Predicting time to prostate cancer recurrence based on joint models for non-linear longitudinal biomarkers and event time outcomes

Illustration of association between change in prostate-specific antigen (PSA) values and time to tumor status after treatment for prostate cancer patients: a joint modelling approach

BACKGROUND

Prostate cancer (PCa) is the most prevalent tumor in men, and Prostate-Specific Antigen (PSA) serves as the primary marker for diagnosis, recurrence, and disease-free status. PSA levels post-treatment guide physicians in gauging disease progression and tumor status (low or high). Clinical follow-up relies on monitoring PSA over time, forming the basis for dynamic prediction. Our study proposes a joint model of longitudinal PSA and time to tumor shrinkage, incorporating baseline variables. The research aims to assess tumor status post-treatment for dynamic prediction, utilizing joint assessment of PSA measurements and time to tumor status.

METHODS

We propose a joint model for longitudinal PSA and time to tumor shrinkage, taking into account baseline BMI and post-treatment factors, including external beam radiation therapy (EBRT), androgen deprivation therapy (ADT), prostatectomy, and various combinations of these interventions. The model employs a mixed-effect sub-model for longitudinal PSA and an event time sub-model for tumor shrinkage.

RESULTS

Results emphasize the significance of baseline factors in understanding the relationship between PSA trajectories and tumor status. Patients with low tumor status consistently exhibit low PSA values, decreasing exponentially within one month post-treatment. The correlation between PSA levels and tumor shrinkage is evident, with the considered factors proving to be significant in both sub-models.

CONCLUSIONS

Compared to other treatment options, ADT is the most effective in achieving a low tumor status, as evidenced by a decrease in PSA levels after months of treatment. Patients with an increased BMI were more likely to attain a low tumor status. The research enhances dynamic prediction for PCa patients, utilizing joint analysis of PSA and time to tumor shrinkage post-treatment. The developed model facilitates more effective and personalized decision-making in PCa care.

Borrowing strength from clinical trials in analysing longitudinal data from a treated cohort: investigating the effectiveness of acetylcholinesterase inhibitors in the management of dementia

BACKGROUND

Health care professionals seek information about effectiveness of treatments in patients who would be offered them in routine clinical practice. Electronic medical records (EMRs) and randomized controlled trials (RCTs) can both provide data on treatment effects; however, each data source has limitations when considered in isolation.

METHODS

A novel modelling methodology which incorporates RCT estimates in the analysis of EMR data via informative prior distributions is proposed. A Bayesian mixed modelling approach is used to model outcome trajectories among patients in the EMR dataset receiving the treatment of interest. This model incorporates an estimate of treatment effect based on a meta-analysis of RCTs as an informative prior distribution. This provides a combined estimate of treatment effect based on both data sources.

RESULTS

The superior performance of the novel combined estimator is demonstrated via a simulation study. The new approach is applied to estimate the effectiveness at 12 months after treatment initiation of acetylcholinesterase inhibitors in the management of the cognitive symptoms of dementia in terms of Mini-Mental State Examination scores. This demonstrated that estimates based on either trials data only (1.10, SE = 0.316) or cohort data only (1.56, SE = 0.240) overestimated this compared with the estimate using data from both sources (0.86, SE = 0.327).

CONCLUSIONS

It is possible to combine data from EMRs and RCTs in order to provide better estimates of treatment effectiveness.

Association of Intra-individual Differences in Estimated GFR by Creatinine Versus Cystatin C With Incident Heart Failure

RATIONALE & OBJECTIVE

Lower estimated glomerular filtration rate (eGFR) is associated with heart failure (HF) risk. However, eGFR based on cystatin C (eGFRcys) and creatinine (eGFRcr) may differ substantially within an individual. The clinical implications of these differences for risk of HF among persons with chronic kidney disease (CKD) are unknown.

STUDY DESIGN

Prospective cohort study.

SETTING & PARTICIPANTS

4,512 adults with CKD and without prevalent HF who enrolled in the Chronic Renal Insufficiency Cohort (CRIC) Study.

EXPOSURE

Difference in GFR estimates (eGFRdiff; ie, eGFRcys minus eGFRcr).

OUTCOME

Incident HF hospitalization.

