A large-scale randomized phase III trial was conducted to assess whether the addition of thalidomide, which has activity against advanced and refractory multiple myeloma, improves survival in the up-front management of patients with multiple myeloma undergoing melphalan-based tandem transplantation (8
). Despite significantly higher complete response rate and superior event-free survival among patients randomized to thalidomide, compared with the control patients with no thalidomide, overall survival (OS) was similar between treatment groups at the time of first publication, with a median follow-up of 42 months (8
), although, with longer follow-up of 72 months, a tendency of long-term effect of thalidomide on OS was observed (9
). As another unique feature of this phase III trial, pretreatment RNA from highly purified plasma cells was applied to Affymetrix U133Plus2.0 microarrays for 351 patients, out of 668 randomized patients. Because the efficacy of thalidomide on OS has been relatively uncertain, we conducted a predictive analysis for OS using the data with a median follow-up of 72 months for 351 patients with microarray gene-expression data. shows an OS curve for 351 patients by treatment arm [175 with thalidomide and 176 with no thalidomide (control)].
For each of 54,675 gene features on the microarray, we standardized gene-expression levels after normalization to have mean 0 and SD 1 across all 351 patients. We first developed the predictive signature score, S
, and the prognostic signature score, W
, using a 5-fold cross-validation. For the training set, we screened predictive genes using the significance level of 0.001 for a score test for no interaction between the gene feature and treatment and developed a compound covariates predictor (see Appendix B
). Similarly, but independently, we screened prognostic genes using the significance level of 0.001 for a score test for no association of the gene feature and OS developed a compound covariates predictor (see Appendix B
). We then obtained the predicted (quantile) signature scores S
for the test set. After the completion of the 5-fold cross-validation, we had obtained the predicted values of these scores for all 351 patients.
We fit the multivariate Cox proportional hazards model with both S
) for the entire patient cohort. We specified linear terms for the main effects of S
, such that f2
) = β2si
) = β4wi
, but the FPs with one term (FP1) for the interaction of R
) (see Appendix C
). The results were similar for the FPs with 2 terms (FP2). The estimated treatment effects function,
), is provided in .
) <0 represents thalidomide’s effects that prolong OS. The estimates
) for 0 ≤ s
≤ 1 represent the underlying smooth function about varying treatment effects for the whole range of the score S
(i.e., the entire patient population). For approximately the half of patients with lower values of S
, thalidomide is expected to prolong OS by varying degrees. On the other hand, for the rest of the patients with larger values of S
, it could have small adverse effects on OS.
We conducted a test of treatment efficacy for the subset of the patient population predicted to benefit from thalidomide based on
). Because the interest in this randomized trial was to assess improvement in survival by adding thalidomide for patients with high-dose therapies, compared with the control arm with no thalidomide, it is reasonable to test treatment efficacy for a subset of patients who are considered to be responsive to thalidomide using the 1-sided test statistic [see (A4
) in Appendix D
]. The observed value of the test statistic was −0.47 in log HR (0.62 in HR). The P
value obtained from 2,000 permutations was 0.019, which is significant if our test is used for a significance level 2% at the second stage of cross-validated ASD (6; see Appendix A
). For reference, the permutation-based P
value for the observed 2-sided test statistic, 0.35 [see (A3
) in Appendix D
], was 0.038.
On the basis of the estimates obtained from fitting the model (4
), we predicted patient-level survival rates for patients with S
= 0.1, 0.5, or 0.9 and W
= 0.1, 0.5, or 0.9. Again, lower values of S
represent larger effects of prolonging OS by receiving thalidomide. Lower values of W
represent higher survival rates (better prognosis). shows the predicted survival curves when receiving either of the 2 treatments (thalidomide and no thalidomide) for 4 combinations with (S
) = (0.1, 0.1), (0.1, 0.9), (0.5, 0.1), and (0.5, 0.9). summarizes the predicted 5-year survival rates with thalidomide and no thalidomide and their difference for all the combinations. Generally, even for the same level of the predictive score, S
, the effect size of thalidomide was larger (larger absolute difference in the predicted survival rate under each treatment) for patients with poor prognosis (larger W
). For example, for patients with S
= 0.1, the difference in the predicted survival rate was 17.9% for W
= 0.1, whereas it was 27.8% for W
= 0.9 (see also ).
Predicted 5-year survival rates for each treatment
Finally, we applied the procedures for selecting genes and developing signature-scoring functions to the entire 351 patients. Eighty-one and 662 genes with no overlap were selected using the significance level of 0.001 for developing the predictive and prognostic signature scoring functions, respectively. The empirical distributions of those scores will serve as reference distributions for predicting patient-level survival curves under each treatment for any new patient on the basis of the fitted model of (4
) obtained in the cross-validated prediction analysis.
For treatment selection, it would be reasonable to withhold thalidomide for approximately half of the patients with
) > 0 because no improvement in survival is expected by receiving thalidomide. For the rest of patients, the decision of whether to use thalidomide would take into consideration the estimated sizes of thalidomide’s effects for individual patients as well as other factors, such as safety issues, including severe peripheral neuropathy and deep-vein thrombosis (8