PubMed · 14241516
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W THEIN, D J MCSWEENEY. 1964-12-01. MULTIPLE REPEAT CESAREAN SECTIONS.. https://doi.org/10.1016/0002-9378(64)90786-0
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The Cox proportional hazards model is the most common method to analyse survival data. However, the proportional hazards assumption might not hold. The natural extension of the Cox model is to introduce time-varying effects of the covariates. For some covariates such as (surgical)treatment non-proportionality could be expected beforehand. For some other covariates the non-proportionality only becomes apparent if the follow-up is long enough. It is often observed that all covariates show similar decaying effects over time. Such behaviour could be explained by the popular (gamma-) frailty model. However, the (marginal) effects of covariates in frailty models are not easy to interpret. In this paper we propose the reduced-rank model for time-varying effects of covariates. Starting point is a Cox model with p covariates and time-varying effects modelled by q time functions (constant included), leading to a pxq structure matrix that contains the regression coefficients for all covariate by time function interactions. By reducing the rank of this structure matrix a whole range of models is introduced, from the very flexible full-rank model (identical to a Cox model with time-varying effects) to the very rigid rank one model that mimics the structure of a gamma-frailty model, but is easier to interpret. We illustrate these models with an application to ovarian cancer patients.
In this paper, we considered a missing outcome problem in causal inferences for a randomized encouragement design study. We proposed both moment and maximum likelihood estimators for the marginal distributions of potential outcomes and the local complier average causal effect (CACE) parameter. We illustrated our methods in a randomized encouragement design study on the effectiveness of flu shots.
We propose a correlated beta-binomial model for the binary response in multi-centre trials. The likelihood function in this case has a closed-form and we avoid multivariate numerical integrations in determining the maximum likelihood estimator. Based on derived asymptotic variance-covariance matrix of the MLE, we obtain relatively simple formulae that relate the number of centres, the total number of patients and the precision of the parameter estimate.