Multiple Imputation of Covariates by Substantive-model Compatible Fully Conditional Specification

Propensity score analysis is a popular method to control for confounding in observational studies. A challenge in propensity methods is missing values in confounders. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. Concurrently, we aimed to provide guidance in choosing the optimal strategy. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Additionally, we demonstrated how missingness graphs help clarifying the missing structure. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random. In some situations, complete case analysis was also able to partially correct for unmeasured confounding. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation may fail when data are missing not at random. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random.

BackgroundMultiple imputation is frequently used to deal with missing data in healthcare research. Although it is known that the outcome should be included in the imputation model when imputing missing covariate values, it is not known whether it should be imputed. Similarly no clear recommendations exist on: the utility of incorporating a secondary outcome, if available, in the imputation model; the level of protection offered when data are missing not-at-random; the implications of the dataset size and missingness levels.MethodsWe used realistic assumptions to generate thousands of datasets across a broad spectrum of contexts: three mechanisms of missingness (completely at random; at random; not at random); varying extents of missingness (20–80% missing data); and different sample sizes (1,000 or 10,000 cases). For each context we quantified the performance of a complete case analysis and seven multiple imputation methods which deleted cases with missing outcome before imputation, after imputation or not at all; included or did not include the outcome in the imputation models; and included or did not include a secondary outcome in the imputation models. Methods were compared on mean absolute error, bias, coverage and power over 1,000 datasets for each scenario.ResultsOverall, there was very little to separate multiple imputation methods which included the outcome in the imputation model. Even when missingness was quite extensive, all multiple imputation approaches performed well. Incorporating a secondary outcome, moderately correlated with the outcome of interest, made very little difference. The dataset size and the extent of missingness affected performance, as expected. Multiple imputation methods protected less well against missingness not at random, but did offer some protection.ConclusionsAs long as the outcome is included in the imputation model, there are very small performance differences between the possible multiple imputation approaches: no outcome imputation, imputation or imputation and deletion. All informative covariates, even with very high levels of missingness, should be included in the multiple imputation model. Multiple imputation offers some protection against a simple missing not at random mechanism.

22101 Background: Maintenance of epithelial integrity plays a major role in tumor suppression but may also be important in metastasis and recurrence of cancer. Loss of E-cadherin (CDH1) is implicated in invasive lobular carcinomas of the breast. Furthermore, a polymorphic variant in the CDH1 promoter has been reported in association studies. We investigated the association of polymorphic variants in CDH1 with recurrence of breast cancer. Methods: TaqMan allelic discrimination assays were performed on genomic DNA prepared from whole blood of breast cancer patients. Genotyping was determined for several loci in CDH1 and were linked to clinical information. Results: CDH1 genotypes for the 3’UTR Ex16+246C>T polymorphism are in Hardy-Weinberg equilibrium with frequencies of: CC 69%, CT 27%, and TT 4%. Population-specific genotype frequencies were observed. There were no frequency differences between invasive ductal and invasive lobular carcinomas, but a trend toward a 4-year earlier age of onset of the latter associated with the low frequency allele. Seventeen percent of women in this cohort recurred, nearly half representing progesterone receptor-negative (PgR−) and half progesterone receptor-positive (PgR+) breast cancers. The recurrence rate for each genotype was 14.3%, 26%, and 7.1% for CC, CT, and TT genotypes, respectively. In women without recurrence, the genotype distribution was the same for PgR+ and PgR− disease. However, in those that recur, women with the CC genotype were more likely to be PgR− OR 2.32 CI [1.13–4.77] with a p value=0.023. The converse could not be evaluated due to small numbers. Conclusions: A polymorphic variant in the 3’UTR region of CDH1 is associated with recurrence of breast cancer. This association is strongest in recurrence of progesterone receptor-negative breast cancers. Recurrence in this SNP association study may reflect the effect of progesterone on proteins in adherence junctions or desmosomes or the role of CDH1 in the beta-catenin pathway. Support was from the New Jersey Commission on Cancer Research. No significant financial relationships to disclose.

