The mean reduction in viral load for the five treatment groups is presented in Fig. . Average viral load decreased rapidly in all treatment groups over the first 2 weeks of treatment. By day 56, viral load rebounded in four of the five treatment groups, with the largest rebounds occurring in the 1,000- and 1,200-mg/day treatment groups. In the 2,250-mg/day group (750 mg TID), plasma HIV-1 RNA levels fell below the limit of detection in four of the five patients by day 28; by day 56, however, viral load had rebounded in all but one of these patients. Plasma HIV-1 RNA levels in the 3,000-mg/day group showed more sustained declines, with viral load remaining at least 10-fold below the baseline level in five out of five subjects at day 56. The reduction in viral load by day 56, log(*V*_{56}/*V*_{0}), was significantly greater in the 3,000-mg/day group than in the 2,250-mg/day group (Mann-Whitney U test, *P* < 0.05).

Relative efficacies based on equation

1 for the five dosage groups are given in Table . To test the extent to which early measures of treatment efficacy based on only two viral load measurements predict viral load at later times, we regressed

_{x,y} for various values of

*x* and

*y* against the logarithm of viral load reduction at day 56, log(

*V*_{56}/

*V*_{0}) (using

*V*_{28} in place of

*V*_{56} for five patients as explained above). No correlation was observed between viral load reduction at day 56 and measures of relative efficacy spanning the first 7 days of treatment,

_{0,4},

_{4,7}, and

_{0,7} (linear regressions:

*R*^{2} = 0.002,

*R*^{2} = 0.105, and

*R*^{2} = 0.053, respectively; none is statistically significant). This is consistent with the similar decays during the first 7 days seen in Fig. . Relative efficacies based on declines up to days 14 and 21 (

_{4,14} and

_{4,21}), however, showed significant correlations with viral load reduction at day 56, with

_{4,21} having a higher

*R*^{2} value than

_{4,14} (Fig. ). As discussed above, for this type of analysis, relative efficacies based on

*x* being 4 are preferable to those based on

*x* being 0 because log(

*V*_{56}/

*V*_{0}) is not statistically independent of efficacies based on

*V*_{0}.

| **TABLE 2**Relative efficacy as a function of drug dose^{a} |

The presence of points in the upper right regions of Fig. a and b shows that a high relative efficacy at weeks 2 and 3 is not always associated with a large viral load reduction at day 56. In the lowest-dosage group, for example, we obtained several early measures of relative efficacy above 1.0 in subjects whose viral loads later rebounded (data not shown). A low relative efficacy, by contrast, is rarely, if ever, associated with a good long-term response. Of the seven subjects with an

_{4,21} value below 0.5, for example, none had viral load reductions of 1 log or more at day 56 (Fig. b).

Relative efficacies based on linear regressions that include intermediate time points were similar to those found using the simple two-point method presented here (mean difference from two-point

_{4,14}, 3.9%; mean difference from two-point

_{4,21}, 8.0%). Correlations between relative efficacies calculated using linear regression over all points and reduction in viral load, log(

*V*_{56}/

*V*_{0}), were also similar to those obtained using our two-point method (regression-based

_{4,14},

*R*^{2} = 0.36,

*P* < 0.002; regression-based

_{4,21},

*R*^{2} = 0.56,

*P* < 0.001). The similarity of the relative efficacies based on linear regressions to those based on our simple two-point method supports the use of this simpler and easier-to-use method.

The correlations in Fig. include five patients for whom we used day 28 values (and one day 38 value) in place of day 56 values. These patients were dropped from the study because viral load was within 1 log of the baseline value at day 28. To verify that the correlations in Fig. were not unduly influenced by these substitutions, we repeated these analyses without these patients. The corresponding

*R*^{2} values for this reduced data set were 0.27 and 0.47, respectively (

*t* tests on regression coefficients,

*P* < 0.02 and

*P* < 0.002, respectively), indicating that

_{4,14} and

_{4,41} continue to be correlated with the reduction in viral load at day 56 when these patients are removed from the analysis.

As expected, our measures of plasma drug concentration,

*C*_{0–14} and

*C*_{0–21}, correlate with drug dose, with

*C*_{0–21} showing a slightly higher correlation with drug dose (Table ).

*C*_{0–14} and

*C*_{0–21} also correlate with

_{0,14} and

_{0,21} (data not shown), as well as

_{4,14},

_{4,21}, and the reduction in viral load, log(

*V*_{56}/

*V*_{0}) (Table ). To see whether changes in drug concentration over time might account for the differences between early (efficacies over the first 14 to 21 days) and very early measures of relative efficacy (efficacies over the first 4 to 7 days), we monitored the concentration of drug in plasma for each of the six dosage regimens as a function of time; however, we saw no changes in drug concentration between days 7 and 21 that could account for this difference, although in the 600 BID and 500 TID groups there was an increase in drug concentration over the first 14 days (Fig. ).

| **TABLE 3**Correlations between plasma drug concentration, dose, relative efficacy, and reduction in viral load by day 56^{a} |

Since both plasma drug concentration and relative efficacy correlate with viral load reduction at day 56 individually, we also performed multiple regression analyses on log(

*V*_{56}/

*V*_{0}) with plasma drug concentration and relative efficacy as independent variables. A forward stepwise regression analysis indicated that

_{4,14} contributes only marginally to the regression sum of squares for viral load reduction at day 56 when the regression model already includes

*C*_{0–14} (

*P* for addition of

_{4,14} to regression model, 0.057). However, a similar forward stepwise regression analysis using

_{4,21} and

*C*_{0–21} reversed the order of importance: in this case

_{4,21}, but not

*C*_{0–21}, contributed significantly to the regression sum of squares for viral load reduction at day 56 (

*P* for adding

*C*_{0–21}, 0.205). In other words, relative efficacy appears to be a more important predictor of longer-term viral load reduction than plasma drug concentration when patients are monitored for 21 days. Of course, as shown in Fig. , in the absence of drug concentration data, both

_{4,14} and

_{4,21} are predictors of longer-term reductions in viral load.

The measure of relative efficacy introduced here is an empirical quantity that does not directly correspond to the antiretroviral efficacies considered in references

3,

9,

14,

31, and

40, in which the efficacy is a parameter in a mathematical model of HIV-1 dynamics. For an RT inhibitor the antiretroviral efficacy is defined in terms of the reduction in the infection rate constant, while for a Pr inhibitor this efficacy is defined in terms of the reduction in the proportion of virions that are infectious. For dual-action combination therapy, the overall efficacy can be calculated in terms of these individual efficacy parameters (see references

40 and

31 for details). The empirical measure introduced in this paper, while lacking the mechanistic appeal of these mathematically motivated definitions, is a practical method for quantifying variation in the response to drug therapy.