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We consider modeling correlated survival data when cluster sizes may be informative to the outcome of interest based on a within-cluster resampling (WCR) approach and a weighted score function (WSF) method. We derive the large sample properties for the WCR estimators under the Cox proportional hazards model. We establish consistency and asymptotic normality of the regression coefficient estimators, and the weak convergence property of the estimated baseline cumulative hazard function. The WSF method is to incorporate the inverse of cluster sizes as weights in the score function. We conduct simulation studies to assess and compare the finite-sample behaviors of the estimators and apply the proposed methods to a dental study as an illustration.

BackgroundIn the phase III LUX-Head & Neck 1 (LUX-H&N1) trial, second-line afatinib significantly improved progression-free survival (PFS) versus methotrexate in patients with recurrent/metastatic head and neck squamous cell carcinoma (R/M HNSCC). Here, we evaluated association of prespecified biomarkers with efficacy outcomes in LUX-H&N1.Patients and methodsRandomized patients with R/M HNSCC and progression following ≥2 cycles of platinum therapy received afatinib (40 mg/day) or methotrexate (40 mg/m2/week). Tumor/serum samples were collected at study entry for patients who volunteered for inclusion in biomarker analyses. Tumor biomarkers, including p16 (prespecified subgroup; all tumor subsites), EGFR, HER2, HER3, c-MET and PTEN, were assessed using tissue microarray cores and slides; serum protein was evaluated using the VeriStrat® test. Biomarkers were correlated with efficacy outcomes.ResultsOf 483 randomized patients, 326 (67%) were included in the biomarker analyses; baseline characteristics were consistent with the overall study population. Median PFS favored afatinib over methotrexate in patients with p16-negative [2.7 versus 1.6 months; HR 0.70 (95% CI 0.50–0.97)], EGFR-amplified [2.8 versus 1.5 months; HR 0.53 (0.33–0.85)], HER3-low [2.8 versus 1.8 months; HR 0.57 (0.37–0.88)], and PTEN-high [1.6 versus 1.4 months; HR 0.55 (0.29–1.05)] tumors. Afatinib also improved PFS in combined subsets of patients with p16-negative and EGFR-amplified tumors [2.7 versus 1.5 months; HR 0.47 (0.28–0.80)], and patients with p16-negative tumors who were EGFR therapy-naïve [4.0 versus 2.4 months; HR 0.55 (0.31–0.98)]. PFS was improved in afatinib-treated patients who were VeriStrat ‘Good’ versus ‘Poor’ [2.7 versus 1.5 months; HR 0.71 (0.49–0.94)], but no treatment interaction was observed. Afatinib improved tumor response versus methotrexate in all subsets analyzed except for those with p16-positive disease (n = 35).ConclusionsSubgroups of HNSCC patients who may achieve increased benefit from afatinib were identified based on prespecified tumor biomarkers (p16-negative, EGFR-amplified, HER3-low, PTEN-high). Future studies are warranted to validate these findings.Clinical trial registrationNCT01345682.