Missing data are nearly always a problem in research, and missing values represent a serious threat to the validity of inferences drawn from findings. Increasingly, social science researchers are turning to multiple imputation to handle missing data. Multiple imputation, in which missing values are replaced by values repeatedly drawn from conditional probability distributions, is an appropriate method for handling missing data when values are not missing completely at random. However, use of this method requires developing an imputation model from the observed data. This is typically a rigorous and time-consuming process. To encourage wider adoption of multiple imputation in social work research, a simple framework for designing imputation models is presented. The framework and its ability to generate unbiased estimates are demonstrated in a simulation study. KEY WORDS: missing data; multiple imputation; nonresponse ********** Missing data are ubiquitous in social research, and missingness or nonresponse can represent a threat to the validity of inferences because of undue effects on efficiency, power, and parameter bias (Shadish, Cook, & Campbell, 2002). Social work researchers are now addressing missing data in a more rigorous manner. Recently, Saunders et al. (2006) and Choi, Golder, Gillmore, and Morrison (2005) described important data imputation methods and dispelled misunderstandings regarding popular imputation methods, such as mean substitution. Recent advances in analytic methods, such as multiple imputation (MI), are taking hold in social work research. With MI, missing values are replaced with values repeatedly drawn from simulated conditional probability distributions (Schafer, 1997), thus creating multiple versions of the data set. Each version of the data set is analyzed according to the data analysis model, and the multiple results are combined into point estimates (Rubin, 1996). A critical task in MI is to devise an imputation model (Allison, 2002) or missing data model (Graham, Olchowski, & Gilreath, 2007), which involves specifying the measures that are putatively associated with the missing values. Although this process adds additional steps, the specification of an imputation model and the creation of multiple data sets can produce less-biased estimates in the presence of missing data across a wide variety of data analysis techniques (Schafer, 1997). Besides MI, there are many other methods for addressing missing data (Schafer, 1999; Schafer & Graham, 2002). An equally rigorous method known as direct or full information maximum likelihood (FIML) estimation can produce unbiased estimates and correct standard errors in the presence of missing data. When the number of imputations is sufficiently large, identical missing data models will produce the same estimates under MI and FIML (Graham et al., 2007). Unlike MI, FIML is limited to maximum likelihood analytic techniques and the missing data model must be included in the analysis model. Although we focus on MI, the steps we describe for developing an imputation model are equally appropriate for use in the missing data model for FIML. On the basis of the MI literature, this article describes a framework for developing an imputation model for use with any free or commercial software package that performs MI. BRIEF REVIEW OF MISSING DATA CONCEPTS Generally, both MI and a broad range of missing data issues have received ample attention in the applied literature (Graham et al., 2007). We briefly discuss the three types of distributions that describe the randomness of nonresponse given that this property has consequences for the development of an imputation model. For a discussion of general missing data concepts that are not critical to understanding our discussion of imputation model development, we refer readers to Schafer and Graham (2002). Distribution of Nonresponse The probability distribution of nonresponse--more frequently referred to as the missing data or nonresponse mechanism (Rubin, 1976)--is both an important factor in the decision to impute with MI and a context for the development of an imputation model. …

The ability to compare genome-wide expression profiles in human tissue samples has the potential to add an invaluable molecular pathology aspect to the detection and evaluation of multiple diseases. Applications include initial diagnosis, evaluation of disease subtype, monitoring of response to therapy and the prediction of disease recurrence. The derivation of molecular signatures that can predict tumor recurrence in breast cancer has been a particularly intense area of investigation and a number of studies have shown that molecular signatures can outperform currently used clinicopathologic factors in predicting relapse in this disease. However, many of these predictive models have been derived using relatively simple computational algorithms and whether these models are at a stage of development worthy of large-cohort clinical trial validation is currently a subject of debate. In this review, we focus on the derivation of optimal molecular signatures from high-dimensional data and discuss some of the expected future developments in the field.

