatment responses in the 3rd month (p = 0.004) had higher metastatic recurrence rates. Nonparametric tests of the cure probability showed that 3-year cure probability from metastatic recurrence was significantly larger than 0, and 5-year cure probability was significantly larger than 0.7 but no larger than 0.8. The empirical cure probability by mixture cure model was 79.2% (95% CI: 78.6-79.9%) for the entire study population, and the overall median metastatic recurrence time for uncured patients (patients susceptible to metastatic recurrence) was 1.60 (95% CI: 1.51-1.69) years. Locally advanced/advanced stage was a risk factor but non-significant against the cure probability (OR = 1.078, p = 0.088). The interaction of age and activity of radioactive source were statistically significant in the incidence model (OR = 0.839, p = 0.025). In subgroup analysis, compared with high activity of radioactive source (HARS), low activity of radioactive source (LARS) significantly contributed to a 16.1% higher cure probability for patients greater than 53 years old, while cure probability was 12.2% lower for the younger patients.

CONCLUSIONS

There was statistically significant evidence in the data showing the existence of a large amount of patients cured by the definitive radiotherapy treatment. HARS is a protective factor against metastatic recurrence for uncured patients, and young patients tend to benefit more than the elderly from the HARS treatment.

Nonparametric kernel estimation of the probability of cure in a mixture cure model when the cure status is partially observed

Cure models are a class of time-to-event models where a proportion of individuals will never experience the event of interest. The lifetimes of these so-called cured individuals are always censored. It is usually assumed that one never knows which censored observation is cured and which is uncured, so the cure status is unknown for censored times. In this paper, we develop a method to estimate the probability of cure in the mixture cure model when some censored individuals are known to be cured. A cure probability estimator that incorporates the cure status information is introduced. This estimator is shown to be strongly consistent and asymptotically normally distributed. Two alternative estimators are also presented. The first one considers a competing risks approach with two types of competing events, the event of interest and the cure. The second alternative estimator is based on the fact that the probability of cure can be written as the conditional mean of the cure status. Hence, nonparametric regression methods can be applied to estimate this conditional mean. However, the cure status remains unknown for some censored individuals. Consequently, the application of regression methods in this context requires handling missing data in the response variable (cure status). Simulations are performed to evaluate the finite sample performance of the estimators, and we apply them to the analysis of two datasets related to survival of breast cancer patients and length of hospital stay of COVID-19 patients requiring intensive care.

On a reparameterization of a flexible family of cure models

The existence of items not susceptible to the event of interest is of both theoretical and practical importance. Although researchers may provide, for example, biological, medical, or sociological evidence for the presence of such items (cured), statistical models performing well under the existence or not of a cured proportion, frequently offer a necessary flexibility. This work introduces a new reparameterization of a flexible family of cure models, which not only includes among its special cases, the most studied cure models (such as the mixture, bounded cumulative hazard, and negative binomial cure model) but also classical survival models (ie, without cured items). One of the main properties of the proposed family, apart from its computationally tractable closed form, is that the case of zero cured proportion is not found at the boundary of the parameter space, as it typically happens to other families. A simulation study examines the (finite) performance of the suggested methodology, focusing to the estimation through EM algorithm and model discrimination, by the aid of the likelihood ratio test and Akaike information criterion; for illustrative purposes, analysis of two real life datasets (on recidivism and cutaneous melanoma) is also carried out.

The analysis of COVID-19 in-hospital mortality: A competing risk approach or a cure model?

