79 Sense and sensitivity when intended data are missing Els Goetghebeur1 Geert Molenberghs2 Michael G. Kenward3 * Abstract Classical inferential procedures infer conclusions from a set of data to a population of inter¬ est, accounting for the imprecision implied by the designed sampling frame. Less attention is devoted to uncertainty arising from unintended incompleteness in the data. Through the choice of an identifiable model for (non-ignorable) non-response, one narrows the possible data gen¬ erating mechanisms to the point where inference only suffers from imprecision, which typically reduces to zero as the sample size tends to infinity. Some proposals have been made for assess¬ ment of sensitivity to these modeling assumptions; many arc based on fitting several plausible but competing models. We develop an alternative approach which identifies and incorporates explicitly both sources of uncertainty in inference: imprecision due to finite sampling and igno¬ rance due to incompleteness. The introduction of sensitivity parameters helps inspection of the whole set of estimators compatible with the observed data, in function of more or less plausible assumptions about which the data carry no information. The developments in this paper focus on contingency tables, and are illustrated using data from an HIV prevalence study and data from a Slovenian plebiscite. Key words: Contingency Table; Imprecision, Missing At Random; Overspecified Model; Saturated Model 1 Introduction The problem of missing intended data in a well designed study is a common one. The reasons for data being missing are many and varied. There is therefore no straightforward approach to statistical inference that accommodates the unknown behavior of unintentionally unobserved data. Rubin (1976) provided one of the first systematic studies of this issue, and we use his terminology for classifying different classes of processes that give rise to missing values. The abbreviations MCAR, MAR and MNAR will refer to missingness processes that are Completely At Random, At Random and Not At Random (i.e. nonignorable) respectively. This paper is concerned with how one might approach inference when the possibility of a non-random missingness process cannot be ruled out on a priori, grounds. Universiteit Gent, TWI, Krijgslaan 281-S9, B-9000 Gent, Belgium; 2 Limburgs Universitair Centrum, Universi- taire Campus Building D, B-3590 Diepenbeek, Belgium; University of Kent, Canterbury, U.K. The authors gratefully acknowledge support from the FWO-Vlaanderen Research Project “Sensitivity Analysis for Incomplete and Coarse Data”