Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.

Fitting ACE Structural Equation Models to Case-Control Family Data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). To this end, we describe a ACE model for binary family data and then introduce an approach to fitting the model to case-control family data. The structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. Our likelihood-based approach to fitting involves conditioning on the proband’s disease status, as well as setting prevalence equal to a pre-specified value that can be estimated from the data themselves if necessary. Simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly-made assumptions hold. These assumptions include: the usual assumptions for the classic ACE and liability-threshold models; assumptions about shared family environment for relative pairs; and assumptions about the case-control family sampling, including single ascertainment. When our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.

Semiparametric Estimation in General Repeated Measures Problems

This paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal/clustered data, conditional logistic regression for matched case-control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile-kernel and backfitting estimation methods for these problems, derive their asymptotic distributions, and show that in likelihood problems the methods are semiparametric efficient. While generally not true, with our methods profiling and backfitting are asymptotically equivalent. We also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm. The proposed methods are evaluated using simulation studies and applied to the Kenya hemoglobin data.

Semiparametric Estimation of Models for Natural Direct and Indirect Effects

In recent years, researchers in the health and social sciences have become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of an exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Natural direct and indirect effects are of particular interest as they generally combine to produce the total effect of the exposure and therefore provide insight on the mechanism by which it operates to produce the outcome. A semiparametric theory has recently been proposed to make inferences about marginal mean natural direct and indirect effects in observational studies (Tchetgen Tchetgen and Shpitser, 2011), which delivers multiply robust locally efficient estimators of the marginal direct and indirect effects, and thus generalizes previous results for total effects to the mediation setting. In this paper we extend the new theory to handle a setting in which a parametric model for the natural direct (indirect) effect within levels of pre-exposure variables is specified and the model for the observed data likelihood is otherwise unrestricted. We show that estimation is generally not feasible in this model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations, given high-dimensional covariates. We thus consider multiply robust estimation and propose a more general model which assumes a subset but not all of several working models holds.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Time-related, cross-sectional and prospective follow-up of pancreatic endocrine function after pancreas allograft transplantation in type 1 (insulin-dependent) diabetic patients

It has been established that successful pancreas transplantation in Type 1 (insulin-dependent) diabetic patients results in normal but exaggerated phasic glucose-induced insulin secretion, normal intravenous glucose disappearance rates, improved glucose recovery from insulin-induced hypoglycaemia, improved glucagon secretion during insulin-induced hypoglycaemia, but no alterations in pancreatic polypeptide responses to hypoglycaemia. However, previous reports have not segregated the data in terms of the length of time following successful transplantation and very little prospective data collected over time in individual patients has been published. This article reports that in general there are no significant differences in the level of improvement when comparing responses as early as three months post-operatively up to as long as two years post-operatively when examining the data cross-sectionally in patients who have successfully maintained their allografts. Moreover, this remarkable constancy in pancreatic islet function is also seen in a smaller group of patients who have been examined prospectively at various intervals post-operatively. It is concluded that successful pancreas transplantation results in remarkable improvements in Alpha and Beta cell but not PP cell function that are maintained for at least one to two years.

How stable are 20th century calibration models? A high-resolution summer temperature reconstruction for the eastern Swiss Alps back to A.D. 1580 derived from proglacial varved sediments

We found a significant positive correlation between local summer air temperature (May-September) and the annual sediment mass accumulation rate (MAR) in Lake Silvaplana (46°N, 9°E, 1800 m a.s.l.) during the twentieth century (r = 0.69, p < 0.001 for decadal smoothed series). Sediment trap data (2001-2005) confirm this relation with exceptionally high particle yields during the hottest summer of the last 140 years in 2003. On this base we developed a decadal-scale summer temperature reconstruction back to AD 1580. Surprisingly, the comparison of our reconstruction with two other independent regional summer temperature reconstructions (based on tree-rings and documentary data) revealed a significant negative correlation for the pre-1900 data (ie, late ‘Little Ice Age’). This demonstrates that the correlation between MAR and summer temperature is not stable in time and the actualistic principle does not apply in this case. We suggest that different climatic regimes (modern/‘Little Ice Age’) lead to changing state conditions in the catchment and thus to considerably different sediment transport mechanisms. Therefore, we calibrated our MAR data with gridded early instrumental temperature series from AD 1760-1880 (r = -0.48, p < 0.01 for decadal smoothed series) to properly reconstruct the late LIA climatic conditions. We found exceptionally low temperatures between AD 1580 and 1610 (0.75°C below twentieth-century mean) and during the late Maunder Minimum from AD 1680 to 1710 (0.5°C below twentieth-century mean). In general, summer temperatures did not experience major negative departures from the twentieth-century mean during the late ‘Little Ice Age’. This compares well with the two existing independent regional reconstructions suggesting that the LIA in the Alps was mainly a phenomenon of the cold season.

