Comparison of methods for handling missing data on immunohistochemical markers in survival analysis of breast cancer

Abstract

Background:Tissue micro-arrays (TMAs) are increasingly used to generate data of the molecular phenotype of tumours in clinical epidemiology studies, such as studies of disease prognosis. However, TMA data are particularly prone to missingness. A variety of methods to deal with missing data are available. However, the validity of the various approaches is dependent on the structure of the missing data and there are few empirical studies dealing with missing data from molecular pathology. The purpose of this study was to investigate the results of four commonly used approaches to handling missing data from a large, multi-centre study of the molecular pathological determinants of prognosis in breast cancer.Patients and methods:We pooled data from over 11 000 cases of invasive breast cancer from five studies that collected information on seven prognostic indicators together with survival time data. We compared the results of a multi-variate Cox regression using four approaches to handling missing data – complete case analysis (CCA), mean substitution (MS) and multiple imputation without inclusion of the outcome (MI−) and multiple imputation with inclusion of the outcome (MI+). We also performed an analysis in which missing data were simulated under different assumptions and the results of the four methods were compared.Results:Over half the cases had missing data on at least one of the seven variables and 11 percent had missing data on 4 or more. The multi-variate hazard ratio estimates based on multiple imputation models were very similar to those derived after using MS, with similar standard errors. Hazard ratio estimates based on the CCA were only slightly different, but the estimates were less precise as the standard errors were large. However, in data simulated to be missing completely at random (MCAR) or missing at random (MAR), estimates for MI+ were least biased and most accurate, whereas estimates for CCA were most biased and least accurate.Conclusion:In this study, empirical results from analyses using CCA, MS, MI− and MI+ were similar, although results from CCA were less precise. The results from simulations suggest that in general MI+ is likely to be the best. Given the ease of implementing MI in standard statistical software, the results of MI+ and CCA should be compared in any multi-variate analysis where missing data are a problem.

Molecular Subtypes of Breast Cancer: Long-term Incidence Trends and Prognostic Differences

“…Consequently, the observed subtype-specific incidence rates would underestimate the true rates, and underestimation would be greater for women born before 1929, because their tumour subtype was more likely to be unknown. To compensate for this, we performed multiple imputations to predict the molecular subtype of these tumours (24,26), assuming samples were missing at random (27) In analyses of prognosis, we distinguished between women diagnosed before 1995 and women diagnosed in 1995 or later, to approximate the gradual implementation of adjuvant treatment (including effective chemotherapy, anti-hormonal treatment and trastuzumab) in Norway (28). For each subtype, we calculated cumulative incidence of death from breast cancer at 5 and 15 years after diagnosis, treating deaths from other causes as competing events.…”

Evaluation of techniques for handling missing cost-to-charge ratios in the USA Nationwide Inpatient Sample: a simulation study

“…However, several other studies have compared handling missing data methods for other types of variables across diverse data sources including the NIS, with the consensus being that differences in the performance of each method became more pronounced as the level of missingness increased and that complete case analysis generally performed the worst in terms of RMSE and bias [8,15,[18][19][20][21]. Langkamp et al [15] compared four methods (complete case analysis, reweighting techniques, hot deck method, and multiple imputation with 'ICE' (Imputation by Chained Equations) to address missing data in three dichotomous variables in the National Maternal and Infant Health Survey linked with the Longitudinal Follow-Up Live Birth Survey.…”

Gradually implemented new biomarkers for prognostication of breast cancer: complete case analysis may introduce bias

“…Possible solutions to address this would be to assess whether missing information on biomarkers of interest is random or nonrandom by comparing characteristics or survival of patients who had information against those with missing information [2], or restricting study to the part of the cohort where biomarkers were routinely determined [5]. Investigators may also use statistical methods, such as imputation that have been found to yield more precise [10] and valid [11,12] results compared with complete case analysis.…”