Does High-Dose Antimicrobial Chemotherapy Prevent the Evolution of Resistance?

<div><p>High-dose chemotherapy has long been advocated as a means of controlling drug resistance in infectious diseases but recent empirical studies have begun to challenge this view. We develop a very general framework for modeling and understanding resistance emergence based on principles from evolutionary biology. We use this framework to show how high-dose chemotherapy engenders opposing evolutionary processes involving the mutational input of resistant strains and their release from ecological competition. Whether such therapy provides the best approach for controlling resistance therefore depends on the relative strengths of these processes. These opposing processes typically lead to a unimodal relationship between drug pressure and resistance emergence. As a result, the optimal drug dose lies at either end of the therapeutic window of clinically acceptable concentrations. We illustrate our findings with a simple model that shows how a seemingly minor change in parameter values can alter the outcome from one where high-dose chemotherapy is optimal to one where using the smallest clinically effective dose is best. A review of the available empirical evidence provides broad support for these general conclusions. Our analysis opens up treatment options not currently considered as resistance management strategies, and it also simplifies the experiments required to determine the drug doses which best retard resistance emergence in patients.</p></div

Example where conventional strategy of high-dose chemotherapy best prevents the emergence of resistance.

<p>(a) The dose-response curves for the wild type in blue (<i>r</i>(<i>c</i>) = 0.6(1−tanh(15(<i>c</i>−0.3)))) and the resistant strain in red (<i>r</i>_<i>m</i>(<i>c</i>) = 0.59(1−tanh(15(<i>c</i>−0.45)))) as well as the therapeutic window in green. Red dots indicate the probability of resistance emergence. Probability of resistance emergence is defined as the fraction of 5000 simulations for which resistance reached a density of at least 100 (and thus caused disease).(b) and (c) wild type density (blue), resistant density (red), and immune molecule density (black) during infection for 1000 representative realizations of a stochastic implementation of the model. (b) treatment at the smallest effective dose <i>c</i>_<i>L</i>, (c) treatment at the maximum tolerable dose <i>c</i>_<i>U</i>. Parameter values are <i>P</i>(0) = 10, <i>P</i>_<i>m</i>(0) = 0, <i>I</i>(0) = 2, <i>α</i> = 0.05, <i>δ</i> = 0.05, <i>κ</i> = 0.075, <i>μ</i> = 10⁻², and <i>γ</i> = 0.01.</p

Simulation Code

Mathematica code for stochastic simulation

Example where low-dose strategy best prevents the emergence of resistance.

<p>(a) The dose-response curves for the wild type in blue (<i>r</i>(<i>c</i>) = 0.6(1−tanh(15(<i>c</i>−0.3)))) and the resistant strain in red (<i>r</i>_<i>m</i>(<i>c</i>) = 0.59(1−tanh(15(<i>c</i>−0.6)))) as well as the therapeutic window in green. Red dots indicate the probability of resistance emergence. Probability of resistance emergence is defined as the fraction of 5000 simulations for which resistance reached a density of at least 100 (and thus caused disease).(b) and (c) wild type density (blue), resistant density (red), and immune molecule density (black) during infection for 1000 representative realizations of a stochastic implementation of the model. (b) treatment at the smallest effective dose <i>c</i>_<i>L</i>, (c) treatment at the maximum tolerable dose <i>c</i>_<i>U</i>. (d) The probability that a resistant strain appears by mutation is indicated by grey bars for low and high dose. The probability of resistance emergence is indicated by the height of the red bars for these cases. The probability of resistance emergence, given a resistant strain appeared by mutation, can be interpreted as the ratio of the red to grey bars. Parameter values are <i>P</i>(0) = 10, <i>P</i>_<i>m</i>(0) = 0, <i>I</i>(0) = 2, <i>α</i> = 0.05, <i>δ</i> = 0.05, <i>κ</i> = 0.075, <i>μ</i> = 10⁻², and <i>γ</i> = 0.01.</p

Frequency distribution of resistant strain outbreak sizes for the simulation underlying Fig 3.

