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More precisely, multiple imputations are drawn from a posterior predictive distribution of the missing data conditional on the observed data.
For analysis with posterior probabilities, it uses the distribution of the missing data conditional upon both the observed data and the values of the model parameters to correct likelihood-based procedure.
For the E-step of the EM algorithm, one first finds the expected log likelihood, where the expectation is over the missing data conditional on the observed data and current estimates of the other parameters.
There are no a priori reasons to suggest that the relationship between the exposure and outcome is different between those with complete data vs. missing data, conditional on the covariates.
At each iteration, in the first step (E-step), the conditional expectation of the log-likelihood of the complete data is evaluated, where the expectation is taken with respect to the distribution of the missing data conditional on the observed data and the parameters estimated at the previous iteration.
THESEUS functions in two modes: (i) one mode for superpositioning structures with identical sequences [such as different (NMR) models] and (ii) an 'alignment mode,' which superpositions structures with different sequences (i.e. with missing data) conditional on a known alignment.
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Table 3 Categories of missing data for conditional appraisalsa and PAMs Conditional appraisals (N = 35 categories) n b PAMs (N = 54 categories) n b Category Efficacy 13 22 Safety 10 22 Effectiveness 5 2 Pharmacology 0 8 Reference to EMAc 7 – PAM post-authorisation measure a19 products with 20 conditional appraisals, 33 products with 34 EPARs bNumber of data requests for each category.
We assumed missing data were conditional on observed covariates, and we performed multiple imputation for all missing values using a regression switching approach (multiple imputation by chained equations) [ 21].
Imputed values are the conditional expectations for the missing data values, conditioned on past values of the series itself and current and past values of the other series.
For respondent characteristics with up to 15% missing data, we used conditional imputation, imputing the mean or median.
For the sake of brevity, we let Y'1 denote a vector including Y1 and D. Thus, P (λ|Y2, Y'1, Z) denotes the augmented and simplified posterior distribution and P (Z, Y'1|Y2, λi) denotes the conditional predictive distribution of missing data Z and Y'1, conditional on the current guess to the posterior mode.
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