Incorporating Time-Dependent Covariates into BG-NBD Model for Churn Prediction in Non-Contractual Settings

2017 ◽  
Author(s):  
Andrey Babkin ◽  
Ina Goldberg
Keyword(s):  
Time Dependent ◽  
Churn Prediction ◽  
Time Dependent Covariates ◽  
Nbd Model

scholarly journals Marginal quantile regression for longitudinal data analysis in the presence of time-dependent covariates

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
I-Chen Chen ◽  
Philip M. Westgate
Keyword(s):  
Parameter Estimation ◽  
Longitudinal Data ◽  
Quantile Regression ◽  
Mean Squared Error ◽  
Time Dependent ◽  
Regression Methods ◽  
Squared Error ◽  
Highly Correlated ◽  
Time Dependent Covariates ◽  
Independence Structure

AbstractWhen observations are correlated, modeling the within-subject correlation structure using quantile regression for longitudinal data can be difficult unless a working independence structure is utilized. Although this approach ensures consistent estimators of the regression coefficients, it may result in less efficient regression parameter estimation when data are highly correlated. Therefore, several marginal quantile regression methods have been proposed to improve parameter estimation. In a longitudinal study some of the covariates may change their values over time, and the topic of time-dependent covariate has not been explored in the marginal quantile literature. As a result, we propose an approach for marginal quantile regression in the presence of time-dependent covariates, which includes a strategy to select a working type of time-dependency. In this manuscript, we demonstrate that our proposed method has the potential to improve power relative to the independence estimating equations approach due to the reduction of mean squared error.

The analysis of binary longitudinal data with time-dependent covariates

2012 ◽  
Vol 31 (10) ◽  
pp. 931-948 ◽  
Author(s):  
Matthew W. Guerra ◽  
Justine Shults ◽  
Jay Amsterdam ◽  
Thomas Ten-Have
Keyword(s):  
Longitudinal Data ◽  
Time Dependent ◽  
Binary Longitudinal Data ◽  
Time Dependent Covariates

scholarly journals Number of Inseminations to Conception in Holstein Cows Using Censored Records and Time-Dependent Covariates

2005 ◽  
Vol 88 (10) ◽  
pp. 3655-3662 ◽  
Author(s):  
O. González-Recio ◽  
Y.M. Chang ◽  
D. Gianola ◽  
K.A. Weigel
Keyword(s):  
Time Dependent ◽  
Holstein Cows ◽  
Time Dependent Covariates

scholarly journals Mortality Risk and The Progression of The Electronic Frailty Index and Hospital Frailty Risk Score Over Time

2020 ◽  
Vol 5 (5) ◽  
Author(s):  
Joe Hollinghurst ◽  
Alan Watkins
Keyword(s):  
Risk Score ◽  
Frailty Index ◽  
Time Frame ◽  
Time Dependent ◽  
Cox Models ◽  
Hazard Ratios ◽  
Increased Risk ◽  
The Matrix ◽  
Time Dependent Covariates ◽  
Over Time

IntroductionThe electronic Frailty Index (eFI) and the Hospital Frailty Risk Score (HFRS) have been developed in primary and secondary care respectively. Objectives and ApproachOur objective was to investigate how frailty progresses over time, and to include the progression of frailty in a survival analysis.To do this, we performed a retrospective cohort study using linked data from the Secure Anonymised Information Linkage Databank, comprising 445,771 people aged 65-95 living in Wales (United Kingdom) on 1st January 2010. We calculated frailty, using both the eFI and HFRS, for individuals at quarterly intervals for 8 years with a total of 11,702,242 observations. ResultsWe created a transition matrix for frailty states determined by the eFI (states: fit, mild, moderate, severe) and HFRS (states: no score, low, intermediate, high), with death as an absorbing state. The matrix revealed that frailty progressed over time, but that on a quarterly basis it was most likely that an individual remained in the same state. We calculated Hazard Ratios (HRs) using time dependent Cox models for mortality, with adjustments for age, gender and deprivation. Independent eFI and HFRS models showed increased risk of mortality as frailty severity increased. A combined eFI and HFRS revealed the highest risk was primarily determined by the HFRS and revealed further subgroups of individuals at increased risk of an adverse outcome. For example, the HRs (95% Confidence Interval) for individuals with an eFI as fit, mild, moderate and severe with a high HFRS were 18.11 [17.25,19.02], 20.58 [19.93,21.24], 21.45 [20.85,22.07] and 23.04 [22.34,23.76] respectively with eFI fit and no HFRS score as the reference category. ConclusionFrailty was found to vary over time, with progression likely in the 8-year time-frame analysed. We refined HR estimates of the eFI and HFRS for mortality by including time dependent covariates.

scholarly journals Targeted Minimum Loss-Based Estimation of Causal Effects in Right-Censored Survival Data with Time-Dependent Covariates: Warfarin, Stroke, and Death in Atrial Fibrillation

2013 ◽  
Vol 1 (2) ◽  
pp. 235-254 ◽  
Author(s):  
Jordan C. Brooks ◽  
Mark J. van der Laan ◽  
Daniel E. Singer ◽  
Alan S. Go
Keyword(s):  
Survival Data ◽  
Causal Effect ◽  
Estimating Equation ◽  
Dependent Censoring ◽  
Time Dependent ◽  
Causal Effects ◽  
Consistent Estimation ◽  
Censored Survival Data ◽  
Inverse Probability ◽  
Time Dependent Covariates

AbstractCausal effects in right-censored survival data can be formally defined as the difference in the marginal cumulative event probabilities under particular interventions. Conventional estimators, such as the Kaplan-Meier (KM), fail to consistently estimate these marginal parameters under dependent treatment assignment or dependent censoring. Several modern estimators have been developed that reduce bias under both dependent treatment assignment and dependent censoring by incorporating information from baseline and time-dependent covariates. In the present article we describe a recently developed targeted minimum loss-based estimation (TMLE) algorithm for general longitudinal data structures and present in detail its application in right-censored survival data with time-dependent covariates. The treatment-specific marginal cumulative event probability is defined via a series of iterated conditional expectations in a time-dependent counting process framework. The TMLE involves an initial estimator of each conditional expectation and sequentially updates these such that the resulting estimator solves the efficient influence curve estimating equation in the nonparametric statistical model. We describe the assumptions required for consistent estimation of statistical parameters and additional assumptions required for consistent estimation of the causal effect parameter. Using simulated right-censored survival data, the mean squared error, bias, and 95% confidence interval coverage probability of the TMLE is compared with those of the conventional KM and the inverse probability of censoring weight estimating equation, conventional maximum likelihood substitution estimator, and the double robustaugmented inverse probability of censoring weighted estimating equation. We conclude the article with estimation of the causal effect of warfarin medical therapy on the probability of “stroke or death” within a 1-year time frame using data from the ATRIA-1 observational cohort of persons with atrial fibrillation. Our results suggest that a fixed policy of warfarin treatment for all patients would result in 2% fewer deaths or strokes within 1-year as compared with a policy of withholding warfarin from all patients.

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