<p>Each distribution is based on 5000 realizations of a stochastic implementation of the model. (a) Low drug dose. (b) High drug dose. Insets show the same distribution on a different vertical scale.</p

Appendix from Why does drug resistance readily evolve but vaccine resistance does not?

Mathematical framework and schematic of treatment mosaic

Figure S2: Dynamics of mixed infections in individual mice from A nutrient mediates intraspecific competition between rodent malaria parasites <i>in vivo</i>

Dynamics of ASpyr (solid lines) and AJ (dashed lines) in mixed infections of mice given unsupplemented water (blue lines) or low (green lines), medium (pink lines) and high (orange lines) concentrations of pABA, as drinking water. Stars represent the number of parasites of each strain that were inoculated and the time at which they were administered. Dots and squares represent the density of ASpyr and AJ parasites, respectively, detected on a particular day, in instances where parasites were not detected the day before or after. A black asterisk indicates that the mouse was inoculated with less parasites than was intended and was excluded from all analyses. A double dagger indicates that the mice died during the experiment. A cross indicates that the mouse had a strong impact on the significance of the effect of pABA on the intensity of competition, as measured by the change total infection size in mixed vs. single infections (see Fig. S3)

How to Use a Chemotherapeutic Agent When Resistance to It Threatens the Patient

<div><p>When resistance to anticancer or antimicrobial drugs evolves in a patient, highly effective chemotherapy can fail, threatening patient health and lifespan. Standard practice is to treat aggressively, effectively eliminating drug-sensitive target cells as quickly as possible. This prevents sensitive cells from acquiring resistance de novo but also eliminates populations that can competitively suppress resistant populations. Here we analyse that evolutionary trade-off and consider recent suggestions that treatment regimens aimed at containing rather than eliminating tumours or infections might more effectively delay the emergence of resistance. Our general mathematical analysis shows that there are situations in which regimens aimed at containment will outperform standard practice even if there is no fitness cost of resistance, and, in those cases, the time to treatment failure can be more than doubled. But, there are also situations in which containment will make a bad prognosis worse. Our analysis identifies thresholds that define these situations and thus can guide treatment decisions. The analysis also suggests a variety of interventions that could be used in conjunction with cytotoxic drugs to inhibit the emergence of resistance. Fundamental principles determine, across a wide range of disease settings, the circumstances under which standard practice best delays resistance emergence—and when it can be bettered.</p></div

Figure S2: Dynamics of mixed infections in individual mice from A nutrient mediates intraspecific competition between rodent malaria parasites <i>in vivo</i>

Dynamics of ASpyr (solid lines) and AJ (dashed lines) in mixed infections of mice given unsupplemented water (blue lines) or low (green lines), medium (pink lines) and high (orange lines) concentrations of pABA, as drinking water. Stars represent the number of parasites of each strain that were inoculated and the time at which they were administered. Dots and squares represent the density of ASpyr and AJ parasites, respectively, detected on a particular day, in instances where parasites were not detected the day before or after. A black asterisk indicates that the mouse was inoculated with less parasites than was intended and was excluded from all analyses. A double dagger indicates that the mice died during the experiment. A cross indicates that the mouse had a strong impact on the significance of the effect of pABA on the intensity of competition, as measured by the change total infection size in mixed vs. single infections (see Fig. S3)

The impact of alternative therapies.

<p>Therapies that either decrease competitive ability (left box) or reduce the intrinsic replication rate (right box) of resistant (R) and/or sensitive (S) populations may increase (↑), decrease (↓), or leave unchanged (—) the resistance management benefits of sensitive cells. Therapies that reduce competitive ability will decrease the balance threshold, making it more likely that containment is indicated. Decreasing intrinsic replication may increase, decrease or have no effect on the balance threshold depending on whether the alternative therapy targets the sensitive cells, the resistant cells, or both. For mathematical details, see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001110#pbio.2001110.s017" target="_blank">S12 Text</a>.</p