ANALYTICAL APPROACH

Fine-Gray proportional subhazards regression was used to investigate the associations of baseline, time-updated, and slope of eGFRdiff with incident HF.

RESULTS

Of 4,512 participants, one-third had eGFRcys and eGFRcr values that differed by over 15 mL/min/1.73 m2. In multivariable-adjusted models, each 15 mL/min/1.73 m2 lower baseline eGFRdiff was associated with higher risk of incident HF hospitalization (hazard ratio [HR], 1.20 [95% CI, 1.07-1.34]). In time-updated analyses, those with eGFRdiff less than -15 mL/min/1.73 m2 had higher risk of incident HF hospitalization (HR, 1.99 [95% CI, 1.39-2.86]), and those with eGFRdiff ≥15 mL/min/1.73 m2 had lower risk of incident HF hospitalization (HR, 0.67 [95% CI, 0.49-0.91]) compared with participants with similar eGFRcys and eGFRcr. Participants with faster declines in eGFRcys relative to eGFRcr had higher risk of incident HF (HR, 1.49 [95% CI, 1.19-1.85]) compared with those in whom eGFRcys and eGFRcr declined in parallel.

LIMITATIONS

Entry into the CRIC Study was determined by eGFRcr, which constrained the range of baseline eGFRcr-but not eGFRcys-values.

CONCLUSIONS

Among persons with CKD who have large differences between eGFRcys and eGFRcr, risk for incident HF is more strongly associated with eGFRcys. Diverging slopes between eGFRcys and eGFRcr over time are also independently associated with risk of incident HF.

Joint models for dynamic prediction in localised prostate cancer: a literature review

BACKGROUND

Prostate cancer is a very prevalent disease in men. Patients are monitored regularly during and after treatment with repeated assessment of prostate-specific antigen (PSA) levels. Prognosis of localised prostate cancer is generally good after treatment, and the risk of having a recurrence is usually estimated based on factors measured at diagnosis. Incorporating PSA measurements over time in a dynamic prediction joint model enables updates of patients' risk as new information becomes available. We review joint model strategies that have been applied to model time-dependent PSA trajectories to predict time-to-event outcomes in localised prostate cancer.

METHODS

We identify articles that developed joint models for prediction of localised prostate cancer recurrence over the last two decades. We report, compare, and summarise the methodological approaches and applications that use joint modelling accounting for two processes: the longitudinal model (PSA), and the time-to-event process (clinical failure). The methods explored differ in how they specify the association between these two processes.

RESULTS

Twelve relevant articles were identified. A range of methodological frameworks were found, and we describe in detail shared-parameter joint models (9 of 12, 75%) and joint latent class models (3 of 12, 25%). Within each framework, these articles presented model development, estimation of dynamic predictions and model validations.

CONCLUSIONS

Each framework has its unique principles with corresponding advantages and differing interpretations. Regardless of the framework used, dynamic prediction models enable real-time prediction of individual patient prognosis. They utilise all available longitudinal information, in addition to baseline prognostic risk factors, and are superior to traditional baseline-only prediction models.

Landmarking 2.0: Bridging the gap between joint models and landmarking

The problem of dynamic prediction with time‐dependent covariates, given by biomarkers, repeatedly measured over time, has received much attention over the last decades. Two contrasting approaches have become in widespread use. The first is joint modeling, which attempts to jointly model the longitudinal markers and the event time. The second is landmarking, a more pragmatic approach that avoids modeling the marker process. Landmarking has been shown to be less efficient than correctly specified joint models in simulation studies, when data are generated from the joint model. When the mean model is misspecified, however, simulation has shown that joint models may be inferior to landmarking. The objective of this article is to develop methods that improve the predictive accuracy of landmarking, while retaining its relative simplicity and robustness. We start by fitting a working longitudinal model for the biomarker, including a temporal correlation structure. Based on that model, we derive a predictable time‐dependent process representing the expected value of the biomarker after the landmark time, and we fit a time‐dependent Cox model based on the predictable time‐dependent covariate. Dynamic predictions based on this approach for new patients can be obtained by first deriving the expected values of the biomarker, given the measured values before the landmark time point, and then calculating the predicted probabilities based on the time‐dependent Cox model. We illustrate the approach in predicting overall survival in liver cirrhosis patients based on prothrombin index.