Background: Recurrent breast cancer occurs as a result of divergent gene expression in response to therapeutic intervention. A recent report showed that SOX11 , an embryogenic mammary transcription factor, is overexpressed in breast cancer. HER2 is also dysregulated in breast cancer stem cells; however, the relative expression of these two genes in recurrent breast cancer has not been investigated. Methods: Mouse models of mild and advanced stage recurrent breast cancer were developed via implantation of different doses of 4T1 Luc2GFP cells. The cellular morphology of normal and recurrent breast cancer tissues was analyzed using standard histological methods. SOX11, HER2 , and ALDH1 expression levels were analyzed via immunohistochemistry and western blotting. Results: Histological analyses revealed that treatment with doxorubicin limited mild recurrent cancer but was ineffective against advanced stage recurrent cancers, as evidenced by increased cell proliferation. SOX11 was consistently overexpressed in mild and advanced stage breast cancers treated with doxorubicin, relative to HER2 , which exhibited reduced expression in response to doxorubicin treatment in both mild and advanced stage recurrent breast cancer. In advanced stage recurrent breast cancer, SOX11 expression was more readily observed across the cell surface and was correlated with the overexpression of the breast cancer stem cell marker ALDH1 . Conclusions: These results show that SOX11 expression was directly associated with breast cancer stem cell populations. In contrast, HER2 expression was strongly associated with drug treatment effects, but was not correlated with breast cancer stem cell survival in recurrent breast cancer.

[This corrects the article on p. 192 in vol. 20, PMID: 28690656.].

Background: Isolated local or regional recurrence (ILRR) of breast cancer (BC) after mastectomy or lumpectomy indicates a poor prognosis and patients with ILRR hold a substantial risk of developing subsequent distant metastasis. Limited randomized evidence supports the recommendation of systemic treatment for hormone receptor-positive (HR+) lLRR. Cyclin-dependent kinases 4 and 6 (CDK4/6) inhibitors, such as palbociclib, have shown activity and safety in the first-line treatment of metastatic HR+/HER2-negative BC. The POLAR hypothesis is based on the results of the CALOR trial (IBCSG Trial 27-02), which showed effectiveness of adjuvant chemotherapy among patients with resected HR-negative ILRR, but not for HR+ ILRR. Considering these findings and compelling evidence supporting the activity of the combination of CDK4/6 inhibitors and endocrine therapy (ET), we hypothesize that palbociclib in combination with ET may be effective as adjuvant therapy in patients with HR+/HER2-negative resected ILRR of BC. Trial design: POLAR is a phase III open-label, multicenter, randomized trial of adjuvant palbociclib in combination with standard ET versus standard ET alone for women and men with histologically confirmed HR+/HER2-negative resected ILRR of BC. Protocol treatment consists of palbociclib (125 mg/d orally for 21 days, followed by 7 days rest) for 3 years plus standard ET for at least 3 years (Arm A) or standard ET for at least 3 years (Arm B). Patients must be enrolled within 6 months of complete gross excision of the ILRR. Patients may have started standard ET prior to entry. Randomization (1:1) is stratified according to (1) gender and menopausal status; (2) planned ET (oral aromatase inhibitor or tamoxifen vs. fulvestrant). The primary endpoint, invasive disease-free survival (iDFS), will be compared between treatment groups using a stratified log-rank test. The sample size provides 80% power to detect a 50% reduction in hazard (HR=0.50) for palbociclib plus ET versus ET-alone, using a log-rank test with two-sided α=0.05 test with 66 iDFS events. The 3-year iDFS is assumed to be 76% on the basis of patients in the CALOR trial who had ER+ ILRRs. Accrual: The trial will recruit 400 patients from approximately 50 Centers in Austria, France, Hungary, Italy, Spain and Switzerland. The first patient was randomized in August 2019. Accrual as of mid-June 2020 was 25 patients. The POLAR trial (IBCSG 59-19 / BIG 18-02) is sponsored and coordinated by IBCSG with financial support from Pfizer. The trial is conducted under the BIG umbrella in collaboration with ABCSG, GEICAM, SOLTI, SAKK and Unicancer. NCT03820830 Citation Format: Elisabetta Munzone, Stefan Aebi, Noelia Martínez Jañez, Uwe Güth, Meritxell Bellet, Barbara Pistilli, Marija Balic, Heidi Roschitzki-Voser, Meredith M Regan. Phase III open-label, multicenter, randomized trial of adjuvant palbociclib in combination with endocrine therapy versus endocrine therapy alone for patients with hormone receptor-positive / HER2-negative resected isolated locoregional recurrence of breast cancer - The POLAR Trial [abstract]. In: Proceedings of the 2020 San Antonio Breast Cancer Virtual Symposium; 2020 Dec 8-11; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2021;81(4 Suppl):Abstract nr OT-26-02.

