Lin, Fleming and DeGruttola (LFD) address the important problem of estimating the proportion of treatment effect (PTE) explained by a surrogate marker. Problems of interpretation of the measure as well as the theoretical basis of its formulation are well explained. This measure has been introduced to validate the main criterion proposed by Prentice which defined a surrogate in the clinical trials setting. Several papers have now published results of clinical trials providing estimates of the PTE for different markers of HIV infection although CD4# have received a great deal of attention.\ Although we agree with the most of the discussion of LFD, we would like to give some examples found in AIDS literature which not only confirm the high variability of the PTE but also indicate that the measure should simply not be used in practice.
To our knowledge, the first use of the PTE was proposed by Freedman et al. They found that the proportion of the treatment (cholestyramine) on the risk of coronary heart disease which is explained by serum cholesterol at 1 year is estimated by 0)498. Using the proposed method to construct a confidence interval, they found that the 95 per cent CI is (7 per cent, 591 per cent). The upper bound is not only far from 100 per cent, but the lower bound indicates that all range of 'acceptable' values lies within the interval. They conclude that 'cholesterol does explain at least some of the treatment effect'. O'Brien et al. found that a 75 per cent decrease in plasma level of HIV-1 RNA and the combination of HIV1-RNA and CD4 explained 59 per cent (95 per cent CI, 13 to 112 per cent) and 79 per cent (95 per cent CI, 27 to 145 per cent) of the treatment effect (AZT) on progression to AIDS, respectively. Bootstrap methods were used to calculate confidence intervals. Although, these intervals were large, the authors concluded that both markers 'can be used to assess the efficacy of zidovudine and possibly other antiretroviral drugs as well'. Both examples of the large variability of PTE are well known to clinicians and statisticians working in this area. What may be less well known is that inadmissible values of the PTE itself may be found in two recent reports and one oral presentation. Since the concept of confidence interval is sometimes not so clear for clinicians such values outside the range 0-100 per cent emphasize the lack of usefulness of the PTE measure.
Choi et al. investigated the extent to which CD4# lymphocytes are a surrogate marker for the development of AIDS using data from the ACTG 019. The initial study compared a placebo group to two groups of 500 mg and 1500 mg total daily dose of zidovudine while for their purpose both doses of zidovudine were pooled. They concluded that CD4# lymphocytes are an incomplete surrogate marker by week 16, since 46 per cent and 74 per cent of zidovudine's effect was explainable by higher CD4# cell count and net CD4# percent, respectively (Table 4, p. 679). The unadjusted relative risk for the treatment effect is 1)70 with corresponding p-value"0)11. They also performed an analysis using the current CD4# cell count (Table 2, p. 678). For the latter analysis, estimate of the PTE is not given but can be claculated since