A novel method to address the association between received dose intensity and survival outcome: benefits of approaching treatment intensification at a more individualised level in a trial of the European Osteosarcoma Intergroup

Target received dose intensity (tRDI) is calculated as the ratio between standardised planned cumulative dose, δ, and standardised planned duration of regimen, τ. The former is obtained by standardising the sum of planned dose of all agents over all cycles of the allocated regimen; if a specific agent is not administered in a certain cycle, the contribution to the sum from that specific agent at that cycle is 0. Standardisation is performed by dividing the cumulative planned dose by the cumulative planned dose of a reference regimen. In MRC BO06, the cumulative planned dose is the same for each arm, 6 × (100 + 75) = 1050 mg/m², therefore standardisation with respect to Reg-DI yields δ = 100% for both Reg-C and Reg-DI. The standardised planned duration of a regimen is obtained by standardising the difference in days between the planned start of the last and the first cycle of the regimen. Standardisation is performed by dividing the cumulative planned dose by the cumulative planned dose of a reference regimen. In MRC BO06, Reg-DI and Reg-C have planned duration of 91 and 126 days, respectively. Standardising with respect to Reg-DI yields a value of τ = 91/126 = 72%. The final computations of tRDI are as follows: for Reg-C, 1050/1050 × 91/126 = 72%; for Reg-DI, 1050/1050 × 91/91 = 100%.

Achieved received dose intensity (aRDI) is also calculated from standardised cumulative dose and standardised time-on-treatment, but these quantities are now computed on observed treatment data. For example, a patient reporting a 20% reduction in cycles 5 and 6 achieved a cumulative dose of 4 × (100 + 75) + 2 × (100 + 75) × 0.8 = 980 mg/m², so δ = 980/1050 = 93%. In case an agent is omitted, the received dose of that agent in the formula is 0 for all the cycles affected by the omission; the same applies for all agents in case of discontinued cycles. Similarly, a patient who completed the protocol reporting a cumulative delay of 2 weeks (e.g. one 2-week delay or two 1-week delays at the beginning of two distinct cycles) would have τ = 105/91 = 115% if allocated to Reg-DI, or τ = 133/84 = 153% if allocated to Reg-C. In general, two patients—even two Reg-C or two Reg-DI—will report different values of τ and δ depending on the individual realisation of their intended treatment, i.e. depending on the delays and dose reductions reported throughout the treatment. In the graphical representation, the ratio δ/τ is the slope of a line connecting the patient point with the origin (0, 0) of the τδ-plane. For patients who completed all planned cycles, the quantity δ/τ is close to the aRDI as defined in [14]. For patients who did not complete all planned cycles, the ratio δ/τ might be difficult to use in practice. A solution is either to work with the pair (δ, τ) or to multiply δ/τ by the proportion of cycles completed.

Clustering forms groups of patients such that members of the same group are similar with respect to received dose intensity.

Clustering based on achieved received dose intensity (aRDI) is performed by grouping patients with similar values of δ and τ. In other words, clustering returns groups of patients who were administered a similar cumulative dose in a similar time window. This means that patients assigned to the same cluster will report similar aRDI, or closer to aRDI of an average patient in the same group than to aRDI of average patient from other groups. In particular, this kind of clustering will not separate well Reg-DI and Reg-C patients. Instead, it will group Reg-DI patients with large cumulative delays (due to a problematic course of therapy) with Reg-C with a regular course of therapy; it will also tend to group Reg-DI patients with a regular course of therapy with Reg-C patients who reported less than average or no delays at all.

Clustering based on regulated received dose intensity (rRDI) is performed by grouping patients with a similar course of therapy. Groups are formed using the relative increase of the cumulative dose over time. As explained in “Appendix 1”, rRDI can be represented as a sequence of (δ, τ)-values, one pair for each cycle administered. In case of MRC BO06, there can be up to 6 (δ, τ)-pairs. In other words, rRDI of a MRC BO06 patients can be described by the sequence [(δ₁, τ₁), (δ₂, τ₂), …, (δ₆, τ₆)], where δ_i and τ_i are the standardised cumulative dose and time on treatment up to at the beginning of the ith cycle. The slopes are obtained as ρ_i = (δ_i+1 − δ_i)/(τ_i+1 − τ_i), i = 1, 2, …, 5. The slopes measure the intensity of the treatment between the ith and the (i + 1)th cycle: if no reduction was applied to the nominal dosage of cycle i + 1, the increase (δ_i+1 − δ_i) equals 1/6 for both a Reg-DI and a Reg-C patient; if the start of cycle i + 1 was not delayed, the increase (τ_i+1 − τ_i) equals 14/84 for a Reg-DI patient and 21/84 for a Reg-C patient. As a consequence, ρ_i equals, respectively, 1 or 2/3 for a Reg-DI and a Reg-C patient who did not report delays or dose reductions in cycle i + 1. If a delay or a reduction is applied, then ρ_i is smaller. In case a patient completes less cycles than anticipated, some ρ_i cannot be calculated and are replaced by 0. Clustering is performed by grouping patients based on the similarity of the whole sequence of values [ρ_1,ρ_2,ρ_3,ρ_4,ρ₅]. With this method, groups tend to separate better Reg-C and Reg-DI patients, because information on the intended treatment (duration of cycles) is embedded in ρ_i at the cycle level and not just regimen-wise. Moreover, ρ_i carries information about the medical interventions that occurred in each cycle, offering a surrogate measure of individual tolerability to the allocated regimen.