Multiple imputation (MI) has become one of the main procedures used to treat missing data, but the guidelines from the methodological literature are not easily transferred to multilevel research. For models including random slopes, proper MI can be difficult, especially when the covariate values are partially missing. In the present article, we discuss applications of MI in multilevel random-coefficient models, theoretical challenges posed by slope variation, and the current limitations of standard MI software. Our findings from three simulation studies suggest that (a) MI is able to recover most parameters, but is currently not well suited to capture slope variation entirely when covariate values are missing; (b) MI offers reasonable estimates for most parameters, even in smaller samples or when its assumptions are not met; and

In patient follow‐up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as “bounded” or “interval‐censored.” Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood‐based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log‐normal regression with postimputation back‐transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.

Multiple imputation and maximum likelihood estimation (via the expectation‐maximization algorithm) are two well‐known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation‐maximization approximation to the likelihood. In this article, we exploit this key result to show that familiar likelihood‐based approaches to model selection, such as Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), can be used to choose the imputation model that best fits the observed data. Poor choice of imputation model is known to bias inference, and while sensitivity analysis has often been used to explore the implications of different imputation models, we show that the data can be used to choose an appropriate imputation model via conventional model selection tools. We show that BIC can be consistent for selecting the correct imputation model in the presence of missing data. We verify these results empirically through simulation studies, and demonstrate their practicality on two classical missing data examples. An interesting result we saw in simulations was that not only can parameter estimates be biased by misspecifying the imputation model, but also by overfitting the imputation model. This emphasizes the importance of using model selection not just to choose the appropriate type of imputation model, but also to decide on the appropriate level of imputation model complexity.

Missing covariate data commonly occur in epidemiological and clinical research, and are often dealt with using multiple imputation. Imputation of partially observed covariates is complicated if the substantive model is non-linear (e.g. Cox proportional hazards model), or contains non-linear (e.g. squared) or interaction terms, and standard software implementations of multiple imputation may impute covariates from models that are incompatible with such substantive models. We show how imputation by fully conditional specification, a popular approach for performing multiple imputation, can be modified so that covariates are imputed from models which are compatible with the substantive model. We investigate through simulation the performance of this proposal, and compare it with existing approaches. Simulation results suggest our proposal gives consistent estimates for a range of common substantive models, including models which contain non-linear covariate effects or interactions, provided data are missing at random and the assumed imputation models are correctly specified and mutually compatible. Stata software implementing the approach is freely available.

ABSTRACTIntroductionIn analysis of time‐to‐event outcomes, a mixture cure (MC) model is preferred over a standard survival model when the sample includes individuals who will never experience the event of interest. Motivated by a cohort study of breast cancer patients with incomplete biomarkers, we develop multiple imputation (MI) methods assuming a Weibull proportional hazards (PH‐MC) analysis model with multiple prognostic factors. However, for MI with fully conditional specification, an incorrectly specified imputation model can impair accuracy of point and interval estimates.Objectives and MethodsOur goal is to propose imputation models that are compatible with the Weibull PH‐MC analysis models. We derive an exact conditional distribution (ECD) imputation model which involves the analysis model likelihood. Using simulation studies, we compare effect estimate bias and confidence interval (CI) coverage under alternative imputation models including the ECD model, an approximation that includes a cure indicator (cECD), and a comprehensive simple (CS) model. For robust parameter estimation in finite and/or sparse samples, we incorporate the Firth‐type penalized likelihood (FT‐PL) and combined likelihood profile (CLIP) methods into the MI.ResultsCompared to complete case analysis, MI with penalization reduces estimation bias and improves coverage. Although ECD and cECD perform similarly at higher event rates, ECD generates smaller bias and higher coverage at lower rates. CS has larger bias and lower coverage than ECD and cECD, but CIs are narrower than for cECD.ConclusionsIn analyses of biomarkers and composite subtypes for prognosis studies such as in breast cancer, the use of compatible imputation models and penalization methods is recommended for MC modeling in samples with low event numbers and/or with covariate imbalance.

