Modeling individual migraine severity with autoregressive ordered probit models

Abstract

This paper considers the problem of modeling migraine severity assessments and their dependence on weather and time characteristics. We take on the viewpoint of a patient who is interested in an individual migraine management strategy. Since factors influencing migraine can differ between patients in number and magnitude, we show how a patient's headache calendar reporting the severity measurements on an ordinal scale can be used to determine the dominating factors for this special patient. One also has to account for dependencies among the measurements. For this the autoregressive ordinal probit (AOP) model of Müller and Czado (2005) is utilized and fitted to a single patient's migraine data by a grouped move multigrid Monte Carlo (GM-MGMC) Gibbs sampler. Initially, covariates are selected using proportional odds models. Model fit and model comparison are discussed. A comparison with proportional odds specifications shows that the AOP models are preferred.

Modeling Dynamic Preferences: A Bayesian Robust Dynamic Latent Ordered Probit Model

“…1 Dynamic panel models for ordinal data are not widely developed in political science. Theoretical work and applications exist in biostatistics, medicine, and finance (e.g., Lunn, Wakefield, and Racine-Poon 2001;Mu¨ller and Czado 2005;Hasegawa 2009;Varin and Czado 2010;Czado, Heyn, and Mu¨ller 2011), but are developed with long time series in mind, and are not concerned with initial conditions in short panels of individuals (note that the start of medical studies often does coincide with the start of the data-generating process). Pang (2010) presents a model for repeated categorical data using correlated residuals.…”

Modeling Ordered Choices: A Primer and Recent Developments

“…The MCMC methodology is often useful in settings which extend beyond the basic model. We will describe below, for example, applications to a bivariate ordered probit model [Biswas and Das (2002)], a model with autocorrelation [Czado et al (2005) and Girard and Parent (2001)] and a model that contains a set of endogenous dummy variables in the latent regression [Munkin and Trivedi (2008). ]…”

“…Methodological contributions are offered by Albert and Chib (1993), Koop and Tobias (2006) and Imai et al (2003) who have developed an "R" routine for some of the computations. Applications include Girard and Parent (2001), Biswas and Das (2002), Czado et al (2005), Tomoyuki et al (2006), Ando (2006), Zhang et al (2007), Kadam and Lenk (2008) and Munkin and Trivedi (2008) and a handful of others. Doubtless there are more to come.…”

“…In the pure time series applications in which researchers have examined asset price movements, interest rate changes and monetary policy, the focus is on inertia, and takes the form of an autoregressive model in the latent variable regression. The Czado, Heyn and Müller (2005) and Müller and Czado (2005) study of migraine headache severity is also presented in this framework, though their study can be usefully viewed as falling somewhere between the time series analysis of, e.g., Eichengreen et al's (1985) study of bank rate policy and the recent panel data studies, e.g., of health satisfaction. In panel data settings, such as Contoyannis, Jones and Rice (2004), the model is directed at state dependence, and, instead, takes the form of lagged effects in the observed variables.…”

“…Third, received models have not adequately accounted for the correlations between price changes and other economic variables -these are captured in the latent regression equation in the ordered probit model. Czado, Heyn and Müller (2005) also used a time series model with dynamics in the latent variable to study the reported severity of migrain headaches reported in the diary of a single patient. The underlying variable, severity of the headache in interval t, is modeled…”