Copas, Andrew John; (1999) The analysis of data where response or selection is dependent on the variable of interest. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In surveys of sensitive subjects non response may be dependent on the variable of interest, both at the unit and item levels. In some clinical and epidemiological studies, units are selected for entry on the basis of the outcome variable of interest. Both of these scenarios pose problems for statistical analysis, and standard techniques may be invalid or inefficient, except in some special cases. A new approach to the analysis of surveys of sensitive topics is developed, central to which is at least one variable which represents the enthusiasm to participate. This variable is included along with demographic variables in the calculation of a response propensity score. The score is derived as the fitted probabilities of item non-response to the question of interest. The distribution of the score for the unit non-responders is assumed equal to that of item non-responders. Response is assumed independent of the variable of interest, conditional on the score. Weights based on the score can be used to derive unbiased estimates of the distribution of the variable of interest. The bootstrap is recommended for confidence interval construction. The technique is applied to data from the National Survey of Sexual Attitudes and Lifestyles. A simplification of the technique is developed that does not use the bootstrap, and which enables users to analyse the data without knowledge of the factors affecting non-response, and using standard statistical software. To analyse the time from an initiating event to illness, a prospective study may be regarded as the optimal design. However, additional data from those already with the illness and still alive may also be available. A standard technique would be to ignore the additional data, and left-truncate the times to illness at study entry. We develop a full likelihood approach, and a weighted pseudo likelihood approach, and compare these with the standard truncated data approach. The techniques are used to fit simple models of time to illness based on data from a study of time to AIDS from HIV seroconversion.

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