Handling missing data in modelling quality of clinician-prescribed routine care: Sensitivity analysis of departure from missing at random assumption

Missing information is a major drawback in analyzing data collected in many routine health care settings. Multiple imputation assuming a missing at random mechanism is a popular method to handle missing data. The missing at random assumption cannot be confirmed from the observed data alone, hence the need for sensitivity analysis to assess robustness of inference. However, sensitivity analysis is rarely conducted and reported in practice. We analyzed routine paediatric data collected during a cluster randomized trial conducted in Kenyan hospitals. We imputed missing patient and clinician-level variables assuming the missing at random mechanism. We also imputed missing clinician-level variables assuming a missing not at random mechanism. We incorporated opinions from 15 clinical experts in the form of prior distributions and shift parameters in the delta adjustment method. An interaction between trial intervention arm and follow-up time, hospital, clinician and patient-level factors were included in a proportional odds random-effects analysis model. We performed these analyses using R functions derived from the jomo package. Parameter estimates from multiple imputation under the missing at random mechanism were similar to multiple imputation estimates assuming the missing not at random mechanism. Our inferences were insensitive to departures from the missing at random assumption using either the prior distributions or shift parameters sensitivity analysis approach.

Budget-feasible Procurement Mechanisms in Two-sided Markets

This paper considers the mechanism design problem in two-sided markets where multiple strategic buyers come with budgets to procure as much value of items as possible from the strategic sellers. Each seller holds an item with public value and is allowed to bid its private cost. Buyers could claim their budgets, not necessarily the true ones. The goal is to seek budget-feasible mechanisms that ensure sellers are rewarded enough payment and buyers' budgets are not exceeded. Our main contribution is a random mechanism that guarantees various desired theoretical guarantees like the budget feasibility, the truthfulness on the sellers' side and the buyers' side simultaneously, and constant approximation to the optimal total procured value of buyers.

The effects of model based missing data methods on guessing parameter in case of ignorable missing data

The present study aims to investigate the effects of model based missing data methods on guessing parameter in case of ignorable missing data. For this purpose, data based on Item Response Theory with 3 parameters logistic model were created in sample sizes of 500, 1000 and 3000; and then, missing values at random and missing values at completely random were created in ratios of 2.00%, 5.00% and 10.00%. These missing values were completed using expectation'maximization (EM) algorithm and multiple imputation methods. It was concluded that the performance of EM algorithm and multiple imputation methods was efficient depending on the rate of missing values on the data sets with missing values completely at random. When the missing value rate was 2.00%, both methods performed well in all sample sizes; however, they moved away from reference point as the number of missing values increased. On the other hand, it was also found that when the sample size was 3000, the cuts were closer to reference point even when the number of missing values was high. As for missing values at random mechanism, it was observed that both methods performed efficiently on guessing parameter when the number of missing values was low. Yet, this performance deteriorated considerably as the number of missing values increased. Both EM algorithm and multiple imputation methods did not perform effectively on guessing parameter in missing values at random mechanism.

Basic mathematical imputation techniques

The article presents the basics of imputation methodology (including the methodology of multiple imputation), focusing on understanding its mathematical background. We analyze the situation when observations in the original sample are independent random variables with identical distributions, and response or its lack is modeled by a random mechanism which is independent of observations. In particular, we point out to problems that arise when the standard Rubin estimate of the multiple imputation variance estimator is used. A possible improvement of this popular estimator is indicated. The starting point of the analysis is when the appearance of response deficiencies is caused by a deterministic mechanism.