Nicola Sartori

Multiple imputation of missing values in a cancer mortality analysis with estimated exposure dose

Imputation of missing values in a cancer mortality analysis in relation to estimated dose of dioxin for a cohort of chemical workers is considered. In particular, some subjects of the cohort have the body mass index (BMI) missing. This quantity is an essential ingredient for a toxicokinetic model that gives the estimated absorbed dose, which is then used for risk estimation in a proportional hazards model. Imputation of BMI allows to recover information and to use the entire cohort for risk estimation. Both conditional mean imputation and multiple imputation are used. The latter is a simulation-based approach to the analysis of missing data which takes into account the uncertainty of the imputation process using several imputations for each missing value. In the present context, the two imputation methods gave similar results, both correcting for bias (although with some questions) and leading to increased efficiency with respect to the complete-case analysis that simply discards the partially unobserved individuals.

Approximate Bayesian computation with composite score functions

Both approximate Bayesian computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.

Marginal posterior simulation via higher-order tail area approximations

In this paper we explore the use of higherorder tail area approximations for Bayesian simulation. These approximations give rise to alternative simulation schemes to MCMC for Bayesian computation of marginal posterior distributions for a scalar parameter of interest, in the presence of nuisance parameters. Their advantage over MCMC methods is that samples are drawn independently and much lower computational time is needed. The methods are illustrated by a genetic linkage model, a normal regression with censored data and a logistic regression model.

Detection of MicroRNAs in Archival Cytology Urine Smears

MicroRNAs’ dysregulation and profiling have been demonstrated to be clinically relevant in urothelial carcinoma (UC). Urine cytology is commonly used as the mainstay non-invasive test for secondary prevention and follow-up of UC patients. Ancillary tools are needed to support cytopathologists in the diagnosis of low-grade UC. The feasibility and reliability of microRNAs profiling by qRT-PCR analysis (miR-145 and miR-205) in archival routine urine cytology smears (affected by fixation/staining [Papanicolau] and room temperature storage) was tested in a series of 15 non-neoplastic and 10 UC urine specimens. Only samples with >5,000 urothelial cells and with <50% of inflammatory cells/red blood cells clusters were considered. Overall, a satisfactory amount of total RNA was obtained from all the considered samples (mean 1.27±1.43 µg, range 0.06–4.60 µg). Twenty nanograms of total RNA have been calculated to be the minimal total RNA concentration for reliable and reproducible miRNAs expression profiling analysis of archival cytological smears (slope = -3.4084; R-squared = 0.99; efficiency = 1.94). miR-145 and miR-205 were significantly downregulated in UC samples in comparison to non-tumor controls. These findings demonstrate that urine archival cytology smears are suitable for obtaining high-quality RNA to be used in microRNAs expression profiling. Further studies should investigate if miRNAs profiling can be successfully translated into clinical practice as diagnostic or prognostic markers.

Empirical and simulated adjustments of composite likelihood ratio statistics

Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward asymptotic distribution. There are many proposals for adjusting composite likelihood ratio tests in order to recover an asymptotic chi-square distribution, but they all depend on the sensitivity and variability matrices. The same is true for Wald-type and score-type counterparts. In realistic applications, sensitivity and variability matrices usually need to be estimated, but there are no comparisons of the performance of composite likelihood-based statistics in such an instance. A comparison of the accuracy of inference based on the statistics considering two methods typically employed for estimation of sensitivity and variability matrices, namely an empirical method that exploits independent observations, and Monte Carlo simulation, is performed. The results in two examples involving the pairwise likelihood show that a very large number of independent observations should be available in order to obtain accurate coverages using empirical estimation, while limited simulation from the full model provides accurate results regardless of the availability of independent observations. This suggests the latter as a default choice, whenever simulation from the model is possible.

Objective Bayesian higher-order asymptotics in models with nuisance parameters

A higher-order approximation to the marginal posterior distribution for a scalar parameter of interest in the presence of nuisance parameters is proposed. The approximation is obtained using a matching prior. The procedure improves the normal first-order approximation and has several advantages. It does not require the elicitation on the nuisance parameters, neither numerical integration nor Monte Carlo simulation, and it enables us to perform accurate Bayesian inference even for small sample sizes. Numerical illustrations are given for models of practical interest, such as linear non-normal models and logistic regression. Finally, it is shown how the proposed approximation can routinely be applied in practice using results from likelihood asymptotics and the R package bundle hoa.