Association between prostate-specific antigen change over time and prostate cancer recurrence risk: A joint model

Background

Prostate specific antigen (PSA) is an important biomarker to monitor patients after treated with radiation therapy (RT). The aim of this study is to evaluate the relationship between the PSA data and prostate cancer recurrence using the joint modeling.

Methods

This historical cohort study was performed on 422 prostate cancer patients. Inclusion criteria included: patients with localized prostate cancer referring to Cancer Institute in Tehran (Iran) from 2007 to 2012, and under radiation therapy. Joint model has two components or sub-models. We showed the results by parameter estimating the longitudinal sub-model and survival sub-model. EM algorithm, Newton-Gauss and Gauss-Hermit law were used for final model parameters. R software version 3.2 was used for statistical analysis.

Results

In this study, considering the inclusion and exclusion criteria, out of 422 patients, the data on 314 cases were selected for analysis and the main result of joint model was obtained. PSA directly and significantly was associated with recurrence risk, therefore increasing 2.6 ml/lit PSA (one unit in transformed PSA) increases 39% recurrence risk (95% CI for RR: 1.09-1.77). Also, slope of PSA trend has significant association with prostate cancer recurrence risk (95% CI for RR: 1.05-1.41).

Conclusion

This study showed a significant relationship between PSA, and its slope with the recurrence risk by joint model, with regard to the pathological, demographic and clinical features in the Iranian population.

An Intelligent Decision-Making Support System for the Detection and Staging of Prostate Cancer in Developing Countries

Most developing countries face huge challenges in the medical field; scarce medical resources and inadequate medical personnel will affect the development and stability of the society. Therefore, for most developing countries, the development of intelligent medical systems can greatly alleviate the social contradictions arising from this problem. In this study, a new data decision-making intelligent system for prostate cancer based on perceptron neural network is proposed, which mainly makes decisions by associating some relevant disease indicators and combining them with medical images. Through data collection, analysis and integration of medical data, as well as the disease detection and decision-making process, patients are given an auxiliary diagnosis and treatment, so as to solve the problems and social contradictions faced by most developing countries. Through the study of hospitalization information of more than 8,000 prostate patients in three hospitals, about 2,156,528 data items were collected and compiled for experiment purposes. Experimental data shows that when the patient base increases from 200 to 8,000, the accuracy of the machine-assisted diagnostic system will increase from 61% to 87%, and the doctor's diagnosis rate will be reduced to 81%. From the study, it is concluded that when the patient base reaches a certain number, the diagnostic accuracy of the machine-assisted diagnosis system will exceed the doctor's expertise. Therefore, intelligent systems can help doctors and medical experts treat patients more effectively.

An introduction to joint models-applications in nephrology

In nephrology, a great deal of information is measured repeatedly in patients over time, often alongside data on events of clinical interest. In this introductory article we discuss how these two types of data can be simultaneously analysed using the joint model (JM) framework, illustrated by clinical examples from nephrology. As classical survival analysis and linear mixed models form the two main components of the JM framework, we will also briefly revisit these techniques.

Joint models for longitudinal and time-to-event data: a review of reporting quality with a view to meta-analysis

BACKGROUND

Joint models for longitudinal and time-to-event data are commonly used to simultaneously analyse correlated data in single study cases. Synthesis of evidence from multiple studies using meta-analysis is a natural next step but its feasibility depends heavily on the standard of reporting of joint models in the medical literature. During this review we aim to assess the current standard of reporting of joint models applied in the literature, and to determine whether current reporting standards would allow or hinder future aggregate data meta-analyses of model results.

METHODS

We undertook a literature review of non-methodological studies that involved joint modelling of longitudinal and time-to-event medical data. Study characteristics were extracted and an assessment of whether separate meta-analyses for longitudinal, time-to-event and association parameters were possible was made.

RESULTS

The 65 studies identified used a wide range of joint modelling methods in a selection of software. Identified studies concerned a variety of disease areas. The majority of studies reported adequate information to conduct a meta-analysis (67.7% for longitudinal parameter aggregate data meta-analysis, 69.2% for time-to-event parameter aggregate data meta-analysis, 76.9% for association parameter aggregate data meta-analysis). In some cases model structure was difficult to ascertain from the published reports.