Competing risk analyses have been widely used for the analysis of in-hospital mortality in which hospital discharge is considered as a competing event. The competing risk model assumes that more than one cause of failure is possible, but there is only one outcome of interest and all others serve as competing events. However, hospital discharge and in-hospital death are two outcomes resulting from the same disease process and patients whose disease conditions were stabilized so that inpatient care was no longer needed were discharged. We therefore propose to use cure models, in which hospital discharge is treated as an observed “cure” of the disease. We consider both the mixture cure model and the promotion time cure model and extend the models to allow cure status to be known for those who were discharged from the hospital. An EM algorithm is developed for the mixture cure model. We also show that the competing risk model, which treats hospital discharge as a competing event, is equivalent to a promotion time cure model. Both cure models were examined in simulation studies and were applied to a recent cohort of COVID-19 in-hospital patients with diabetes. The promotion time model shows that statin use improved the overall survival; the mixture cure model shows that while statin use reduced the in-hospital mortality rate among the susceptible, it improved the cure probability only for older but not younger patients. Both cure models show that treatment was more beneficial among older patients.

Exposure assessment for Cox proportional hazards cure models with interval-censored survival data

Mixture cure models have been developed as an effective tool to analyze failure time data with a cure fraction. Used in conjunction with the logistic regression model, this model allows covariate-adjusted inference of an exposure effect on the cured probability and the hazard of failure for the uncured subjects. However, the covariate-adjusted inference for the overall exposure effect is not directly provided. In this paper, we describe a Cox proportional hazards cure model to analyze interval-censored survival data in the presence of a cured fraction and then apply a post-estimation approach by using model-predicted estimates difference to assess the overall exposure effect on the restricted mean survival time scale. For baseline hazard/survival function estimation, simple parametric models as fractional polynomials or restricted cubic splines are utilized to approximate the baseline logarithm cumulative hazard function, or, alternatively, the full likelihood is specified through a piecewise linear approximation for the cumulative baseline hazard function. Simulation studies were conducted to demonstrate the unbiasedness of both estimation methods for the overall exposure effect estimates over various baseline hazard distribution shapes. The methods are applied to analyze the interval-censored relapse time data from a smoking cessation study.

Application of non-parametric models for analyzing survival data of COVID-19 patients

BACKGROUND

COVID-19 Coronavirus variants are emerging across the globe causing ongoing pandemics. It is important to estimate the case fatality ratio (CFR) during such an epidemic of a potentially fatal disease.

METHODS

Firstly, we have performed a non-parametric approach for odds ratios with corresponding confidence intervals (CIs) and illustrated relative risks and cumulative mortality rates of COVID-19 data of Spain. We have demonstrated the modified non-parametric approach based on Kaplan-Meier (KM) technique using COVID-19 data of Italy. We have also performed the significance of characteristics of patients regarding outcome by age for both genders. Furthermore, we have applied a non-parametric cure model using Nadaraya-Watson weight to estimate cure-rate using Israel data. Simulations are based on R-software.

RESULTS

The analytical illustrations of these approaches predict the effects of patients based on covariates in different scenarios. Sex differences are increased from ages less than 60 years to 60-69 years but decreased thereafter with the smallest sex difference at ages 80 years in a case for estimating both purposes RR (relative risk) and OR (odds ratio). The non-parametric approach investigates the range of cure-rate ranges from 5.3% to 9% and from 4% to 7% approximately for male and female respectively. The modified KM estimator performs for such censored data and detects the changes in CFR more rapidly for both genders and age-wise.

CONCLUSION

Older-age, male-sex, number of comorbidities and access to timely health care are identified as some of the risk factors associated with COVID-19 mortality in Spain. The non-parametric approach has investigated the influence of covariates on models and it provides the effect in both genders and age. The health impact of public for inaccurate estimates, inconsistent intelligence, conflicting messages, or resulting in misinformation can increase awareness among people and also induce panic situations that accompany major outbreaks of COVID-19.

Cure models to estimate time until hospitalization due to COVID-19: A case study in Galicia (NW Spain)

A short introduction to survival analysis and censored data is included in this paper. A thorough literature review in the field of cure models has been done. An overview on the most important and recent approaches on parametric, semiparametric and nonparametric mixture cure models is also included. The main nonparametric and semiparametric approaches were applied to a real time dataset of COVID-19 patients from the first weeks of the epidemic in Galicia (NW Spain). The aim is to model the elapsed time from diagnosis to hospital admission. The main conclusions, as well as the limitations of both the cure models and the dataset, are presented, illustrating the usefulness of cure models in this kind of studies, where the influence of age and sex on the time to hospital admission is shown.

