Multiple imputation is a well-established general technique for analyzing data with missing values. A convenient way to implement multiple imputation is sequential regression multiple imputation, also called chained equations multiple imputation. In this approach, we impute missing values using regression models for each variable, conditional on the other variables in the data. This approach, however, assumes that the missingness mechanism is missing at random, and it is not well-justified under not-at-random missingness without additional modification. In this paper, we describe how we can generalize the sequential regression multiple imputation imputation procedure to handle missingness not at random in the setting where missingness may depend on other variables that are also missing but not on the missing variable itself, conditioning on fully observed variables. We provide algebraic justification for several generalizations of standard sequential regression multiple imputation using Taylor series and other approximations of the target imputation distribution under missingness not at random. Resulting regression model approximations include indicators for missingness, interactions, or other functions of the missingness not at random missingness model and observed data. In a simulation study, we demonstrate that the proposed sequential regression multiple imputation modifications result in reduced bias in the final analysis compared to standard sequential regression multiple imputation, with an approximation strategy involving inclusion of an offset in the imputation model performing the best overall. The method is illustrated in a breast cancer study, where the goal is to estimate the prevalence of a specific genetic pathogenic variant.

Purpose: There are no standardized prognostication algorithms for metastatic radioiodine-refractory (RAI-R) differentiated thyroid cancer (DTC). We hypothesize that [¹⁸F]-FDG PET/CT may predict progression versus stability of disease based on quantitative analysis of metabolic tumor volume (MTV) and total lesion glycolysis (TLG). Methods: Retrospective study of 62 patients with metastatic RAI-R DTC to determine clinical outcomes with median follow-up from initial diagnosis of 11.1 years (8.38, 14.1) (range, 1.2–20 years). Baseline [¹⁸F]-FDG PET/CT scans were evaluated qualitatively for regional and distant metastases and quantitatively for tumor burden based on MTV and TLG obtained using gradient segmentation method. Results: After diagnosis of metastatic RAI-R disease was established, the 5-year overall survival (OS) probability was 34%, and median OS was 3.56 years (2.87, infinity). The 5-year progression-free survival (PFS) probability was 19%, and median PFS was 1.31 years (1.03, 2.38). TSH-suppressed thyroglobulin (Tg) levels greater than 100 ng/mL and Tg doubling time (Tg-DT) less than 6 months were significantly associated with worse OS and PFS. Higher than median values of MTV and TLG were associated with worse OS (P = 0.06) and PFS (P = 0.007). Higher hazard of death was noted for higher values of log-MTV and log-TLG (HR, 1.17 [95% confidence interval, 0.99–1.39], P = 0.05, and HR, 1.14 [95% confidence interval, 1.00–1.31], P = 0.05, respectively). Conclusions: [¹⁸F]-FDG PET/CT metabolic parameters can help define the volume and biologic variations of metastatic tumor burden. Metabolic tumor volume and TLG can be used for dynamic risk stratification of patients with metastatic RAI-R DTC regarding PFS and complement Tg-DT for prognosis of clinical disease course.

A diagnosis of perineural invasion (PNI), defined as cancer within or surrounding at least 33% of the nerve, leads to selection of aggressive treatment in squamous cell carcinoma (SCC). Recent mechanistic studies show that cancer and nerves interact prior to physical contact. The purpose of this study was to explore cancer-nerve interactions relative to clinical outcome. Biopsy specimens from 71 patients with oral cavity SCC were stained with hematoxylin and eosin and immunohistochemical (IHC; cytokeratin, S100, GAP43, Tuj1) stains. Using current criteria, PNI detection was increased with IHC. Overall survival (OS) tended to be poor for patients with PNI (P = .098). OS was significantly lower for patients with minimum tumor-nerve distance smaller than 5 μm (P = .011). The estimated relative death rate decreased as the nerve-tumor distance increased; there was a gradual drop off in death rate from distance equal to zero that stabilized around 500 μm. In PNI-negative patients, nerve diameter was significantly related to OS (HR 2.88, 95%CI[1.11,7.49]). Among PNI-negative nerves, larger nerve-tumor distance and smaller nerve diameter were significantly related to better OS, even when adjusting for T-stage and age (HR 0.82, 95% CI[0.72,0.92]; HR 1.27, 95% CI[1.00,1.62], respectively). GAP43, a marker for neuronal outgrowth, stained less than Tuj1 in nerves at greater distances from tumor (OR 0.76, 95% CI[0.73,0.79]); more GAP43 staining was associated with PNI. Findings from a small group of patients suggest that nerve parameters other than presence of PNI can influence outcome and that current criteria of PNI need to be re-evaluated to integrate recent biological discoveries.

Penalized regression methods are used in many biomedical applications for variable selection and simultaneous coefficient estimation. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors. This article considers a general class of penalized objective functions which, by construction, force selection of the same variables across imputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as “stacked” and “grouped” objective functions. Building on existing work, we (i) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for continuous and binary outcome data, (ii) incorporate adaptive shrinkage penalties, (iii) compare these methods through simulation, and (iv) develop an R package miselect. Simulations demonstrate that the “stacked” approaches are more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Biorepository aiming to identify the association between environmental pollutants and ALS risk. Supplementary materials for this article are available online.