Use of a toxicokinetic model in the analysis of cancer mortality in relation to the estimated absorbed dose of dioxin (2,3,7,8-tetrachlorodibenzo-p-dioxin, TCDD)

We performed an analysis of All cancer and Lung cancer mortality in relation to estimated absorbed dose of dioxin (2,3,7,8-tetrachlorodibenzo-p-dioxin, TCDD) in the cohort of chemical workers at 12 US plants assembled by the US National Institute for Occupational Safety and Health (NIOSH) (n = 5172). Estimates of cumulative exposure to TCDD were based on a minimal physiologic toxicokinetic model (MPTK) that accounts for inter- and intra-individual variations in body mass index (BMI) over time. Population-level parameters related to liver elimination and background (input or concentration) of TCDD were estimated from separate data with repeated measures of serum TCDD (US Air Force Health Study). An occupational TCDD input parameter was estimated based on one-point-in-time TCDD data available for a subset (n = 253) of the NIOSH cohort. Model-based time-dependent cumulative dose estimates (area under the curve (AUC) of the lipid-adjusted serum TCDD concentration over time) were obtained for members of the full cohort with recorded body height and weight (n = 4049), as this information is required by the MPTK model to compute dose. Missing-value problems arose in the estimation of the occupational input parameter (n = 42) and in TCDD-dose calculation in the full cohort (n = 886) and they were handled with multiple imputation methods. Risk-regression analyses were based on Cox log-linear models including age at entry, year of entry and duration of employment as categorical covariates in addition to the logarithm of cumulative TCDD dose in ppt-years. Risk sets were stratified on birth cohort. Estimates of the unlagged exposure coefficient in these models were 0.1249 [95% confidence interval (CI) 0.0144, 0.2354] for All cancer and 0.2158 (95% CI 0.02376, 0.4078) for lung cancer. A 10-year lag produced an increase in the estimate for all cancer (0.1539, 95% CI 0.0387, 0.2691), whereas, the estimate for lung cancer was not affected much (0.2125, 95% CI 0.0138, 0.4112). At a dose level of 100 times the background the estimates obtained with a 10-year lag translate into a relative risk of 2.03 (95% CI 1.19-3.45) for all cancer and of 2.66 (95% CI 1.07-6.64) for lung cancer. Higher estimates of the exposure coefficients were obtained after imputation of missing values. This increase in risk seemed due to the inclusion of short-term workers, who may exhibit a higher mortality for reasons other than dioxin exposure.

Modified Profile Likelihood for Fixed-Effects Panel Data Models

We show how modified profile likelihood methods, developed in the statistical literature, may be effectively applied to estimate the structural parameters of econometric models for panel data, with a remarkable reduction of bias with respect to ordinary likelihood methods. Initially, the implementation of these methods is illustrated for general models for panel data including individual-specific fixed effects and then, in more detail, for the truncated linear regression model and dynamic regression models for binary data formulated along with different specifications. Simulation studies show the good behavior of the inference based on the modified profile likelihood, even when compared to an ideal, although infeasible, procedure (in which the fixed effects are known) and also to alternative estimators existing in the econometric literature. The proposed estimation methods are implemented in an R package that we make available to the reader.

A note on directed adjusted profile likelihoods

Abstract Several adjustments to the profile likelihood have been proposed in recent years, to take into proper account the effects of fitting nuisance parameters. In some cases, adjusted profile likelihoods are higher-order approximations of suitable conditional or marginal target likelihoods. However, the xadjustments seem to provide accurate inference also when an exact marginal or conditional target likelihood is not available. Here, we consider adjusted profile likelihoods as approximations of a suitable general target likelihood. This is the likelihood for the parameter of interest with a known orthogonal nuisance parameter. Attention is focused on a scalar parameter of interest. Some new results are obtained concerning the null and non-null distributions of the directed likelihood calculated from an adjusted profile likelihood. In particular, we show that, while these distributions match the corresponding null and non-null distributions of the directed likelihood computed from the target likelihood up to order O(n−1/2) included, the agreement does not in general carry over to terms of order O(n−1), even if the information bias is of order O(n−1).

Integrated likelihoods in models with stratum nuisance parameters

Inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudo-likelihood in a two-index asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that the integrated likelihood, if chosen wisely, largely outperforms standard likelihood methods, such as the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.