A product-limit estimator of the conditional survival function when cure status is partially known

We introduce a nonparametric estimator of the conditional survival function in the mixture cure model for right-censored data when cure status is partially known. The estimator is developed for the setting of a single continuous covariate but it can be extended to multiple covariates. It extends the estimator of Beran, which ignores cure status information. We obtain an almost sure representation, from which the strong consistency and asymptotic normality of the estimator are derived. Asymptotic expressions of the bias and variance demonstrate a reduction in the variance with respect to Beran's estimator. A simulation study shows that, if the bandwidth parameter is suitably chosen, our estimator performs better than others for an ample range of covariate values. A bootstrap bandwidth selector is proposed. Finally, the proposed estimator is applied to a real dataset studying survival of sarcoma patients.

Onset of action under antidepressant treatment

The issues of timing in antidepressant treatment are of great theoretical and practical relevance, even more so since recent meta-analyses yielded no evidence for a specific mode of action of antidepressants, which, according to the theory of delayed onset of action, is expected to emerge after 2 weeks of therapy. To address the issues of timing on a methodologically sound basis, future trials should adapt a ‘longitudinal’ rather than ‘cross-sectional’ design, standardized with respect to a washout period, baseline and first 2 week assessments. With this in mind, special attention should be paid to parameters which potentially enable the identification of placebo responders, true drug responders and patients at risk of non-improvement. Results and methods of the Zurich meta-analyses may serve as a starting point for further steps in this direction.

Vertical modeling: analysis of competing risks data with a cure fraction

In this paper, we extend the vertical modeling approach for the analysis of survival data with competing risks to incorporate a cure fraction in the population, that is, a proportion of the population for which none of the competing events can occur. The proposed method has three components: the proportion of cure, the risk of failure, irrespective of the cause, and the relative risk of a certain cause of failure, given a failure occurred. Covariates may affect each of these components. An appealing aspect of the method is that it is a natural extension to competing risks of the semi-parametric mixture cure model in ordinary survival analysis; thus, causes of failure are assigned only if a failure occurs. This contrasts with the existing mixture cure model for competing risks of Larson and Dinse, which conditions at the onset on the future status presumably attained. Regression parameter estimates are obtained using an EM-algorithm. The performance of the estimators is evaluated in a simulation study. The method is illustrated using a melanoma cancer data set.

Exploratory Failure Time Analysis in Large Scale Genomics

In large scale genomic analyses dealing with detecting genotype-phenotype associations, such as genome wide association studies (GWAS), it is desirable to have numerically and statistically robust procedures to test the stochastic independence null hypothesis against certain alternatives. Motivated by a special case in a GWAS, a novel test procedure called correlation profile test (CPT) is developed for testing genomic associations with failure-time phenotypes subject to right censoring and competing risks. Performance and operating characteristics of CPT are investigated and compared to existing approaches, by a simulation study and on a real dataset. Compared to popular choices of semiparametric and nonparametric methods, CPT has three advantages: it is numerically more robust because it solely relies on sample moments; it is more robust against the violation of the proportional hazards condition; and it is more flexible in handling various failure and censoring scenarios. CPT is a general approach to testing the null hypothesis of stochastic independence between a failure event point process and any random variable; thus it is widely applicable beyond genomic studies.

Flexible modelling of simultaneously interval censored and truncated time-to-event data

This paper deals with the analysis of data from a HET-CAM(VT) experiment. From a statistical perspective, such data yield many challenges. First of all, the data are typically time-to-event like data, which are at the same time interval censored and right truncated. In addition, one has to cope with overdispersion as well as clustering. Traditional analysis approaches ignore overdispersion and clustering and summarize the data into a continuous score that can be analysed using simple linear models. In this paper, a novel combined frailty model is developed that simultaneously captures all of the aforementioned statistical challenges posed by the data.