Osteoporosis case finding in the general practice: phalangeal radiographic absorptiometry with and without risk factors for osteoporosis to select postmenopausal women eligible for lumbar spine and hip densitometry

Mass screening for osteoporosis using DXA measurements at the spine and hip is presently not recommended by health authorities. Instead, risk factor questionnaires and peripheral bone measurements may facilitate the selection of women eligible for axial bone densitometry. The aim of this study was to validate a case finding strategy for postmenopausal women who would benefit most from subsequent DXA measurement by using phalangeal radiographic absorptiometry (RA) alone or in combination with risk factors in a general practice setting. The sensitivity and specificity of this strategy in detecting osteoporosis (T-score < or =2.5 SD at the spine and/or the hip) were compared with those of the current reimbursement criteria for DXA measurements in Switzerland. Four hundred and twenty-three postmenopausal women with one or more risk factors for osteoporosis were recruited by 90 primary care physicians who also performed the phalangeal RA measurements. All women underwent subsequent DXA measurement of the spine and the hip at the Osteoporosis Policlinic of the University Hospital of Berne. They were allocated to one of two groups depending on whether they matched with the Swiss reimbursement conditions for DXA measurement or not. Logistic regression models were used to predict the likelihood of osteoporosis versus "no osteoporosis" and to derive ROC curves for the various strategies. Differences in the areas under the ROC curves (AUC) were tested for significance. In women lacking reimbursement criteria, RA achieved a significantly larger AUC (0.81; 95% CI 0.72-0.89) than the risk factors associated with patients' age, height and weight (0.71; 95% C.I. 0.62-0.80). Furthermore, in this study, RA provided a better sensitivity and specificity in identifying women with underlying osteoporosis than the currently accepted criteria for reimbursement of DXA measurement. In the Swiss environment, RA is a valid case finding tool for patients with risk factors for osteoporosis, especially for those who do not qualify for DXA reimbursement.

Steady-state function of the ubiquitous mammalian Na/H exchanger (NHE1) in relation to dimer coupling models with 2Na/2H stoichiometry

We describe the steady-state function of the ubiquitous mammalian Na/H exchanger (NHE)1 isoform in voltage-clamped Chinese hamster ovary cells, as well as other cells, using oscillating pH-sensitive microelectrodes to quantify proton fluxes via extracellular pH gradients. Giant excised patches could not be used as gigaseal formation disrupts NHE activity within the patch. We first analyzed forward transport at an extracellular pH of 8.2 with no cytoplasmic Na (i.e., nearly zero-trans). The extracellular Na concentration dependence is sigmoidal at a cytoplasmic pH of 6.8 with a Hill coefficient of 1.8. In contrast, at a cytoplasmic pH of 6.0, the Hill coefficient is <1, and Na dependence often appears biphasic. Results are similar for mouse skin fibroblasts and for an opossum kidney cell line that expresses the NHE3 isoform, whereas NHE1(-/-) skin fibroblasts generate no proton fluxes in equivalent experiments. As proton flux is decreased by increasing cytoplasmic pH, the half-maximal concentration (K(1/2)) of extracellular Na decreases less than expected for simple consecutive ion exchange models. The K(1/2) for cytoplasmic protons decreases with increasing extracellular Na, opposite to predictions of consecutive exchange models. For reverse transport, which is robust at a cytoplasmic pH of 7.6, the K(1/2) for extracellular protons decreases only a factor of 0.4 when maximal activity is decreased fivefold by reducing cytoplasmic Na. With 140 mM of extracellular Na and no cytoplasmic Na, the K(1/2) for cytoplasmic protons is 50 nM (pH 7.3; Hill coefficient, 1.5), and activity decreases only 25% with extracellular acidification from 8.5 to 7.2. Most data can be reconstructed with two very different coupled dimer models. In one model, monomers operate independently at low cytoplasmic pH but couple to translocate two ions in "parallel" at alkaline pH. In the second "serial" model, each monomer transports two ions, and translocation by one monomer allosterically promotes translocation by the paired monomer in opposite direction. We conclude that a large fraction of mammalian Na/H activity may occur with a 2Na/2H stoichiometry.

