Bootstrap hypothesis testing in generalized additive models for comparing curves of treatments in longitudinal studies

Florianópolis

Congreso; XXVth Internacional Biometric Conference; 2010

Región brasilera y región argentina de la Sociedad Internacional de Biometría

In many studies, the evaluation of the effect of a treatment requires to observe a random variable at several points in time. The mean response along time can be modelled assuming a smooth curve. Spline regression, within the generalized additive model (GAM) framework, becomes an appropriate methodology for the analysis of this kind of data. In this work, hypothesis tests were constructed to compare two curves of treatments in an interval of time. Since GAMs suppose independence among follow-up observations, the correlation was considered through bootstrap simulation to obtain valid inferences. We proposed two bootstrap approaches for hypothesis testing. In the first, semi-parametric bootstrap, observations satisfying the null hypothesis of equality of curves are obtained by resampling vectors of residuals. The second approach, non-parametric bootstrap, is based on resampling response vectors and thus needs a modification of the test statistic applied to the bootstrap sample in order that its distribution approximates the null distribution. Simulation studies were conducted to assess the performance of the proposed tests, considering different responses in the exponential family (Gamma, Bernoulli) and varying the correlation between observations along time. Results encouraged using the bootstrap for hypothesis testing in longitudinal data. We showed that the sizes of the bootstrap tests are close to the nominal value, with tests based on a standardized statistic having slightly better size properties. The power increases as the distance between curves increases and decreases when correlation gets higher. The utility of these statistical tools was confirmed using real data, thus allowing detecting changes in fish behaviour when exposed to toxics.