Joint Modeling of Longitudinal and Cure-survival Data

This article presents semiparametric joint models to analyze longitudinal measurements and survival data with a cure fraction. We consider a broad class of transformations for the cure-survival model, which includes the popular proportional hazards structure and the proportional odds structure as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we demonstrate the good performance of the method through extensive simulation studies and a real-data application.

Multiple testing for a combination drug with two study endpoints

A combination drug product with two or more active compounds may be superior to each of its components with higher dose levels and, therefore, is preferred in terms of efficacy, cost, and safety. To study a combination drug, researchers often conduct trials by using a factorial design with combinations of dose levels of each drug component. By applying some bootstrap methods, we construct multiple testing procedures to simultaneously identify combinations superior to each drug component with any dose level. These multiple testing procedures are more powerful than Holm's step-down procedure that is known to be very conservative. When there is only one study endpoint, applying the bootstrap is straightforward. In many studies, however, there are two or more study endpoints and it is not simple to apply the bootstrap. We apply one version of the bootstrap and then use an upper bound to control the familywise error defined as the probability of rejecting at least one true null hypothesis. Properties of the bootstrap multiple testing procedures are discussed and examined in some simulation studies.

Sample size calculation for the proportional hazards cure model

In clinical trials with time-to-event endpoints, it is not uncommon to see a significant proportion of patients being cured (or long-term survivors), such as trials for the non-Hodgkins lymphoma disease. The popularly used sample size formula derived under the proportional hazards (PH) model may not be proper to design a survival trial with a cure fraction, because the PH model assumption may be violated. To account for a cure fraction, the PH cure model is widely used in practice, where a PH model is used for survival times of uncured patients and a logistic distribution is used for the probability of patients being cured. In this paper, we develop a sample size formula on the basis of the PH cure model by investigating the asymptotic distributions of the standard weighted log-rank statistics under the null and local alternative hypotheses. The derived sample size formula under the PH cure model is more flexible because it can be used to test the differences in the short-term survival and/or cure fraction. Furthermore, we also investigate as numerical examples the impacts of accrual methods and durations of accrual and follow-up periods on sample size calculation. The results show that ignoring the cure rate in sample size calculation can lead to either underpowered or overpowered studies. We evaluate the performance of the proposed formula by simulation studies and provide an example to illustrate its application with the use of data from a melanoma trial.

Cure models as a useful statistical tool for analyzing survival

Cure models are a popular topic within statistical literature but are not as widely known in the clinical literature. Many patients with cancer can be long-term survivors of their disease, and cure models can be a useful tool to analyze and describe cancer survival data. The goal of this article is to review what a cure model is, explain when cure models can be used, and use cure models to describe multiple myeloma survival trends. Multiple myeloma is generally considered an incurable disease, and this article shows that by using cure models, rather than the standard Cox proportional hazards model, we can evaluate whether there is evidence that therapies at the University of Arkansas for Medical Sciences induce a proportion of patients to be long-term survivors.

Empirical receiver operating characteristic curve for two-sample comparison with cure fractions

Two-sample comparison of survival times with "cured patients" is of major interest and a challenging issue in many areas, particularly in cancer clinical research. Recently, several authors have proposed various procedures of comparison, including tests of no overall, no short-term and no long-term differences between two samples. In clinical practice, it is often of interest to detect the difference in treatment effects among noncured patients regardless of the difference between cure fractions. In this paper, we propose a statistical test to compare two samples with cured patients and possibly heterogeneous treatment effects based on a class of semi-parametric transformation models, and our main focus is on the survival times of noncured patients. The empirical and quantile processes are used to construct strong approximations for the empirical curves. The two-sample test is then constructed from general least squares estimators derived from these processes. Simulation results show that the proposed test perform well. As an example of application, a set of bladder cancer data is analyzed to illustrate the proposed methods.

