Robust Estimates of the Negative Binomial Model

We consider robust parametric procedures for univariate discrete distributions, focusing on the negative binomial model. The procedures are based on three steps: ?First, a very robust, but possibly inefficient, estimate of the model parameters is computed. ?Second, this initial model is used to identify outliers, which are then removed from the sample. ?Third, a corrected maximum likelihood estimator is computed with the remaining observations. The final estimate inherits the breakdown point (bdp) of the initial one and its efficiency can be significantly higher. Analogous procedures were proposed in [1], [2], [5] for the continuous case. A comparison of the asymptotic bias of various estimates under point contamination points out the minimum Neyman's chi-squared disparity estimate as a good choice for the initial step. Various minimum disparity estimators were explored by Lindsay [4], who showed that the minimum Neyman's chi-squared estimate has a 50% bdp under point contamination; in addition, it is asymptotically fully efficient at the model. However, the finite sample efficiency of this estimate under the uncontaminated negative binomial model is usually much lower than 100% and the bias can be strong. We show that its performance can then be greatly improved using the three step procedure outlined above. In addition, we compare the final estimate with the procedure described in

Radioimmunotherapy of human colon carcinoma by 131I-labelled monoclonal anti-CEA antibodies in a nude mouse model.

A mixture of 3 MAbs directed against 3 different CEA epitopes was radiolabelled with 131I and used for the treatment of a human colon carcinoma transplanted s.c. into nude mice. Intact MAbs and F(ab')2 fragments were mixed because it had been shown by autoradiography that these 2 antibody forms can penetrate into different areas of the tumor nodule. Ten days after transplantation of colon tumor T380 a single dose of 600 microCi of 131I MAbs was injected i.v. The tumor grafts were well established (as evidenced by exponential growth in untreated mice) and their size continued to increase up to 6 days after radiolabelled antibody injection. Tumor shrinking was then observed lasting for 4-12 weeks. In a control group injected with 600 microCi of 131I coupled to irrelevant monoclonal IgG, tumor growth was delayed, but no regression was observed. Tumors of mice injected with the corresponding amount of unlabelled antibodies grew like those of untreated mice. Based on measurements of the effective whole-body half-life of injected 131I, the mean radiation dose received by the animals was calculated to be 382 rads for the antibody group and 478 rads for the normal IgG controls. The genetically immunodeficient animals exhibited no increase in mortality, and only limited bone-marrow toxicity was observed. Direct measurement of radioactivity in mice dissected 1, 3 and 7 days after 131I-MAb injection showed that 25, 7.2 and 2.2% of injected dose were recovered per gram of tumor, the mean radiation dose delivered to the tumor being thus more than 5,000 rads. These experiments show that therapeutic doses of radioactivity can be selectively directed to human colon carcinoma by i.v. injection of 131I-labelled anti-CEA MAbs.