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

Incorporating longitudinal biomarkers for dynamic risk prediction in the era of big data: A pseudo-observation approach

Longitudinal biomarker data are often collected in studies, providing important information regarding the probability of an outcome of interest occurring at a future time. With many new and evolving technologies for biomarker discovery, the number of biomarker measurements available for analysis of disease progression has increased dramatically. A large amount of data provides a more complete picture of a patient's disease progression, potentially allowing us to make more accurate and reliable predictions, but the magnitude of available data introduces challenges to most statistical analysts. Existing approaches suffer immensely from the curse of dimensionality. In this article, we propose methods for making dynamic risk predictions using repeatedly measured biomarkers of a large dimension, including cases when the number of biomarkers is close to the sample size. The proposed methods are computationally simple, yet sufficiently flexible to capture complex relationships between longitudinal biomarkers and potentially censored events times. The proposed approaches are evaluated by extensive simulation studies and are further illustrated by an application to a data set from the Nephrotic Syndrome Study Network.

Plasma Tie2 is a tumor vascular response biomarker for VEGF inhibitors in metastatic colorectal cancer

Oncological use of anti-angiogenic VEGF inhibitors has been limited by the lack of informative biomarkers. Previously we reported circulating Tie2 as a vascular response biomarker for bevacizumab-treated ovarian cancer patients. Using advanced MRI and circulating biomarkers we have extended these findings in metastatic colorectal cancer (n = 70). Bevacizumab (10 mg/kg) was administered to elicit a biomarker response, followed by FOLFOX6-bevacizumab until disease progression. Bevacizumab induced a correlation between Tie2 and the tumor vascular imaging biomarker, Ktrans (R:-0.21 to 0.47) implying that Tie2 originated from the tumor vasculature. Tie2 trajectories were independently associated with pre-treatment tumor vascular characteristics, tumor response, progression free survival (HR for progression = 3.01, p = 0.00014; median PFS 248 vs. 348 days p = 0.0008) and the modeling of progressive disease (p < 0.0001), suggesting that Tie2 should be monitored clinically to optimize VEGF inhibitor use. A vascular response is defined as a 30% reduction in Tie2; vascular progression as a 40% increase in Tie2 above the nadir. Tie2 is the first, validated, tumor vascular response biomarker for VEGFi.

Heterogeneous growth bent-cable models for time-to-event and longitudinal data: application to AIDS studies

The major limitations of growth curve mixture models for HIV/AIDS data are the usual assumptions of normality and monophasic curves within latent classes. This article addresses these limitations by using non-normal skewed distributions and multiphasic patterns for outcomes of prospective studies. For such outcomes, new skew-t (ST) distributions are proposed for modeling heterogeneous growth trajectories, which exhibit not abrupt but gradual multiphasic changes from a declining trend to an increasing trend over time. We assess these clinically important features of longitudinal HIV/AIDS data using the bent-cable framework within a context of a joint modeling of time-to-event process and response process. A real dataset from an AIDS clinical study is used to illustrate the proposed methods.

Exploration of time points and cut-off values for early tumour shrinkage to predict survival outcomes of patients with metastatic colorectal cancer treated with first-line chemotherapy using a biexponential model for change in tumour size

Background

Several studies reported that early tumour shrinkage (ETS) was associated with overall survival in patients with metastatic colorectal cancer (mCRC) treated with first-line chemotherapy. However, appropriate time point and cut-off value for ETS remain unclear because these varied in previous studies.

Patients and methods

We investigated patients with mCRC who received FOLFOX or FOLFIRI with/without molecular-targeted agents as first-line treatment between 2005 and 2014. Using a biexponential model for change in tumour size, a relative change in the sum of the longest diameters of target lesions from baseline was estimated at a certain time point in each individual patient. Associations of survival outcomes with ETS at various time points based on various cut-off values were evaluated by Cox regression analysis with a landmark approach.

Results

Among the 67 patients reviewed, the objective response rate was 73.1% (95% CI 62.5% to 83.7%), the median progression-free survival was 10.9 months (95% CI 8.7 to 13.0 months) and the median overall survival was 25.6 months (95% CI 20.1 to 27.3 months). The model for change in tumour size agreed with the actual measured sizes well. Multivariate Cox regression analysis, including performance status, number of metastatic sites and use of targeted agents, showed that ETS at 8 weeks based on a cut-off value of 20% was most significantly associated with overall survival (HR: 0.404, 95% CI 0.231 to 0.707, P=0.0015).

Conclusion

It is suggested that a time point of 8 weeks and a cut-off value of 20% may be optimal criteria for defining ETS.

Bayesian two-part bent-cable Tobit models with skew distributions: Application to AIDS studies

This paper presents a new development of a bent-cable two-part Tobit model to identify both phasic patterns and mixture of advancing (to AIDS) and non-advancing patients of HIV. In identification of such phasic patterns, estimation of a transition period for the development of drug resistance to antiretroviral (ARV) drug or therapy is carried out using longitudinal data that have a gradual change from a declining phase to an increasing phase. In addition to phasic changes, there are also problems of skewness and left-censoring in the response variable because of a lower limit of detection. A relatively large percentage of data below limit of detection are recorded more than expected under an assumed skew-distribution. To properly accommodate these features, we present an extension of the random effects bent-cable Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for a response with left-censoring, skewness and phasic patterns. The proposed methods are illustrated using real data from an AIDS clinical study.

Joint bent-cable Tobit models for longitudinal and time-to-event data

In this article, we show how to estimate a transition period for the evolvement of drug resistance to antiretroviral (ARV) drug or other related treatments in the framework of developing a Bayesian method for jointly analyzing time-to-event and longitudinal data. For HIV/AIDS longitudinal data, developmental trajectories of viral loads tend to show a gradual change from a declining trend after initiation of treatment to an increasing trend without an abrupt change. Such characteristics of trajectories are also associated with a time-to-event process. To assess these clinically important features, we develop a joint bent-cable Tobit model for the time-to-event and left-censored response variable with skewness and phasic developments. Random effects are used to determine the stochastic dependence between the time-to-event process and response process. The proposed method is illustrated using real data from an AIDS clinical study.

Bayesian bent-cable growth mixture tobit models for longitudinal data with skewness and detection limit: application to AIDS studies

This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change. We assess this clinically important feature of the longitudinal HIV/AIDS data using the bent-cable framework within a growth mixture Tobit model. To account for heterogeneity of drug resistance among subjects, the parameters of the bent-cable growth mixture Tobit model are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left-censoring. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2016 John Wiley & Sons, Ltd.

A comparison of change point models with application to longitudinal lung function measurements in children with cystic fibrosis

Cystic fibrosis (CF) is a hereditary lung disease characterized by loss of lung function over time. Lung function in CF is believed to decline at a higher rate during the adolescence period. It has been also hypothesized that there is a subgroup of individuals for whom lung disease remains relatively stable with only a slight decline over their lifetime. Using data from the University of Colorado CF Children's Registry, we investigate four change point models to model the decline of lung function in children and adolescents: (i) a two-component mixture random change point model, (ii) a two-component mixture-fixed change point model, (iii) a random change point model, and (iv) a fixed change point model. The models are investigated through posterior predictive simulation at the individual and population levels, and a simulation study examining the effects of model misspecification. The data support the mixed random change point model as the preferred model, with roughly 30% of adolescents experiencing a steady decline of 0.5 %FEV1 per year and 70% experiencing an increase in decline of 4.4 %FEV1 per year beginning on average at 14.6 years of age. Copyright © 2016 John Wiley & Sons, Ltd.