The Gini concentration test for survival data

We apply the well known Gini index to the measurement of concentration in survival times within groups of patients, and as a way to compare the distribution of survival times across groups of patients in clinical studies. In particular, we propose an estimator of a restricted version of the index from right censored data. We derive the asymptotic distribution of the resulting Gini statistic, and construct an estimator for its asymptotic variance. We use these results to propose a novel test for differences in the heterogeneity of survival distributions, which may suggest the presence of a differential treatment effect for some groups of patients. We focus in particular on traditional and generalized cure rate models, i.e., mixture models with a distribution of the lifetimes of the cured patients that is either degenerate at infinity or has a density. Results from a simulation study suggest that the Gini index is useful in some situations, and that it should be considered together with existing tests (in particular, the Log-rank, Wilcoxon, and Gray-Tsiatis tests). Use of the test is illustrated on the classic data arising from the Eastern Cooperative Oncology Group melanoma clinical trial E1690.

Daily process methodology for measuring earlier antidepressant response

OBJECTIVE

Rapid onset of therapeutic action for antidepressant medication represents a major area of unmet medical need, and any such effects have been difficult to detect using standard study designs and measurement strategies. We conducted a randomized, open-label study with blinded raters using daily process assessment vs. standard weekly assessment to answer the following study questions: 1) is it possible to detect an antidepressant response more rapidly with daily assessment than with standard assessment approaches? 2) what is the burden of daily assessment on participants relative to standard clinical assessments? and 3) does the process of completing daily assessments have any effect on clinic-based assessments such as the Hamilton Depression Rating Scale (HAM-D)?

METHOD

Seventy-eight outpatients with major depressive disorder who received open-label fluoxetine were randomized to standard weekly clinic assessment or standard weekly clinic assessment plus daily assessment, and were followed for 28 days. Data were collected between September, 2002 and August, 2003.

RESULTS

Daily assessment appeared to have no effect on 17-item HAM-D or MADRS scores obtained in the clinic. Survival analyses revealed that daily diaries detected therapeutic effects more quickly than did standard weekly clinic assessments, across most endpoints. Perceived burden of study participation was not significantly increased by daily diary completion, nor reflected in higher dropout rates.

CONCLUSION

Daily process assessment improves the ability to detect an early antidepressant response.

Modelling menstrual status during and after adjuvant treatment for breast cancer

Failure time data may consist of the observation of an event whose cause is unknown due to the censoring or lack of a second event that could identify the cause of the first event. Standard competing-risks methodology does not apply to this setting because the cause of the event is not always identifiable. Moreover, one cannot assume that the entire population will eventually experience the event of interest, and the observation is potentially censored for all patients. The model that we describe in this article is motivated by a breast cancer clinical trial conducted by the International Breast Cancer Study Group (IBCSG). Because some breast cancer adjuvant treatments for premenopausal patients who have undergone surgery cause the interruption of menses, or amenorrhoea, it is of interest to describe the process by which menses discontinue and resume after treatment is completed. The process is complicated by the fact that natural menopause also occurs in the patient population, and that treatment-induced amenorrhoea is not distinguishable from menopause unless menses are observed to resume after treatment completion. We discuss a parametric model for the time to amenorrhoea and for the time to the recovery of menses, also accounting for the presence of censoring and for the possibility that treatment causes an anticipation of natural menopause.

Application of the promotion time cure model with time-changing exposure to the study of HIV/AIDS and other infectious diseases

Infectious diseases are caused by single or successive contacts with pathogens. Nevertheless, contacts with pathogens do not implicate infection. In 1993, Yakovlev et al. proposed a model to study a population of cancer patients with a cured fraction, a well adapted model to describe an infectious disease with a unique infection occasion. Extensions of this model have been proposed in the recent years. We present a mechanistic formulation in the context of infectious diseases with multiple infection occasions. It is a mixture model that enables to study risk factors associated with infection intensity at each infection occasion and factors shortening the delay from exposure to clinical event. Simulations are performed to evaluate the model fitting and two examples are presented for illustration: an analysis of an HIV-1 mother-to-child transmission data set and an analysis of nosocomial urinary tract infections data set.

