Introduction

When chemotherapy agents are used to treat cancer, they are most effective when administered in combination. The development of drug combinations evolved from the pioneering work by medical oncologists in the 1950s and 1960s. For example, clinical studies led by Frei and Freireich demonstrated that dramatic improvements in the treatment of childhood leukemia could be achieved through the use of increasing numbers of drugs (1,2). Specifically, response rates in the range of 40% and no cures with methotrexate alone increased to >95% complete response and 35% cure rates with the inclusion of 6-mercaptopurine, prednisone, and vincristine into the treatment regimen. Eventually, cure rates increased to 75% to 80% with the inclusion of asparaginase, daunorubicin, and cytarabine. The principle underlying this approach was to administer combinations of chemotherapeu-tic drugs with nonoverlapping toxicities in full doses as early as possible in the disease (3).

In practical terms, executing the development of combination chemotherapy regimens relies on escalating the drugs to their maximum tolerated dose (MTD). This principle has remained largely unchanged from the trials conducted in the 1960s to today. Clinical evaluation of drug combinations typically establishes the recommended dose of one agent and then adds subsequent drugs to the combination, increasing the dose until the aggregate effects of toxicity are considered to be the maximum tolerated (4). The efficacy of such combinations in patients is then determined in postmarketing trials under the assumption that maximum therapeutic activity will be achieved with maximum dose intensity for all drugs in the combination. As we will describe below, this assumption may be incorrect due to the ways in which combinations of chemotherapy drugs interact when exposed to tumor cells.

Clinicians and research scientists have been actively searching for synergistic anticancer drug combinations since the concept of combination chemotherapy was adopted into widespread use (5). Combining different antitumor agents with distinct and independent therapeutic effects can improve patient responses. However, these benefits can be significantly enhanced if the agents interact synergistically where the responses are greater than predicted based on the contribution of individual agents. In contrast, combined drugs can interact antagonistically so that the combination is less active than predicted for additive activity of the individual agents. In reality, it is very difficult to determine whether drug combinations are acting in a synergistic, additive, or antagonistic fashion in cancer patients. Ultimately, one can only determine whether a new combination provides a statistically significant increase in an efficacy end point such as response rate, time to progression, or survival. As a result, one cannot resolve whether such combinations are truly optimized for potential synergistic interactions in the clinic.

Because of the difficulties associated with evaluating drug synergy in a clinical setting, researchers have utilized in vitro tumor cell lines to determine how drug combinations interact. Although this approach has the disadvantage of working with immortalized tumor cells in nonphysio-logical conditions, it provides a well-controlled environment where the cytotoxic effects of anticancer drug combinations can be carefully studied and analyzed by any one of a number of methods available to quantify whether drug combinations interact in a synergistic, additive, or antagonistic fashion. Also, the availability of a wide range of human tumor cell lines allows for common trends to be established, thereby enhancing the reliability of synergy predictions based on preclinical behavior. The following section provides a summary of several methods currently utilized for the quantitative evaluation of drug-drug interactions.

DETERMINATION OF DRUG-DRUG INTERACTION EFFECTS: SYNERGY VS. ANTAGONISM

Before discussing the results of drug interaction analyses, it is important that proper definitions of synergy and antagonism be defined. In order to evaluate synergy, the quantification of additivity is first required. Simply put, additivity is defined as the combined effect of two drugs predicted from the sum of the quantitative effects of the individual components. Synergy is therefore defined as a more than expected additive effect, and antagonism as a less than expected additive effect when the drugs are evaluated in combination. Although these definitions are basic, there are many complexities of synergy evaluations as described by Chou (6,7).

A variety of mathematical methods have been proposed to evaluate drug combination effects in the context of synergy and antagonism, ranging in complexity from general techniques requiring simple manual calculations to sophisticated algorithms aided by computers (8-11). Table 1 highlights some of the more commonly used methods. The underlying principles of

Table 1 Various Drug Interaction Methods Used for Evaluating Synergy Evaluation models

Approaches for continuous response data Isobologram (1870) Loewe additivity (1926) Bliss independence (1939) Fractional product method of Webb (1963) Method of Valeriote and Lin (1975) Method of Drewinko et al. (1976) Interaction index calculation of Berenbaum (1977) Method of Steel and Peckman (1979) Median-effect method of Chou and Talalay (1984) Method of Berenbaum (1985) Bliss independence response surface approach Method of Pritchard and Shipman (1990) Nonparametric response surface approaches

Bivariate spline fitting (Sühnel, 1990) Parametric response surface approaches Models of Greco et al. (1990) Models of Weinstein et al. (1990) Approaches for discrete success/failure data

Approach of Gessner (1974) Parametric response surface approaches Method of Greco and Lawrence (1988) Multivariate linear logistic model

Source: From Ref. 8.

the numerous models do vary but many of the models are modifications on existing models. Consequently, prior to selecting a method for data analysis, a thorough understanding of a particular model's origin as well as its strengths and weakness is required for proper data interpretation.

By far the most prevalent model used for drug combination analysis is the median-effect method of Chou and Talalay (12). The advantages of this method include the following: (i) the fundamental equations used were derived from basic mass action enzyme kinetic models; (ii) the experimental design efficiently utilizes experimental data points compared to other methods; and (iii) the analysis method is available as a software package allowing for easy data entry and modeling. After a comprehensive evaluation, the median-effect model was the primary model that we have chosen to apply to drug-combination analysis. However, to reduce any bias that could be incurred from the use of a single data analysis method and associated assumptions we also analyze selected data using isobologram and response surface methods. For a comprehensive review of the median effect, isobolo-gram, response surface, and other various methods, the reader is referred to Greco et al. (8).

METHODOLOGICAL APPROACHES TO DETERMINING SYNERGY/ANTAGONISM

When studying in vitro drug combinations for antitumor activity, two parameters inevitably must be established, namely drug concentration (dose) and drug:drug ratio. As described above, the different methodologies that one uses to evaluate synergy/antagonism relationships for drug combinations may lead to different drug doses and ratios evaluated, but nonetheless, distinct ratios and doses will result. Considering the application of carriers to deliver drug combinations, we recognized that drug:drug ratios will be fixed in the carrier, and consequently drug-ratio effects on synergy must be evaluated in vitro. This leads to the selection of the median-effect analysis method developed by Chou where different fixed-ratio combinations can be compared as a function of drug concentration employing the commercially available software CalcuSyn (13). This mimics the application of carrier-based drug combinations in vivo where the amount of the two drugs will be fixed in the delivery vehicle that maintains the ratio after administration and the dose injected can then be escalated at that fixed ratio.

The median-effect model introduced by Chou and Talalay (12) is the most widely utilized method for synergy determinations by investigators. A key element in its wide use can be attributed to its commercial availability as a software package, CalcuSyn (BioSoft). The original model was based upon the derivation of hundreds of enzyme kinetic models from mass-action law principles using methods of mathematical induction and deduction.

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