### Article

## A new meta-regression method to analyse all chemotherapy-comparing randomised clinical trials in advanced colorectal cancer

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Published: | September 8, 2005 |
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### Outline

### Text

#### Introduction and Objective

Planning of new chemotherapy regimens in a chemo-sensitive cancer entity should be based on all the available evidence from reliable chemotherapy studies published in the literature.

For example in a Medline search in colorectal cancer we found 79 randomised clinical trials (RCT) comparing chemotherapies. How can one summarise this vast amount of data to obtain insights that help the design of better treatment regimens and allow roughly predicting their outcome? We would like to learn about the growth pattern of the disease and the relative effectiveness of the cytostatic drugs used in past trials.

For each randomised pair-wise chemotherapy comparison we can extract two sorts of information from the respective publication:

b) details of the chemotherapy regimen compared (dosage of all drugs employed, treatment duration, scheduling etc.).

In order to make sense of these data, in addition we need a regression equation predicting the observed outcome difference from the difference in a summary measure of chemotherapy strength which is calculated from the treatment details of both arms. Such an equation is best derived from a simplified model of how chemotherapy works. Having specified such an equation-ansatz we can use standard statistical regression techniques to estimate the unknown parameters it contains (e.g. relative weights for cytostatic drugs) and to assess the model fit to the data.

We already developed such a meta-regression technique for tumour entities with a substantial cure rate and applied it successfully in lymphoma [Ref. 1]. Chemotherapy design based on modelling lead to a break-through trial in advanced stage Hodgkin’s disease [Ref. 2]. Here we develop a meta-regression technique for tumour entities like colorectal cancer in which the objective of chemotherapy is not tumour eradication (cure), but postponement of disease progression and treatment is given until disease progression.

#### Method

The choice of an appropriate measure of the observed treatment difference is based on the following facts on metastatic colorectal cancer: It is not curable with current CT except in very rare cases. Chemotherapy is typically cyclic and is given with constant dose intensity until progression is observed. Freedom from progression (FFP) curves decrease almost linearly with median time to progression in the order of 15-30 weeks. Treatment differences are in the order of a few weeks in median time to progression. An accelerated failure time model appears appropriate.

For the purpose of meta-regression we propose to extract estimates of the median times to progression from both arms: t^{^}
_{50}
^{A}, t^{^}
_{50}
^{B} and measure the difference in treatment outcome as: ln(t^{^}
_{50}
^{A}/ t^{^}
_{50}
^{B}) i.e. as log median progression time ratio. A variance estimate can be obtained from the steepness of the FFP curves at the median.

Arguing within the framework of the generalised Skipper chemotherapy model, we assume that the tumour consist of many clones which grow roughly linearly on the log scale and that the outcome is dominated by the worst clone. Each clone may be characterised by a hypothetical total controlling dose-intensity, namely the dose intensity that would just control the growth of the clone indefinitely. Let tdi be the total controlling dose-intensity of the worst clone of a median patient. We show that ln(t^{^}
_{50}
^{A}/ t^{^}
_{50}
^{B}) = ln(1-tdi^{B}/ tdi)-ln(1-tdi^{A}/ tdi) in a trial comparing therapy A and B. We use a simple weighted linear ansatz to calculate the total dose intensity from the dose intensities of the cyctostatic drugs used: tdi^{A}=sum beta_{j}*di^{A}
_{j}. Standard non-linear regression weighted by the precision of the trials is used to estimate the drug specific beta_{j} from which crude equipotency relations can be derived.

#### Materials

An extensive literature search initially identified 79 randomised studies in advanced colorectal cancer. Thirty-one trials were excluded mainly because of missing or incomplete data about FFP. Eight further papers were excluded because they studied drugs that were investigated in less than 3 pair-wise comparisons. Thus 40 studies reporting data of 11,676 patients and providing 74 pair-wise comparisons were entered into the final meta-regression analysis.

#### Results

Starting with a full model we analysed 11 drugs that occurred informatively in at least 6 pair-wise comparisons. The model converged without problem and explained about 70% of the observed variance. Four drugs with non-significant coefficients were discarded to obtain the final model. All these non-significant drugs are no longer used in current clinical practice. The weight estimates of the active drugs suggest that these drugs are currently used in roughly equipotent dose-intensities.

Total dose intensities typically ranged 0.2-0.6 as a fraction of the median total controlling dose intensity. This reflects the clinical fact that nearly all patients will show progressive disease within a few months.

#### Discussion

We present a novel meta-regression method to analyse randomised chemotherapy comparing trials in a palliative setting in which chemotherapy is given with constant dose-intensity until disease progression is observed. The method allows synthesising evidence scattered in the literature that is not accessible to conventional meta-analysis techniques. The method is based on a simplified model of chemotherapy. It provides for estimates of the relative weights of the cytostatic drugs used and indicates how far chemotherapy is from controlling the disease. This information may be a valuable help in designing new chemotherapy regimen and treatment strategies.

#### Acknowledgement

We thank Dr. Luisa Mantovani for encouraging our cooperation.

### References

- 1.
- Hasenclever D, Brosteanu O, Gerike T, Loeffler M. Modelling of chemotherapy: the effective dose approach. Ann Hematol. 2001;80 Suppl 3:B89-94.
- 2.
- Diehl V, Franklin J, Pfreundschuh M, Lathan B, Paulus U, Hasenclever D, Tesch H, Herrmann R, Dorken B, Muller-Hermelink HK, Duhmke E, Loeffler M; German Hodgkin's Lymphoma Study Group. Standard and increased-dose BEACOPP chemotherapy compared with COPP-ABVD for advanced Hodgkin's disease. N Engl J Med. 2003 Jun 12;348(24):2386-95.