A nonparametric comparison of conditional distributions with nonnegligible cure fractions

Survival data with nonnegligible cure fractions are commonly encountered in clinical cancer clinical research. Recently, several authors (e.g. Kuk and Chen, Biometrika 79 (1992) 531; Maller and Zhou, Journal of Applied Probability, 30 (1993) 602; Peng and Dear, Biometrics, 56 (2000) 237; Sy and Taylor, Biometrics 56 (2000) 227) have proposed to use semiparametric cure models to analyze such data. Much of the existing work has been emphasized on cure detections and regression techniques. In contrast, this project focuses on the hypothesis testing in the presence of a cure fraction. Specifically, our interest lies in detecting whether there exists survival differences among noncured patients between treatment arms. For this purpose, we investigate the use of a modified Cramér-von Mises statistic for two-sample survival comparisons within the framework of cure models. Such a test has been studied by Tamura et al., (Statistics in Medicine 19, 2000, 2169) using bootstrap procedure. We will focus on developing asymptotic theory and convergent algorithms in this paper. We show that the limiting distributions of the Cramér-von Mises statistic under the null hypothesis can be represented by stochastic integrals and a weighted noncentral chi-squares. Both representations lead to concrete numerical schemes for computing the limiting distributions. The algorithms can be easily implemented for data analysis and significantly reduce computing time compared to the bootstrap approach. For illustrative purposes, we apply the proposed test to a published clinical trial.

Safety and efficacy of ?-vinyl GABA (GVG) for the treatment of methamphetamine and/or cocaine addiction

This study examined the safety and efficacy of gamma vinyl-GABA (GVG, vigabatrin) for the treatment of methamphetamine and/or cocaine addiction. A total of 30 subjects, who met DSM-IV criteria for methamphetamine and/or cocaine dependence, were enrolled in an open label 9-week safety study. The protocol was specifically designed to include extensive visual field monitoring as well as outcome measures of therapeutic efficacy. Patients were screened twice weekly for the presence of urinary cocaine, methamphetamine, heroin, alcohol, and marijuana. In total, 18/30 subjects completed the study and 16/18 tested negative for methamphetamine and cocaine during the last 6 weeks of the trial. GVG did not produce any visual field defects or alterations in visual acuity. Furthermore, it did not produce changes in vital signs even with continued use of methamphetamine and cocaine. Thus, under conditions that appear to be appropriate for the successful treatment of methamphetamine and/or cocaine addiction, GVG is safe.

A score test for establishing non-inferiority with respect to short-term survival in two-sample comparisons with identical proportions of long-term survivors

In recent years randomized trials designed to establish non-inferiority of a new treatment as compared to a standard one have been more widely used. Two-sample statistics have been proposed for this equivalence testing problem. However, they are not suited to situations where a long-term survivor fraction is expected. In this paper we propose a score test designed for establishing non-inferiority for the new treatment as compared to the standard one while assuming identical long-term survivor rates. Simulations results show that the proposed statistic has satisfactory size and power as long as certain restricting conditions are verified. A breast cancer trial is analysed as an example.

The pharmacology of putative early-onset antidepressant strategies

Depression is a serious and burdensome illness. Although selective serotonin reuptake inhibitors (SSRIs) have improved safety and tolerability of antidepressant treatment efficacy, the delay in the onset of action have not been improved. There is evidence to suggest that the delay in onset of therapeutic activity is a function of the drugs, rather than the disease. This suggests that research into the biological characteristics of depression and its treatments may yield faster-acting antidepressants. Emerging evidence from clinical studies with mirtazapine, venlafaxine and SSRI augmentation with pindolol suggests that these treatments may relieve antidepressant symptoms more rapidly than SSRIs. The putative mechanism of action of faster-acting antidepressant strategies presented here purports that conventional antidepressants acutely increase the availability of serotonin (5-hydroxytryptamine, 5-HT) or noradrenaline (NA), preferentially at their cell body level, which triggers negative feedback mechanisms. After continued stimulation, these feedback mechanisms become desensitised and the enhanced 5-HT availability is able to enhance 5-HT and/or NA neurotransmission. Putative fast-onset antidepressants, on the other hand, may uncouple such feedback control mechanisms and enhance 5-HT and/or NA neurotransmission more rapidly. Further studies are required to characterise in detail the interactions between NA and 5-HT systems and to definitively establish the early onset of candidate antidepressants such as mirtazapine, venlafaxine and pindolol augmentation.

