Dynamic prediction of recurrent events data by landmarking with application to a follow-up study of patients after kidney transplant

© 2016, © The Author(s) 2016. This paper extends dynamic prediction by landmarking to recurrent event data. The motivating data comprised post-kidney transplantation records of repeated infections and repeated measurements of multiple markers. At each landmark time point t s , a Cox proportional hazards model with a frailty term was fitted using data of individuals who were at risk at landmark s. This model included the time-updated marker values at t s as time-fixed covariates. Based on a stacked data set that merged all landmark data sets, we considered supermodels that allow parameters to depend on the landmarks in a smooth fashion. We described and evaluated four ways to parameterize the supermodels for recurrent event data. With both the study data and simulated data sets, we compared supermodels that were fitted on stacked data sets that consisted of either overlapping or non-overlapping landmark periods. We observed that for recurrent event data, the supermodels may yield biased estimates when overlapping landmark periods are used for stacking. Using the best supermodel amongst the ones considered, we dynamically estimated the probability to remain infection free between t s and a prediction horizon t hor , conditional on the information available at t s

Dynamic prediction of recurrent events data by landmarking with application to a follow-up study of patients after kidney transplant

© 2016, © The Author(s) 2016. This paper extends dynamic prediction by landmarking to recurrent event data. The motivating data comprised post-kidney transplantation records of repeated infections and repeated measurements of multiple markers. At each landmark time point t s , a Cox proportional hazards model with a frailty term was fitted using data of individuals who were at risk at landmark s. This model included the time-updated marker values at t s as time-fixed covariates. Based on a stacked data set that merged all landmark data sets, we considered supermodels that allow parameters to depend on the landmarks in a smooth fashion. We described and evaluated four ways to parameterize the supermodels for recurrent event data. With both the study data and simulated data sets, we compared supermodels that were fitted on stacked data sets that consisted of either overlapping or non-overlapping landmark periods. We observed that for recurrent event data, the supermodels may yield biased estimates when overlapping landmark periods are used for stacking. Using the best supermodel amongst the ones considered, we dynamically estimated the probability to remain infection free between t s and a prediction horizon t hor , conditional on the information available at t s

Dynamic prediction of mortality among patients in intensive care using the sequential organ failure assessment (SOFA) score: a joint competing risk survival and longitudinal modeling approach

In intensive care units (ICUs), besides routinely collected admission data, a daily monitoring of organ dysfunction using scoring systems such as the sequential organ failure assessment (SOFA) score has become practice. Such updated information is valuable in making accurate predictions of patients' survival. Few prediction models that incorporate this updated information have been reported. We used follow-up data of ICU patients who either died or were discharged at the end of hospital stay, without censored cases. We propose a joint model comprising a linear mixed effects submodel for the development of longitudinal SOFA scores and a proportional subdistribution hazards submodel for death as end point with discharge as competing risk. The two parts are linked by shared latent terms. Because there was no censoring, it was straightforward to fit our joint model using available software. We compared predictive values, based on the Brier score and the area under the receiver operating characteristic curve, from our model with those obtained from an earlier modeling approach by Toma et al. [Journal of Biomedical Informatics 40, 649, (2007)] that relied on patterns discovered in the SOFA scores over a given period of time

Simulated maximum likelihood estimation in joint models for multiple longitudinal markers and recurrent events of multiple types, in the presence of a terminal event

In medical studies we are often confronted with complex longitudinal data. During the follow-up period, which can be ended prematurely by a terminal event (e.g. death), a subject can experience recurrent events of multiple types. In addition, we collect repeated measurements from multiple markers. An adverse health status, represented by ‘bad’ marker values and an abnormal number of recurrent events, is often associated with the risk of experiencing the terminal event. In this situation, the missingness of the data is not at random and, to avoid bias, it is necessary to model all data simultaneously using a joint model. The correlations between the repeated observations of a marker or an event type within an individual are captured by normally distributed random effects. Because the joint likelihood contains an analytically intractable integral, Bayesian approaches or quadrature approximation techniques are necessary to evaluate the likelihood. However, when the number of recurrent event types and markers is large, the dimensionality of the integral is high and these methods are too computationally expensive. As an alternative, we propose a simulated maximum-likelihood approach based on quasi-Monte Carlo integration to evaluate the likelihood of joint models with multiple recurrent event types and markers

Simulated maximum likelihood estimation in joint models for multiple longitudinal markers and recurrent events of multiple types, in the presence of a terminal event

