Changepoint Modeling of Longitudinal PSA as a Biomarker for Prostate Cancer. In: Gatsonis C, Hodges JS, Kass RE, Mcculloch R, Rossi P, Singpurwalla ND, editors. Case Studies in Bayesian Statistics. New York: Springer; 1997. pp. 435-56. [DOI: 10.1007/978-1-4612-2290-3_14]

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.

Validation and characterization of human kallikrein 11 as a serum marker for diagnosis of ovarian carcinoma

PURPOSE

The serum tumor marker CA 125 is elevated in most clinically advanced ovarian carcinomas, and currently, one of the most promising early detection strategies for ovarian cancer uses CA 125 level in conjunction with imaging. However, CA 125 is elevated in only 50% of early-stage ovarian cancer and is often elevated in women with benign ovarian tumors and other gynecologic diseases. Additional markers may improve on its individual performance if they increase sensitivity and specificity and are less sensitive to other gynecologic conditions. The human kallikrein 11 (hK11) marker has been reported to have favorable predictive value for ovarian cancer, although, by itself, it may be inferior to CA 125.

EXPERIMENTAL DESIGN

We here validate the performance of hK11 on an independent data set and further characterize its behavior in multiple types of controls. We also investigate its behavior when combined with CA 125 to form a composite marker. hK11 had not previously been evaluated on these serum samples. CA 125, hK11, and the composite marker were evaluated for their performance in identifying ovarian cancer and for temporal stability.

RESULTS

hK11 significantly distinguished ovarian cancer cases from healthy controls and is less sensitive to benign ovarian disease than is CA 125.

CONCLUSION

We conclude that hK11 is a valuable new biomarker for ovarian cancer and its temporal stability implies that it may do even better when used in a longitudinal screening program for early detection.

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.

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

Biological markers that are both sensitive and specific for tumour regrowth or metastasis are increasingly becoming available and routinely monitored during the regular follow-up of patients treated for cancer. Obtained by a simple blood test, these markers provide an inexpensive non-invasive means for the early detection of recurrence (or progression). Currently, the longitudinal behaviour of the marker is viewed as an indicator of early disease progression, and is applied by a physician in making clinical decisions. One marker that has been studied for use in both population screening for early disease and for detection of recurrence in prostate cancer patients is PSA. The elevation of PSA levels is known to precede clinically detectable recurrence by 2 to 5 years, and current clinical practice often relies partially on multiple recent rises in PSA to trigger a change in treatment. However, the longitudinal trajectory for individual markers is often non-linear; in many cases there is a decline immediately following radiation therapy or surgery, a plateau during remission, followed by an exponential rise following the recurrence of the cancer. The aim of this article is to determine the multiple aspects of the longitudinal PSA biomarker trajectory that can be most sensitive for predicting time to clinical recurrence. Joint Bayesian models for the longitudinal measures and event times are utilized based on non-linear hierarchical models, implied by unknown change-points, for the longitudinal trajectories, and a Cox proportional hazard model for progression times, with functionals of the longitudinal parameters as covariates in the Cox model. Using Markov chain Monte Carlo sampling schemes, the joint model is fit to longitudinal PSA measures from 676 patients treated at Massachusetts General Hospital between the years 1988 and 1995 with follow-up to 1999. Based on these data, predictive schemes for detecting cancer recurrence in new patients based on their longitudinal trajectory are derived.

A mixture model for longitudinal data with application to assessment of noncompliance

In clinical trials of a self-administered drug, repeated measures of a laboratory marker, which is affected by study medication and collected in all treatment arms, can provide valuable information on population and individual summaries of compliance. In this paper, we introduce a general finite mixture of nonlinear hierarchical models that allows estimates of component membership probabilities and random effect distributions for longitudinal data arising from multiple subpopulations, such as from noncomplying and complying subgroups in clinical trials. We outline a sampling strategy for fitting these models, which consists of a sequence of Gibbs, Metropolis-Hastings, and reversible jump steps, where the latter is required for switching between component models of different dimensions. Our model is applied to identify noncomplying subjects in the placebo arm of a clinical trial assessing the effectiveness of zidovudine (AZT) in the treatment of patients with HIV, where noncompliance was defined as initiation of AZT during the trial without the investigators' knowledge. We fit a hierarchical nonlinear change-point model for increases in the marker MCV (mean corpuscular volume of erythrocytes) for subjects who noncomply and a constant mean random effects model for those who comply. As part of our fully Bayesian analysis, we assess the sensitivity of conclusions to prior and modeling assumptions and demonstrate how external information and covariates can be incorporated to distinguish subgroups.