Semi-parametric models of long- and short-term survival: an application to the analysis of breast cancer survival in Utah by age and stage

A flexible class of semi-parametric survival models is proposed that takes account of long- and short-term covariate effects in cancer survival. The diversity of responses described by the models include non-proportional and crossing survival curves as well as a fraction of long-term survivors. Restricted non-parametric maximum likelihood estimation procedures (RNPMLE) are developed to provide point estimates, confidence intervals and tests for the models. Numerical algorithms to fit semi-parametric survival models are emphasized. The methods are applied to analyse post-treatment survival of breast cancer patients diagnosed in Utah by age and stage.

Cure model analysis in cancer: an application to data from the Children's Cancer Group

The most commonly used statistical methods for evaluating treatment or prognostic effects on cancer outcome--the logrank test and Cox regression analysis--rely on the proportional hazards (PH) assumption in that they have maximal power in this circumstance. Implicitly, these methods emphasize covariate effects on failure times rather than their effects on the proportion of long-term survivors ('cures'), which may be of equal or primary interest. In paediatric cancer, treatment has progressed dramatically in recent decades, and in many diagnoses cures are obtained in a large fraction of patients. A primary focus of clinical research is therefore the achievement of cure. Parametric cure model (PCM) analysis, introduced 50 years ago, is arguably better suited to the analytic requirements of clinical research in paediatric and other cancers where cure is achieved. In this paper two classes of PCMs are described and used to analyse examples from the Children's Cancer Group. These are compared to analyses using Cox regression analysis. Results from PCM analyses are similar or identical to Cox regression analysis when the PH assumption is appropriate. When it is not, PCMs can provide a coherent way to investigate and report covariate effects on the proportion cured separately from their effect on time to failure. Despite their reliance on explicit parametric forms, PCMs often provide a good description of cancer outcome, and are insensitive to lack of fit provided that follow-up is sufficient.

A semiparametric approach for the two-sample comparison of survival times with long-term survivors

In the two-sample comparison of survival times with long-term survivors, the overall difference between the two distributions reflects differences occurring in early follow-up for susceptible subjects and in long-term follow-up for nonsusceptible subjects. In this setting, we propose statistics for testing (i) no overall, (ii) no short-term, and (iii) no long-term difference between the two distributions to be compared. The statistics are derived as follows. A semiparametric model is defined that characterizes a short-term effect and a long-term effect. By approximating this model about no difference in early survival, a time-dependent proportional hazards model is obtained. The statistics are obtained from this working model. The asymptotic distributions of the statistics for testing no overall or no short-term effects are ascertained, while that of the statistic for testing no long-term effect is valid only when the short-term effect is small. Simulation studies investigate the power properties of the proposed tests for different configurations. The results show the interesting behavior of the proposed tests for situations where a short-term effect is expected. An example investigating the impact of progesterone receptors status on local tumor relapse for patients with early breast cancer illustrates the use of the proposed tests.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environmental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed.

Maximum likelihood methods for cure rate models with missing covariates

We propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction, in which the covariates are allowed to be missing. We allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one-dimensional conditional distributions. We propose a novel EM algorithm for maximum likelihood estimation and derive standard errors by using Louis's formula (Louis, 1982, Journal of the Royal Statistical Society, Series B 44, 226-233). Computational techniques using the Monte Carlo EM algorithm are discussed and implemented. A real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology.