Parametric bootstrap and penalized quasi-likelihood inference in conditional autoregressive models.
This paper discusses a variety of conditional autoregressive (CAR) models for mapping disease rates, beyond the usual first-order intrinsic CAR model. We illustrate the utility and scope of such models for handling different types of data structures. To encourage their routine use for map production at statistical and health agencies, a simple algorithm for fitting such models is presented. This is derived from penalized quasi-likelihood (PQL) inference which uses an analogue of best-linear unbiased estimation for the regional risk ratios and restricted maximum likelihood for the variance components. We offer the practitioner here the use of the parametric bootstrap for inference. It is more reliable than standard maximum likelihood asymptotics for inference purposes since relevant hypotheses for the mapping of rates lie on the boundary of the parameter space. We illustrate the parametric bootstrap test of the practically relevant and important simplifying hypothesis that there is no spatial autocorrelation. Although the parametric bootstrap requires computational effort, it is straightforward to implement and offers a wealth of information relating to the estimators and their properties. The proposed methodology is illustrated by analysing infant mortality in the province of British Columbia in Canada.
MacNab
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YC
Centre for Health Evaluation Research, British Columbia Institute for Children's and Women's Health, 4480 Oak Street, Rm E-414, Vancouver, B.C., Canada V6H 3V4. ymacnab@cw.bc.ca
Dean
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CB
D000465:Algorithms; D001955:British Columbia / Q000453:epidemiology; D006801:Humans; D007226:Infant Mortality; D007231:Infant, Newborn; D016013:Likelihood Functions; D008377:Maps as Topic; D015233:Models, Statistical; D012044:Regression Analysis; D017062:Small-Area Analysis