In medical studies we are often confronted with complex longitudinal data. During the follow-up period, which can be ended prematurely by a terminal event (e.g. death), a subject can experience recurrent events of multiple types. In addition, we collect repeated measurements from multiple markers. An adverse health status, represented by ‘bad’ marker values and an abnormal number of recurrent events, is often associated with the risk of experiencing the terminal event. In this situation, the missingness of the data is not at random and, to avoid bias, it is necessary to model all data simultaneously using a joint model. The correlations between the repeated observations of a marker or an event type within an individual are captured by normally distributed random effects. Because the joint likelihood contains an analytically intractable integral, Bayesian approaches or quadrature approximation techniques are necessary to evaluate the likelihood. However, when the number of recurrent event types and markers is large, the dimensionality of the integral is high and these methods are too computationally expensive. As an alternative, we propose a simulated maximum-likelihood approach based on quasi-Monte Carlo integration to evaluate the likelihood of joint models with multiple recurrent event types and markers

Simulated maximum likelihood estimation in joint models for multiple longitudinal markers and recurrent events of multiple types, in the presence of a terminal event

In medical studies we are often confronted with complex longitudinal data. During the follow-up period, which can be ended prematurely by a terminal event (e.g. death), a subject can experience recurrent events of multiple types. In addition, we collect repeated measurements from multiple markers. An adverse health status, represented by ‘bad’ marker values and an abnormal number of recurrent events, is often associated with the risk of experiencing the terminal event. In this situation, the missingness of the data is not at random and, to avoid bias, it is necessary to model all data simultaneously using a joint model. The correlations between the repeated observations of a marker or an event type within an individual are captured by normally distributed random effects. Because the joint likelihood contains an analytically intractable integral, Bayesian approaches or quadrature approximation techniques are necessary to evaluate the likelihood. However, when the number of recurrent event types and markers is large, the dimensionality of the integral is high and these methods are too computationally expensive. As an alternative, we propose a simulated maximum-likelihood approach based on quasi-Monte Carlo integration to evaluate the likelihood of joint models with multiple recurrent event types and markers

Minimally important differences for the EORTC QLQ-C30 in prostate cancer clinical trials

BACKGROUND The aim of the study was to estimate the minimally important difference (MID) for interpreting group-level change over time, both within a group and between groups, for the European Organisation for Research and Treatment of Cancer Quality of Life Questionnaire Core 30 (EORTC QLQ-C30) scores in patients with prostate cancer. METHODS We used data from two published EORTC trials. Clinical anchors were selected by strength of correlations with QLQ-C30 scales. In addition, clinicians' input was obtained with regard to plausibility of the selected anchors. The mean change method was applied for interpreting change over time within a group of patients and linear regression models were fitted to estimate MIDs for between-group differences in change over time. Distribution-based estimates were also evaluated. RESULTS Two clinical anchors were eligible for MID estimation; performance status and the CTCAE diarrhoea domain. MIDs were developed for 7 scales (physical functioning, role functioning, social functioning, pain, fatigue, global quality of life, diarrhoea) and varied by scale and direction (improvement vs deterioration). Within-group MIDs ranged from 4 to 14 points for improvement and - 13 to - 5 points for deterioration and MIDs for between-group differences in change scores ranged from 3 to 13 for improvement and - 10 to - 5 for deterioration. CONCLUSIONS Our findings aid the meaningful interpretation of changes on a set of EORTC QLQ-C30 scale scores over time, both within and between groups, and for performing more accurate sample size calculations for clinical trials in prostate cancer

Interpreting European Organisation for Research and Treatment for Cancer Quality of life Questionnaire core 30 scores as minimally importantly different for patients with malignant melanoma

Introduction Health-related quality of life (HRQOL) is increasingly recognised as an important end-point in cancer clinical trials. The concept of minimally important difference (MID) enables interpreting differences and changes in HRQOL scores in terms of clinical meaningfulness. We aimed to estimate MIDs for interpreting group-level change of European Organisation for Research and Treatment for Cancer Quality of life Questionnaire core 30 (EORTC QLQ-C30) scores in patients with malignant melanoma. Methods Data were pooled from three published melanoma phase III trials. Anchors relying on clinician's ratings, e.g. performance status, were selected using correlation strength and clinical plausibility of associating the anchor/EORTC QLQ-C30 scale pair. HRQOL change was evaluated between time periods that were common to all trials: start of treatment to end of treatment and end of treatment to end of follow-up. Three change status groups were formed: deteriorated by one anchor category, improved by one anchor category and no change. Patients with greater anchor change were excluded. The mean change method and linear regression were used to estimate MIDs for change in HRQOL scores within the group and between the groups of patients, respectively. Results MIDs varied according to QLQ-C30 scale, direction (improvement versus deterioration), anchor and period. MIDs for within-group change ranged from 4 to 18 points (improvement) and −16 to −4 points (deterioration), and MIDs for between-group change ranged from 3 to 16 points and from −16 to −3 points. MIDs for most of QLQ-C30 scales ranged from 5 to 10 points in absolute values. Conclusions These results are useful for interpreting changes in EORTC QLQ-C30 scores over time and for performing more accurate sample size calculations in adjuvant melanoma settings