Background: Breast cancer exhibits familiar aggregation. Such susceptibility is found to be largely polygenic-with susceptibility conferred by a large number of low-penetrance loci. We have been using a bioinformatics approach to identify potential functional genetic variants, reducing the test complexities and costs compared to Genome Wide Association Study. Several single nucleotide polymorphisms (SNPs) in human histone deacetylase (HDAC) 9 were identified via such approach to test for associations with breast cancer risk and prognosis. It is well known that estrogen receptor (ER) and progesterone receptor (PR) expression are important markers for prognosis and prediction of response to endocrine therapy. Recent studies and clinical trials suggest that inhibition of HDAC may represent a novel strategy to modulate ER expression through epigenetic regulation of ER-a. Methods: This study evaluated the association of human HDAC9 SNPs at three loci (rs2239926, rs2240279 and rs2286003) with age of onset and recurrence of breast cancer in a cohort of 1101 patients enrolled prospectively from 2004 to 2009 at The Cancer Institute of New Jersey. Genotyping was performed using an Applied Biosystems TaqMan assay on the ABI 7900HT Fast Real-Time PCR System. A permutation test was performed to determine the statistical significance of differences in mean age at diagnosis between different genotypes. Logistic regression model was used to determine odds ratios for recurrence. Results: To limit potential differences due to the ethnicity and breast cancer subtypes, the association between the HDAC9 genotypes and the age at diagnosis was evaluated in Caucasian women with ductal carcinomas. Of the 1101 patients, 516 patients were Caucasians with ductal carcinomas; among which 74.8% were ER(+) with a mean age of diagnosis of 53.7 years; 25.2% were ER(-) with a mean age of diagnosis of 48.4 years. For patients with ER(+) breast cancer, the homozygous variant CC at HDAC9 rs2239926 developed breast cancer at an earlier age (49.3 years) than G allele carriers (GG+CG) (54.1 years) such that the age at diagnosis was accelerated by 4.8 years (P = 0.043). Conversely, for patients with ER(-) breast cancer, the CC variant appears to develop breast cancer at a later age (53.7 years) than G allele carriers (48.0 years) such that the age at diagnosis was delayed by 5.7 years, although this comparison was statistically limited due to the fewer number of cases. SNPs at the two other HDAC9 loci (rs2240279 and rs2286003) were not shown to be associated with age of onset of breast cancer. However, the homozygous variant CC at rs2240279 exhibits a strong association with recurrence in Caucasians with PR(+) breast cancer: OR 4.1, 95% CI (1.18-7.85) (P = 0.01). Conclusions: A polymorphic variant of human HDAC9 rs2239926 associates with an earlier age of onset of ER positive breast cancer while rs2240279 associates with recurrence of PR positive disease. We hypothesize that such polymorphisms may modulate ER and/or PR and its downstream gene expression leading to alteration of the clinical features of breast cancer including age of diagnosis and natural biology. Citation Information: Cancer Res 2010;70(24 Suppl):Abstract nr P3-12-03.

ObjectivesEpidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). Standard (default) MI procedures use simple linear covariate functions in the imputation model. We examine the bias that may be caused by acceptance of this default option and evaluate methods to identify problematic imputation models, providing practical guidance for researchers. Study Design and SettingUsing simulation and real data analysis, we investigated how imputation model mis-specification affected MI performance, comparing results with complete records analysis (CRA). We considered scenarios in which imputation model mis-specification occurred because (i) the analysis model was mis-specified or (ii) the relationship between exposure and confounder was mis-specified. ResultsMis-specification of the relationship between outcome and exposure, or between exposure and confounder, can cause biased CRA and MI estimates (in addition to any bias in the full-data estimate due to analysis model mis-specification). MI by predictive mean matching can mitigate model mis-specification. Methods for examining model mis-specification were effective in identifying mis-specified relationships. ConclusionWhen using MI methods that assume data are MAR, compatibility between the analysis and imputation models is necessary, but not sufficient to avoid bias. We propose a step-by-step procedure for identifying and correcting mis-specification of imputation models.