analysis will be performed for those patients for whom marrow samples are available to 
learn if these additional factors contribute to predicting time to engraftment. The least 
squares technique is used to summarize data repeatedly measured for each patient, and 
since no inference will be made on these estimates, the usual regression assumptions 
(which are not true in this case) of normally distributed independent errors are not 
required. The time dependent covariates will be recomputed at each successful 
engraftment. As time progresses, more and more weekly measurements will be available 
for estimation of the hyjx)thesized functions to be included in the Cox model. 
One significant difficulty with this approach is that the proportions will be estimated with 
error and the magnitude of that error is not known. Indeed, we will only know that a 
particular proportion lies between two numbers. We will investigate the effect of this 
uncertainty on our resulting model. Furthermore, no data presently exist which would 
permit reasonable statistical statements regarding confidence that the proposed approach 
will be successful or that the basic hypotheses will be tested with prescribed statistical 
power. Therefore, we propose to conduct a pilot study of 20 patients in order to 
estimate errors associated with the discussed estimates of important covariates and to the 
examine the hypothesized functions which could be used to model time to engraftment. 
After a thorough analysis, a second study will be designed to confirm the model and to 
test with adequate statistical power, the basic hypothesis that exposure to growth factors 
accelerates engraftment. 
10.2 Modeling Time From Engraftment to Failure to Detect Cells Exposed to Growth Factors 
Following engraftment, patients will be monitored as described in other sections of the 
protocol for the presence and proportion of AN contributed by cells generated by those 
cells exposed and not exposed to growth factors ex vivo. Similar to the above approach, 
we will model the time to loss of evidence of the cells of interest beginning from the date 
of engraftment. Loss will be established by two consecutive assays being negative. 
10.3 Safety Monitoring 
There is now considerable experience documenting the toxicity and failure rate of ABMT 
in this setting as well as the safety of the gene marking techniques. Nonetheless, we will 
sequentially monitor the study for an unexpectedly high frequency of these events. 
Death during ABMT: 
If four deaths during transplantation (first 100 days) are observed in the treatment of the 
first 20 patients, accrual to the study will be terminated and a complete evaluation of all 
information made as to whether continuation is warranted. Accrual will be halted when 
the fourth death is observed. Using the negative binomial distribution, one can show that 
this decision rule provides for terminating the study early with probabilities of 0.02, 0. 13 
and 0.35 if the true unknown death rate is 0.05, 0.10 or 0. 15, respectively. If the true 
[ 498 ] 
Recombinant DNA Research, Volume 19 