CONCLUSIONS

Whilst extraction of sufficient information to permit meta-analyses was possible in a majority of cases, the standard of reporting of joint models should be maintained and improved. Recommendations for future practice include clear statement of model structure, of values of estimated parameters, of software used and of statistical methods applied.

Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers

Prostate-specific antigen (PSA) is a widely used marker in clinical trials for patients with prostate cancer. We develop a mixture model to estimate longitudinal PSA trajectory in response to treatment. The model accommodates subjects responding and not responding to therapy through a mixture of two functions. A responder is described by a piecewise linear function, represented by an intercept, a PSA decline rate, a period of PSA decline, and a PSA rising rate; a nonresponder is described by an increasing linear function with an intercept and a PSA rising rate. Each trajectory is classified as a linear or a piecewise linear function with a certain probability, and the weighted average of these two functions sufficiently characterizes a variety of patterns of PSA trajectories. Furthermore, this mixture structure enables us to derive clinically useful endpoints such as a response rate and time-to-progression, as well as biologically meaningful endpoints such as a cancer cell killing fraction and tumor growth delay. We compare our model with the most commonly used dynamic model in the literature and show its advantages. Finally, we illustrate our approach using data from two multicenter prostate cancer trials. The R code used to produce the analyses reported in this paper is available on request.

Timing and effect of a safe routes to school program on child pedestrian injury risk during school travel hours: Bayesian changepoint and difference-in-differences analysis

BACKGROUND

In 2005, the US Congress allocated $612 million for a national Safe Routes to School (SRTS) program to encourage walking and bicycling to schools. We evaluated the effectiveness of a SRTS in controlling pedestrian injuries among school-age children.

METHODS

Bayesian changepoint analysis was applied to model the quarterly counts of pedestrian injuries among 5- to 19-year old children in New York City between 2001 and 2010 during school-travel hours in census tracts with and without SRTS. Overdispersed Poisson model was used to estimate difference-in-differences in injury risk between census tracts with and without SRTS following the changepoint.

RESULTS

In SRTS-intervention census tracts, a change point in the quarterly counts of injuries was identified in the second quarter of 2008, which was consistent with the timing of the implementation of SRTS interventions. In census tracts with SRTS interventions, the estimated quarterly rates of pedestrian injury per 10,000 population among school-age children during school-travel hours were 3.47 (95% Credible Interval [CrI] 2.67, 4.39) prior to the changepoint, and 0.74 (95% CrI 0.30, 1.50) after the changepoint. There was no change in the average number of quarterly injuries in non-SRTS census tracts. Overdispersed Poisson modeling revealed that SRTS implementation was associated with a 44% reduction (95% Confidence Interval [CI] 87% decrease to 130% increase) in school-age pedestrian injury risk during school-travel hours.

CONCLUSIONS

Bayesian changepoint analysis of quarterly counts of school-age pedestrian injuries successfully identified the timing of SRTS intervention in New York City. Implementation of the SRTS program in New York City appears to be effective in reducing school-age pedestrian injuries during school-travel hours.

Deriving benefit of early detection from biomarker-based prognostic models

Many prognostic models for cancer use biomarkers that have utility in early detection. For example, in prostate cancer, models predicting disease-specific survival use serum prostate-specific antigen levels. These models typically show that higher marker levels are associated with poorer prognosis. Consequently, they are often interpreted as indicating that detecting disease at a lower threshold of the biomarker is likely to generate a survival benefit. However, lowering the threshold of the biomarker is tantamount to early detection. For survival benefit to not be simply an artifact of starting the survival clock earlier, we must account for the lead time of early detection. It is not known whether the existing prognostic models imply a survival benefit under early detection once lead time has been accounted for. In this article, we investigate survival benefit implied by prognostic models where the predictor(s) of disease-specific survival are age and/or biomarker level at disease detection. We show that the benefit depends on the rate of biomarker change, the lead time, and the biomarker level at the original date of diagnosis as well as on the parameters of the prognostic model. Even if the prognostic model indicates that lowering the threshold of the biomarker is associated with longer disease-specific survival, this does not necessarily imply that early detection will confer an extension of life expectancy.

