A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

BACKGROUND: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. RESULTS: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. CONCLUSIONS: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt

Variables with time-varying effects and the Cox model: Some statistical concepts illustrated with a prognostic factor study in breast cancer

International audienceBACKGROUND: The Cox model relies on the proportional hazards (PH) assumption, implying that the factors investigated have a constant impact on the hazard - or risk - over time. We emphasize the importance of this assumption and the misleading conclusions that can be inferred if it is violated; this is particularly essential in the presence of long follow-ups. METHODS: We illustrate our discussion by analyzing prognostic factors of metastases in 979 women treated for breast cancer with surgery. Age, tumour size and grade, lymph node involvement, peritumoral vascular invasion (PVI), status of hormone receptors (HRec), Her2, and Mib1 were considered. RESULTS: Median follow-up was 14 years; 264 women developed metastases. The conventional Cox model suggested that all factors but HRec, Her2, and Mib1 status were strong prognostic factors of metastases. Additional tests indicated that the PH assumption was not satisfied for some variables of the model. Tumour grade had a significant time-varying effect, but although its effect diminished over time, it remained strong. Interestingly, while the conventional Cox model did not show any significant effect of the HRec status, tests provided strong evidence that this variable had a non-constant effect over time. Negative HRec status increased the risk of metastases early but became protective thereafter. This reversal of effect may explain non-significant hazard ratios provided by previous conventional Cox analyses in studies with long follow-ups. CONCLUSIONS: Investigating time-varying effects should be an integral part of Cox survival analyses. Detecting and accounting for time-varying effects provide insights on some specific time patterns, and on valuable biological information that could be missed otherwise

Levels of different subtypes of tumour-infiltrating lymphocytes correlate with each other, with matched circulating lymphocytes, and with survival in breast cancer

Purpose: Breast cancer tumour-infiltrating lymphocytes associate with clinico-pathological factors, including survival, although the literature includes many conflicting findings. Our aim was to assess these associations for key lymphocyte subtypes and in different tumour compartments, to determine whether these provide differential correlations and could, therefore, explain published inconsistencies. Uniquely, we also examine whether infiltrating levels merely reflect systemic lymphocyte levels or whether local factors are predominant in recruitment. Methods: Immunohistochemistry was used to detect tumour-infiltrating CD20+ (B), CD4+ (helper T), CD8+ (cytotoxic T) and FoxP3+ (regulatory T) cells in breast cancers from 62 patients, with quantification in tumour stroma, tumour cell nests, and tumour margins. Levels were analysed with respect to clinico-pathological characteristics and matched circulating levels (determined by flow-cytometry). Results: CD4+ lymphocytes were the most prevalent subtype in tumour stroma and at tumour edge and CD8+ lymphocytes were most prevalent in tumour nests; FoxP3+ lymphocytes were rarest in all compartments. High grade or hormone receptor negative tumours generally had significantly increased lymphocytes, especially in tumour stroma. Only intra-tumoural levels of CD8+ lymphocytes correlated significantly with matched circulating levels (p < 0.03), suggesting that recruitment is mainly unrelated to systemic activity. High levels of stromal CD4+ and CD20+ cells associated with improved survival in hormone receptor negative cases (p < 0.04), while tumour nest CD8+ and FoxP3+ cells associated with poor survival in hormone receptor positives (p < 0.005). Conclusions: Lymphocyte subtype and location define differential impacts on tumour biology, therefore, roles of tumour-infiltrating lymphocytes will only be unravelled through thorough analyses that take this into account