Fitting multilevel multivariate models with missing data in responses and covariates that may include interactions and non-linear terms

The paper extends existing models for multilevel multivariate data with mixed response types to handle quite general types and patterns of missing data values in a wide range of multilevel generalized linear models. It proposes an efficient Bayesian modelling approach that allows missing values in covariates, including models where there are interactions or other functions of covariates such as polynomials. The procedure can also be used to produce multiply imputed complete data sets. A simulation study is presented as well as the analysis of a longitudinal data set. The paper also shows how existing multiprocess models for handling endogeneity can be extended by the framework proposed

Estimating excess hazard ratios and net survival when covariate data are missing: strategies for multiple imputation.

BACKGROUND: Net survival is the survival probability we would observe if the disease under study were the only cause of death. When estimated from routinely collected population-based cancer registry data, this indicator is a key metric for cancer control. Unfortunately, such data typically contain a non-negligible proportion of missing values on important prognostic factors (eg, tumor stage). METHODS: We carried out an empirical study to compare the performance of complete records analysis and several multiple imputation strategies when net survival is estimated via a flexible parametric proportional hazards model that includes stage, a partially observed categorical covariate. Starting from fully observed cancer registry data, we induced missingness on stage under three scenarios. For each of these scenarios, we simulated 100 incomplete datasets and evaluated the performance of the different strategies. RESULTS: Ordinal logistic models are not suitable for the imputation of tumor stage. Complete records analysis may lead to grossly misleading estimates of net survival, even when the missing data mechanism is conditionally independent of survival time given the covariates and the bias on the excess hazard ratios estimates is negligible. CONCLUSIONS: As key covariates are unlikely missing completely at random, studies estimating net survival should not use complete records. When the missingness can be inferred from available data, appropriate multiple imputation should be performed. In the context of flexible parametric proportional hazards models with a partially observed stage covariate, a multinomial logistic imputation model for stage should be used and should include the Nelson-Aalen cumulative hazard estimate and the event indicator

Correcting bias due to missing stage data in the non-parametric estimation of stage-specific net survival for colorectal cancer using multiple imputation.

BACKGROUND: Population-based net survival by tumour stage at diagnosis is a key measure in cancer surveillance. Unfortunately, data on tumour stage are often missing for a non-negligible proportion of patients and the mechanism giving rise to the missingness is usually anything but completely at random. In this setting, restricting analysis to the subset of complete records gives typically biased results. Multiple imputation is a promising practical approach to the issues raised by the missing data, but its use in conjunction with the Pohar-Perme method for estimating net survival has not been formally evaluated. METHODS: We performed a resampling study using colorectal cancer population-based registry data to evaluate the ability of multiple imputation, used along with the Pohar-Perme method, to deliver unbiased estimates of stage-specific net survival and recover missing stage information. We created 1000 independent data sets, each containing 5000 patients. Stage data were then made missing at random under two scenarios (30% and 50% missingness). RESULTS: Complete records analysis showed substantial bias and poor confidence interval coverage. Across both scenarios our multiple imputation strategy virtually eliminated the bias and greatly improved confidence interval coverage. CONCLUSIONS: In the presence of missing stage data complete records analysis often gives severely biased results. We showed that combining multiple imputation with the Pohar-Perme estimator provides a valid practical approach for the estimation of stage-specific colorectal cancer net survival. As usual, when the percentage of missing data is high the results should be interpreted cautiously and sensitivity analyses are recommended

The American Upper Ordovician Standard. VI, The Covington Sequence at Maysville, Kentucky

Author Institution: Department of Geology, The Ohio State University, Columbus 1

Specific Gravity, Fiber Length, and Extractive Content of Young Paulownia

The potential of using paulownia (Paulownia tomentosa) as a pulpwood species was assessed by evaluating the within-tree variation in specific gravity, fiber length, and extractive content of young trees growing on surface-mined land. Stem-wood fiber length and extractive-free specific gravity averaged 0.79 mm and 0.249, respectively. Total average extractive content approached 13%. Compared with other fast-growing hardwoods, paulownia has a lower specific gravity, shorter fiber length, and higher extractive content. All of these factors make paulownia a poor pulpwood species for most types of paper. Its fast growth rate may, however, favor the species as a valuable fiber source for some specialty-type papers where strength is not important

Ursodeoxycholic acid improves bilirubin but not albumin in primary biliary cirrhosis: further evidence for nonefficacy.

BACKGROUND/AIM: In randomised controlled trials (RCTs) of ursodeoxycholic acid (UDCA), although serum bilirubin is frequently reduced, its effect on disease progression and mortality is unclear. As serum albumin is an established independent prognostic marker, one might expect less deterioration of serum albumin values in a UDCA-treated group. We therefore modelled the typical evolution of serum bilirubin and albumin levels over time in UDCA-untreated patients and compared it with the observed levels in UDCA RCTs. METHODS: Multilevel modelling was used to relate the evolution of serum albumin to serum bilirubin and time since patient referral. For each considered RCT, the derived model was used to predict the relationship between final mean serum albumin and bilirubin concentration, adjusted for mean serum albumin at referral and followup duration. RESULTS: Five RCTs were eligible in terms of available data, of which two had long followup. In all trials, serum albumin did not significantly differ between UDCA- and placebo-treated patients, despite the UDCA effect on serum bilirubin. Therefore, there is no evidence over time for changes or maintenance of albumin levels for UDCA-treated patients above the levels predicted for placebo-treated patients. CONCLUSIONS: Our findings suggest that UDCA does not alter serum albumin in a way that is consistent with its effect on serum bilirubin. Therefore, reductions in serum bilirubin of UDCA-treated PBC do not parallel another validated and independent prognostic marker, further questioning the validity of serum bilirubin reduction with UDCA as a surrogate therapeutic marker

Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station