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

Abstract

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.

Fig 1. Generic model of infection under aggressive treatment (A) and containment (B).

Grey shading indicates the drug-sensitive density. Red shading indicates the drug-resistant density. Once a patient is infected, the total pathogen density (black curve) will increase until the patient experiences symptoms and seeks treatment. The infection will be treated to rapidly lower the total pathogen density to the acceptable burden (blue line). At this point (black dot), the management period begins and the time to treatment failure then depends on the subsequent treatment strategy. Under aggressive treatment (A), the total pathogen density continues to decline sharply until the infection consists only of completely drug-resistant pathogens. Under containment (B), the total pathogen density is maintained at the acceptable burden until the infection consists only of completely drug-resistant pathogens. Containment will modify the expansion of the resistant population, increasing or decreasing it (patterned areas), depending on the rate at which sensitive cells become resistant and the strength of competitive suppression.

Fig 2. Schematic comparing aggressive treatment to containment.

Sensitive cells competitively suppress resistance (resistance management benefits) but can also mutate to resistance (resistance management costs). The shaded blue region is where benefits dominate costs. Red and black lines are densities of resistant and total pathogens, respectively, under aggressive (solid lines) and containment strategies (dashed lines); dots indicate densities at the start of the management period. Panel A: The acceptable burden (blue solid line) is below the balance threshold (blue dashed line), so there is no region where competition is strong enough to offset the mutational dangers of sensitive pathogens. Consequently, containment is never advantageous. Panel B: Resistant density at the start of the management period exceeds the balance threshold (red dot is inside blue shaded area). In this case, competition is strong enough to outweigh the cost of mutation, and so containment delays treatment failure longer than aggressive treatment. Panels C and D: Resistant density at the start of the management period is below the balance threshold (red dot is below blue shaded area). In Panel C, aggressive treatment manages infection longer than containment. In Panel D, the converse is true.

Fig 3. Ratio of duration of management period under containment to duration of management period under aggressive treatment.

The horizontal axis is the starting resistant density R(0) divided by the self-limiting density R_lim. Each colour corresponds to a different acceptable burden (blue, green, red, purple, and black correspond to acceptable burdens of 10%, 20%, 30%, 60%, and 80% of R_lim). The balance threshold is varied from 0% to 1% of R_lim. For each colour the upper curve corresponds to R_balance = 0, and the lower curve corresponds to a R_balance equal to 1% of R_lim. This range for R_balance will cover the actual expected range unless the mutation rate is quite large (see S6 Text for details). Values are plotted for when the starting resistant density exceeds the balance threshold (i.e., for cases described by Fig 2B). This figure was generated using an analytic expression for the ratio of times to treatment failure (see S6 Text for the mathematical derivation).

Fig 4. The impact of alternative therapies.

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 S12 Text.