Dynamic Optimal Strategy for Monitoring Disease Recurrence

Surveillance to detect cancer recurrence is an important part of care for cancer survivors. In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient's distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study. We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly, to address heterogeneity of patients and disease, to discover distinct biomarker trajectory patterns, to classify patients into different risk groups, and to predict the risk of disease recurrence. The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients' current risk derived from periodically updated biomarker measurements and other indicators of disease spread. The optimal biomarker assessment time is derived using a utility function. We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment. We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.

Screening for prostate cancer using multivariate mixed-effects models

Using several variables known to be related to prostate cancer, a multivariate classification method is developed to predict the onset of clinical prostate cancer. A multivariate mixed-effects model is used to describe longitudinal changes in prostate specific antigen (PSA), a free testosterone index (FTI), and body mass index (BMI) before any clinical evidence of prostate cancer. The patterns of change in these three variables are allowed to vary depending on whether the subject develops prostate cancer or not and the severity of the prostate cancer at diagnosis. An application of Bayes' theorem provides posterior probabilities that we use to predict whether an individual will develop prostate cancer and, if so, whether it is a high-risk or a low-risk cancer. The classification rule is applied sequentially one multivariate observation at a time until the subject is classified as a cancer case or until the last observation has been used. We perform the analyses using each of the three variables individually, combined together in pairs, and all three variables together in one analysis. We compare the classification results among the various analyses and a simulation study demonstrates how the sensitivity of prediction changes with respect to the number and type of variables used in the prediction process.

The nesting of search contexts within natural scenes: evidence from contextual cuing

In a contextual cuing paradigm, we examined how memory for the spatial structure of a natural scene guides visual search. Participants searched through arrays of objects that were embedded within depictions of real-world scenes. If a repeated search array was associated with a single scene during study, then array repetition produced significant contextual cuing. However, expression of that learning was dependent on instantiating the original scene in which the learning occurred: Contextual cuing was disrupted when the repeated array was transferred to a different scene. Such scene-specific learning was not absolute, however. Under conditions of high scene variability, repeated search array were learned independently of the scene background. These data suggest that when a consistent environmental structure is available, spatial representations supporting visual search are organized hierarchically, with memory for functional subregions of an environment nested within a representation of the larger scene.

Confirmation of a low α/β ratio for prostate cancer treated by external beam radiation therapy alone using a post-treatment repeated-measures model for PSA dynamics

PURPOSE

To estimate the α/β ratio of prostate cancer treated with external beam radiation only by use of a model of long-term prostate-specific antigen (PSA) dynamics.

METHODS AND MATERIALS

Repeated measures of PSA from 5,093 patients from 6 institutions treated for localized prostate cancer by external beam radiation therapy (EBRT) without planned androgen deprivation were analyzed. A biphasic linear mixed model described the post-treatment evolution of PSA, rather than a conventional model of time to biochemical recurrence. The model was adjusted for standard prognostic factors (T stage, initial PSA level, and Gleason score) and cohort-specific effects. The radiation dose fractionation effect was estimated from the long-term rate of rise of PSA level.

RESULTS

Adjusted for other factors, total dose of EBRT and sum of squared doses per fraction were associated with long-term rate of change of PSA level (p = 0.0017 and p = 0.0003, respectively), an increase of each being associated with a lower rate of rise. The α/β ratio was estimated at 1.55 Gy (95% confidence band, 0.46-4.52 Gy). This estimate was robust to adjustment of the linear mixed model.

CONCLUSIONS

By analysis of a large EBRT-only cohort along with a method that uses all the repeated measures of PSA after the end of treatment, a low and precise α/β was estimated. These data support the use of hypofractionation at fractional doses up to 2.8 Gy but cannot presently be assumed to accurately represent higher doses per fraction.

An examination of Bayesian statistical approaches to modeling change in cognitive decline in an Alzheimer's disease population

The mini mental state examination (MMSE) is a common tool for measuring cognitive decline in Alzhiemer's Disease (AD) subjects. Subjects are usually observed for a specified period of time or until death to determine the trajectory of the decline which for the most part appears to be linear. However, it may be noted that the decline may not be modeled by a single linear model over a specified period of time. There may be a point called a change point where the rate or gradient of the decline may change depending on the length of time of observation. A Bayesian approach is used to model the trajectory and determine an appropriate posterior estimate of the change point as well as the predicted model of decline before and after the change point. Estimates of the appropriate parameters as well as their posterior credible regions or regions of interest are established. Coherent prior to posterior analysis using mainly non informative priors for the parameters of interest is provided. This approach is applied to an existing AD database.

