Dataset Information

Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism.

ABSTRACT: In missing data analysis, the assumption of the missing data mechanism is crucial. Under different assumptions, different statistical methods have to be developed accordingly; however, in reality this kind of assumption is usually unverifiable. Therefore a less stringent, and hence more flexible, assumption is preferred. In this paper, we consider a generally applicable missing data mechanism, which includes various instances in all three scenarios: missing completely at random, missing at random, and missing not at random. Under this general missing data mechanism, we introduce the conditional likelihood and its approximate version as the base for estimating the unknown parameter of interest. Since this approximate conditional likelihood uses the completely observed samples only, it may result in large estimation bias, which could deteriorate the statistical inference and also jeopardize other statistical procedure. To tackle this problem, we propose to use some resampling techniques to reduce the estimation bias. We consider both the Jackknife and the Bootstrap in our paper. We compare their asymptotic biases through a higher order expansion up to O(n -1). We also derive some results for the mean squared error in terms of estimation accuracy. We conduct comprehensive simulation studies under different situations to illustrate our proposed method. We also apply our method to a prostate cancer data analysis.

SUBMITTER: Zhao J

PROVIDER: S-EPMC6759332 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism.

Zhao Jiwei J

Journal of nonparametric statistics 20170614 3

In missing data analysis, the assumption of the missing data mechanism is crucial. Under different assumptions, different statistical methods have to be developed accordingly; however, in reality this kind of assumption is usually unverifiable. Therefore a less stringent, and hence more flexible, assumption is preferred. In this paper, we consider a generally applicable missing data mechanism, which includes various instances in all three scenarios: missing completely at random, missing at rando ...[more]

PMID: 31551650

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Project description:BackgroundThe UN's Sustainable Development Goals are devoted to eradicate a range of infectious diseases to achieve global well-being. These efforts require monitoring disease transmission at a level that differentiates between pathogen variants at the genetic/molecular level. In fact, the advantages of genetic (molecular) measures like multiplicity of infection (MOI) over traditional metrics, e.g., R0, are being increasingly recognized. MOI refers to the presence of multiple pathogen variants within an infection due to multiple infective contacts. Maximum-likelihood (ML) methods have been proposed to derive MOI and pathogen-lineage frequencies from molecular data. However, these methods are biased.Methods and findingsBased on a single molecular marker, we derive a bias-corrected ML estimator for MOI and pathogen-lineage frequencies. We further improve these estimators by heuristical adjustments that compensate shortcomings in the derivation of the bias correction, which implicitly assumes that data lies in the interior of the observational space. The finite sample properties of the different variants of the bias-corrected estimators are investigated by a systematic simulation study. In particular, we investigate the performance of the estimator in terms of bias, variance, and robustness against model violations. The corrections successfully remove bias except for extreme parameters that likely yield uninformative data, which cannot sustain accurate parameter estimation. Heuristic adjustments further improve the bias correction, particularly for small sample sizes. The bias corrections also reduce the estimators' variances, which coincide with the Cramér-Rao lower bound. The estimators are reasonably robust against model violations.ConclusionsApplying bias corrections can substantially improve the quality of MOI estimates, particularly in areas of low as well as areas of high transmission-in both cases estimates tend to be biased. The bias-corrected estimators are (almost) unbiased and their variance coincides with the Cramér-Rao lower bound, suggesting that no further improvements are possible unless additional information is provided. Additional information can be obtained by combining data from several molecular markers, or by including information that allows stratifying the data into heterogeneous groups.

Dataset Information

Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism.

Publications

Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism.

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