PubMed · 13676140
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F E RANTSCH. 1959. [Extrapulmonary tuberculosis in repatriates].. https://pubmed.ncbi.nlm.nih.gov/13676140/
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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.
The self-controlled case series method was developed to investigate associations between acute outcomes and transient exposures, using only data on cases, that is, on individuals who have experienced the outcome of interest. Inference is within individuals, and hence fixed covariates effects are implicitly controlled for within a proportional incidence framework. We describe the origins, assumptions, limitations, and uses of the method. The rationale for the model and the derivation of the likelihood are explained in detail using a worked example on vaccine safety. Code for fitting the model in the statistical package STATA is described. Two further vaccine safety data sets are used to illustrate a range of modelling issues and extensions of the basic model. Some brief pointers on the design of case series studies are provided. The data sets, STATA code, and further implementation details in SAS, GENSTAT and GLIM are available from an associated website.
In biomedical studies often multiple measures of disease severity are recorded over time. Although correlated, such measures are frequently analysed separately of one another. Joint analysis of the outcomes variables has several potential advantages over separate analyses. However, models for response variables of different types (discrete and continuous) are challenging to define and to fit. Herein we propose correlated probit models for joint analysis of repeated measurements on ordinal and continuous variables measuring the same underlying disease severity over time. We demonstrate how to rewrite the models so that maximum-likelihood estimation and inference can be performed with standard software. Simulation studies are performed to assess efficiency gains in fitting the responses together rather than separately and to guide response variable selection for future studies. Data from a depression clinical trial are used for illustration.