A Bayesian semiparametric survival model with longitudinal markers

We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.

Interpreting trial results in light of conflicting evidence: a Bayesian analysis of adjuvant chemotherapy for non-small-cell lung cancer

PURPOSE

When successive randomized trials contradict prior evidence, clinicians may be unsure how to evaluate them: Does accumulating evidence warrant changing practice? An increasingly popular solution, Bayesian statistics quantitatively evaluate new results in context. This study provides a clinically relevant example of Bayesian methods.

METHODS

Three recent non-small-cell lung cancer adjuvant chemotherapy trials were evaluated in light of prior conflicting data. Results were used from International Adjuvant Lung Trial (IALT), JBR.10, and Adjuvant Navelbine International Trialist Association (ANITA). Prior evidence was sequentially updated to calculate the probability of each survival benefit level (overall and by stage) and variance. Sensitivity analysis was performed using expert opinion and uninformed estimates of survival benefit prior probability.

RESULTS

The probability of a 4% survival benefit increased from 33% before IALT to 64% after IALT. After sequential updating with JBR.10 and ANITA, this probability was 82% (hazard ratio = 0.84; 95% CI, 0.77 to 0.91). IALT produced the largest decrease in variance (61%) and decreased the chance of survival decrement to 0%. Sensitivity analysis did not support a survival benefit after IALT. However, sequential updating substantiated a 4% survival benefit and, for stage II and III, more than 90% probability of a 6% benefit and 50% probability of a 12% benefit.

CONCLUSION

When evaluated in context with prior data, IALT did not support a 4% survival benefit. However, sequential updating with JBR.10 and ANITA did. A model for future assessments, this study demonstrates the unique ability of Bayesian analysis to evaluate results that contradict prior evidence.

Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: a joint modeling approach

Prostate-specific antigen (PSA) is a biomarker routinely and repeatedly measured on prostate cancer patients treated by radiation therapy (RT). It was shown recently that its whole pattern over time rather than just its current level was strongly associated with prostate cancer recurrence. To more accurately guide clinical decision making, monitoring of PSA after RT would be aided by dynamic powerful prognostic tools that incorporate the complete posttreatment PSA evolution. In this work, we propose a dynamic prognostic tool derived from a joint latent class model and provide a measure of variability obtained from the parameters asymptotic distribution. To validate this prognostic tool, we consider predictive accuracy measures and provide an empirical estimate of their variability. We also show how to use them in the longitudinal context to compare the dynamic prognostic tool we developed with a proportional hazard model including either baseline covariates or baseline covariates and the expected level of PSA at the time of prediction in a landmark model. Using data from 3 large cohorts of patients treated after the diagnosis of prostate cancer, we show that the dynamic prognostic tool based on the joint model reduces the error of prediction and offers a powerful tool for individual prediction.

Hierarchical changepoint models for biochemical markers illustrated by tracking postradiotherapy prostate-specific antigen series in men with prostate cancer

PURPOSE

Biomarkers provide valuable information when detecting disease onset or monitoring disease progression; examples include bone mineral density (for osteoporosis), cholesterol (for coronary artery diseases), or prostate-specific antigens (PSA, for prostate cancer). Characteristics of markers series can then be used as prognostic factors of disease progression, such as the postradiotherapy PSA doubling time in men treated for prostate cancer. The statistical analysis of such data has to incorporate the within and between-series variabilities, the complex patterns of the series over time, the unbalanced format of the data, and the possibly nonconstant precision of the measurements.

METHODS

We base our analysis on a population-based cohort of 470 men treated with radiotherapy for prostate cancer; after treatment, the log(2)PSA concentrations follow a piecewise-linear pattern. We illustrate the flexibility of Bayesian hierarchical changepoint models by estimating the individual and population postradiotherapy log(2)PSA profiles; parameters such as the PSA nadir and the PSA doubling time were estimated, and their associations with baseline patient characteristics were investigated. The residual PSA variability was modeled as a function of the PSA concentration. For comparison purposes, two alternative models were briefly considered.