Can decision making in general surgery be based on evidence? An empirical study of Cochrane Reviews

BACKGROUND: This empirical study analyzes the current status of Cochrane Reviews (CRs) and their strength of recommendation for evidence-based decision making in the field of general surgery. METHODS: Systematic literature search of the Cochrane Database of Systematic Reviews and the Cochrane Collaboration's homepage to identify available CRs on surgical topics. Quantitative and qualitative characteristics, utilization, and formulated treatment recommendations were evaluated by 2 independent reviewers. Association of review characteristics with treatment recommendation was analyzed using univariate and multivariate logistic regression models. RESULTS: Ninety-three CRs, including 1,403 primary studies and 246,473 patients, were identified. Mean number of included primary studies per CR was 15.1 (standard deviation [SD] 14.5) including 2,650 (SD 3,340) study patients. Two and a half (SD 8.3) nonrandomized trials were included per analyzed CR. Seventy-two (77%) CRs were published or updated in 2005 or later. Explicit treatment recommendations were given in 45 (48%). Presence of a treatment recommendation was associated with the number of included primary studies and the proportion of randomized studies. Utilization of surgical CRs remained low and showed large inter-country differences. The most surgical CRs were accessed in UK, USA, and Australia, followed by several Western and Eastern European countries. CONCLUSION: Only a minority of available CRs address surgical questions and their current usage is low. Instead of unsystematically increasing the number of surgical CRs it would be far more efficient to focus the review process on relevant surgical questions. Prioritization of CRs needs valid methods which should be developed by the scientific surgical community.

Outcome evaluation of early placed maxillary anterior single-tooth implants using objective esthetic criteria: a cross-sectional, retrospective study in 45 patients with a 2- to 4-year follow-up using pink and white esthetic scores

BACKGROUND: To validate the concept of early implant placement for use in the esthetically sensitive anterior maxilla, clinical trials should ideally include objective esthetic criteria when assessing outcome parameters. METHODS: In this cross-sectional, retrospective 2- to 4-year study involving 45 patients treated with maxillary anterior single-tooth implants according to the concept of early implant placement, a novel comprehensive index, comprising pink esthetic score and white esthetic score (PES/WES; the highest possible combined score is 20), was applied for the objective esthetic outcome assessment of anterior single-tooth implants. RESULTS: All 45 anterior maxillary single-tooth implants fulfilled strict success criteria for dental implants with regard to osseointegration, including the absence of peri-implant radiolucency, implant mobility, suppuration, and pain. The mean total PES/WES was 14.7 +/- 1.18 (range: 11 to 18). The mean total PES of 7.8 +/- 0.88 (range: 6 to 9) documents favorable overall peri-implant soft tissue conditions. The two PES variables facial mucosa curvature (1.9 +/- 0.29) and facial mucosa level (1.8 +/- 0.42) had the highest mean values, whereas the combination variable root convexity/soft tissue color and texture (1.2 +/- 0.53) proved to be the most difficult to fully satisfy. Mean scores were 1.6 +/- 0.5 for the mesial papilla and 1.3 +/- 0.5 for the distal papilla. A mean value of 6.9 +/- 1.47 (range: 4 to 10) was calculated for WES. CONCLUSIONS: This study demonstrated that anterior maxillary single-tooth replacement, according to the concept of early implant placement, is a successful and predictable treatment modality, in general, and from an esthetic point of view, in particular. The suitability of the PES/WES index for the objective outcome assessment of the esthetic dimension of anterior single-tooth implants was confirmed. However, prospective clinical trials are needed to further validate and refine this index.