PubMed · 14877064
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M I SHANHOLTZ. 1951. Diphtheria.. https://pubmed.ncbi.nlm.nih.gov/14877064/
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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 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.
In a wide variety of medical research scenarios one is interested in the question whether regression curves differ for subgroups in the sample. Examples are gender differences in the effect of drug treatment or the study of genotype-environment interactions. To address this question exploratory techniques are often required because detailed knowledge concerning the shape of the regression curves and how that shape differs across subgroups is lacking. In this article we explored the power of two such exploratory techniques: multivariate adaptive regression splines (MARS) and least squares curve fitting using polynomials. For this purpose simulations were performed using linear, logistic, and complex non-linear curves. The power obtained from MARS was on average 1.4 times higher than with polynomials. It was shown that power was higher even if the regression curve was linear, that gains increased with the complexity of the curve, and that for highly non-linear curves model-free methods such as MARS might be the only alternative.