Score Tests for Exploring Complex Models: Application to HIV Dynamics Models

Abstract

In biostatistics, more and more complex models are being developed. This is particularly the case in system biology. Fitting complex models can be very time-consuming, since many models often have to be explored. Among the possibilities are the introduction of explanatory variables and the determination of random effects. The particularity of this use of the score test is that the null hypothesis is not itself very simple; typically, some random effects may be present under the null hypothesis. Moreover, the information matrix cannot be computed, but only an approximation based on the score. This article examines this situation with the specific example of HIV dynamics models. We examine the score test statistics for testing the effect of explanatory variables and the variance of random effect in this complex situation. We study type I errors and the statistical powers of this score test statistics and we apply the score test approach to a real data set of HIV-infected patients.

Tests for Hazard Transformation

“…Methods for similar complex and semiparametric tests such as those described by Commenges and Andersen [3], Commenges and Jacqmin-Gadda [4], and Drylewicz et al [8] can be adapted to show that with appropriate adjustment for using estimatesβ andΛ 0 and given regularity conditions, the score test…”

Dynamical models of biomarkers and clinical progression for personalized medicine: The HIV context

“…We used the data of the controlled randomized open-label ALBI ANRS 070 trial [42] To take inter-patient variability into account, parameters can be modelled as the sum of a population (fixed) parameter and a random effect having independent standard normal distributions: + leading to a mixed effects model. After a forward selection strategy [43], parameters , and were found to vary substantially among patients and were selected for having random effects, while the other parameters were assumed constant in the population. Because the antiretroviral drugs considered were inhibitors of the reverse transcriptase, the treatment was assumed to act on the infectivity parameter [44].…”

Modeling the dynamics of biomarkers during primary HIV infection taking into account the uncertainty of infection date

“…Usually, random effects are assumed to be independent in ODE models [Putter et al (2002); Samson, Lavielle and Mentré (2006); ; Guedj, Thiébaut and Commenges (2007a)]. To test a possible correlation between the two random effects included in our models, we developed a score test based on our previous work [Drylewicz, Commenges and Thiébaut (2010)]. For both models, the test was not significant (p = 0.87 and p = 0.92, respectively).…”

“…In Drylewicz, Commenges and Thiébaut (2010), we have developed score tests for explanatory variables and variance of random effects in complex models. We propose here to develop a test for the covariance parameter of random effects.…”