RESULTS

Precise estimates of all parameters of the PSA trajectory are provided at both the individual and population levels. Estimates suggest greater PSA variability at lower PSA concentrations, as well as an association between shorter PSAdts and greater baseline PSA levels, higher Gleason scores, and older age.

CONCLUSIONS

The use of Bayesian hierarchical changepoint models accommodates multiple complex features of longitudinal data, permits realistic modeling of the variability as a function of the marker concentration, and provides precise estimates of all clinically important parameters. This type of model should be applicable to the study of marker series in other diseases.

Quantifying the Predictive Performance of Prognostic Models for Censored Survival Data with Time-Dependent Covariates

Prognostic models in survival analysis typically aim to describe the association between patient covariates and future outcomes. More recently, efforts have been made to include covariate information that is updated over time. However, there exists as yet no standard approach to assess the predictive accuracy of such updated predictions. In this article, proposals from the literature are discussed and a conditional loss function approach is suggested, illustrated by a publicly available data set.

Semiparametric modeling of longitudinal measurements and time-to-event data--a two-stage regression calibration approach

SUMMARY

In this article we investigate regression calibration methods to jointly model longitudinal and survival data using a semiparametric longitudinal model and a proportional hazards model. In the longitudinal model, a biomarker is assumed to follow a semiparametric mixed model where covariate effects are modeled parametrically and subject-specific time profiles are modeled nonparametrially using a population smoothing spline and subject-specific random stochastic processes. The Cox model is assumed for survival data by including both the current measure and the rate of change of the underlying longitudinal trajectories as covariates, as motivated by a prostate cancer study application. We develop a two-stage semiparametric regression calibration (RC) method. Two variations of the RC method are considered, risk set regression calibration and a computationally simpler ordinary regression calibration. Simulation results show that the two-stage RC approach performs well in practice and effectively corrects the bias from the naive method. We apply the proposed methods to the analysis of a dataset for evaluating the effects of the longitudinal biomarker PSA on the recurrence of prostate cancer.

Exploiting flow injection system with mini-immunoaffinity chromatographic column for chondroitin sulfate proteoglycans assay

A flow injection (FI) system with a mini-immunoaffinity chromatographic column was used to perform on-line assays of specific proteoglycans. The 300-microL mini-column contained beads coupled with monoclonal antibodies against the specific sulfation pattern of chondroitin sulfate proteoglycans, which have been reported to be a potential biomarker for cancer. The amount of these proteoglycans present was estimated indirectly from their protein content using the Bradford assay, which is an alternative to a direct carbohydrate assay. The system developed was tested by assaying for chondroitin sulfate proteoglycans in sera from patients with various cancers and comparing the results to those obtained for sera from healthy people. The results indicated that this approach could be used as a cost-effective alternative system for determining the amount of these specific biomarker proteoglycans. The column could be reused at least 90 times, with each run consisting of 200 microL of serum sample diluted twofold; an analysis rate of 30 min per run was achieved, as compared to 4 h for a batch procedure.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Random change point model for joint modeling of cognitive decline and dementia

We propose a joint model for cognitive decline and risk of dementia to describe the pre-diagnosis phase of dementia. We aim to estimate the time when the cognitive evolution of subjects in the pre-dementia phase becomes distinguishable from normal evolution and to study whether the shape of cognitive decline depends on educational level. The model combines a piecewise polynomial mixed model with a random change point for the evolution of the cognitive test and a log-normal model depending on the random change point for the time to dementia. Parameters are estimated by maximum likelihood using a Newton-Raphson-like algorithm. The expected cognitive evolution given age to dementia is then derived and the marginal distribution of dementia is estimated to check the log-normal assumption.

