The efficiency of the sets and the cuscore techniques under biased baseline rates

Statistical techniques used for surveillance of disease incidence rates are generally based on the assumption of known baseline rate of the disease monitored, whereas actually it is an estimate obtained from a large sample. As a result, the time interval until true or false alarm is shorter or longer than assumed. In this study, we evaluate the performance of the sets and of the cuscore techniques when the estimate of the baseline rate is biased. We evaluate the effect of an underestimated baseline rate with respect to frequency of false alarms and to that of an over estimated rate with respect to the delay until elicitation of a true alarm. We evaluate the effects of 5 per cent and 10 per cent bias in the estimated baseline rate for specified conditions associated with sparse data. The results show that the effect of plus or minus 5 per cent bias in the estimate are moderate and those of 10 per cent are substantial. In general, the effect of an overestimated baseline rate is greater on the sets technique than it is on the cuscore technique and the effect of an underestimated rate is greater on the cuscore technique than it is on the sets technique. However, the differences between the two techniques are small on both perspectives. The two methods differ also with respect to the expected time until true alarm when the specified baseline rate is unbiased. The sets technique is the more efficient in detecting a two-fold increased rate when the number of diagnoses expected annually (E(X)) is less than 1.62, and the cuscore is the more efficient technique when E(X) > 1.62. We use the term 'turning point' to define the regions in which the sets technique and the cuscore techniques are preferred. With an estimated baseline rate that is 5 per cent higher than the actual rate, the turning point falls from 1.62 to 1.45 when the rate is twice the baseline rate, and from 5.75 to 4.34 when the rate is triple the baseline rate.