A shared random effects model for censored medical costs and mortality

In this paper, we propose a model for medical costs recorded at regular time intervals, e.g. every month, as repeated measures in the presence of a terminating event, such as death. Prior models have related monthly medical costs to time since entry, with extra costs at the final observations at the time of death. Our joint model for monthly medical costs and survival time incorporates two important new features. First, medical cost and survival may be correlated because more 'frail' patients tend to accumulate medical costs faster and die earlier. A joint random effects model is proposed to account for the correlation between medical costs and survival by a shared random effect. Second, monthly medical costs usually increase during the time period prior to death because of the intensive care for dying patients. We present a method for estimating the pattern of cost prior to death, which is applicable if the pattern can be characterized as an additive effect that is limited to a fixed time interval, say b units of time before death. This 'turn back time' method for censored observations censors cost data b units of time before the actual censoring time, while keeping the actual censoring time for the survival data. Time-dependent covariates can be included. Maximum likelihood estimation and inference are carried out through a Monte Carlo EM algorithm with a Metropolis-Hastings sampler in the E-step. An analysis of monthly outpatient EPO medical cost data for dialysis patients is presented to illustrate the proposed methods.

Critical analysis of prostate-specific antigen doubling time calculation methodology

BACKGROUND

Prostate-specific antigen (PSA) doubling time (PSADT) has emerged as an important surrogate marker of disease progression and survival in men with prostate carcinoma. The literature is replete with different methods for calculating PSADT. The objective of the current study was to identify the method that best described PSA growth over time and predicted disease-specific survival in men with androgen-independent prostate carcinoma.

METHODS

PSADT was calculated for 122 patients with androgen-independent prostate carcinoma using 2 commonly used methods: best-line fit (BLF) and first and last observations (FLO). Then, PSADT was calculated by using both a random coefficient linear (RCL) model and a random coefficient quadratic (RCQ) model. Statistical analysis was used to compare the ability of the methods to fit the patients' PSA profiles and to predict disease-specific survival.

RESULTS

The RCQ model provided the best fit of the patients' PSA profiles, as determined according to the significance of the added parameters for the RCQ equation (P < or = 0.002). The PSADT estimates from the FLO method, the RCL model, and the RCQ model were highly significant predictors (P < 0.001) of disease-specific survival, whereas estimates from the BLF method were not found to be significant predictors (P = 0.66). PSADT estimates from the RCQ and RCL models provided an improved correlation of disease-specific survival (both R(2) = 0.55) compared to the FLO (R(2) = 0.11) and BFL (R(2) = 0.003) methods.

CONCLUSIONS

Random coefficient methods provided a more reliable fit of PSA profiles than other models and were superior to other available models for predicting disease-specific survival in patients with androgen-independent prostate carcinoma. The authors concluded that consideration should be given to applying the RCL or RCQ models in future assessments of PSADT as a predictive parameter.

Use of joint models to assess treatment effects on disease markers and clinical events: the Proscar Long-Term Efficacy and Safety Study (PLESS)

Clinical trials often collect longitudinal measurements of a disease marker and time to a major clinical event of the disease to assess treatment effects. It makes sense to combine the treatment effects on both the longitudinal disease marker and the time to clinical event, especially when the clinical event is also mediated through the disease marker over time. In this paper we apply a joint modeling approach in the assessment of the treatment effects in treating benign prostatic hyperplasia (BPH) for the Proscar Long-Term Efficacy and Safety Study (PLESS).

Individualized predictions of disease progression following radiation therapy for prostate cancer

PURPOSE

Following treatment for localized prostate cancer, men are monitored with serial prostate-specific antigen (PSA) measurements. Refining the predictive value of post-treatment PSA determinations may add to clinical management, and we have developed a model that predicts future PSA values and the time to future clinical recurrence for individual patients.

PATIENTS AND METHODS

Data from 934 patients treated between 1987 and 2000 were used to develop a comprehensive statistical model to fit the clinical recurrence events and patterns of PSA data. A logistic model was used for the probability of cure, mixed models were used for serial PSA measurements, and a proportional hazards model was used for recurrences. Data available through February 2001 were fit to the model, and data collected between February 2001 and September 2003 were used for validation.

RESULTS

T-stage, baseline PSA, and radiotherapy dosage are all associated with probability of cure. The risk of clinical recurrence in those not cured is strongly affected by the slope of PSA values. We show how the model can be used for individual monitoring of disease progression. For each patient the model predicts, based on baseline characteristics and all post-treatment PSA values, the probability of future clinical recurrences and future PSA values. The model accurately predicts risk of recurrence and future PSA values in the validation data set.

CONCLUSION

This predictive information on future PSA values and the risk of clinical relapse for each individual patient, which can be updated with each additional PSA value, may prove useful to patients and physicians in determining post-treatment salvage strategies.