Estimating mean response as a function of treatment duration in an observational study, where duration may be informatively censored

After a treatment is found to be effective in a clinical study, attention often focuses on the effect of treatment duration on outcome. Such an analysis facilitates recommendations on the most beneficial treatment duration. In many studies, the treatment duration, within certain limits, is left to the discretion of the investigators. It is often the case that treatment must be terminated prematurely due to an adverse event, in which case a recommended treatment duration is part of a policy that treats patients for a specified length of time or until a treatment-censoring event occurs, whichever comes first. Evaluating mean response for a particular treatment-duration policy from observational data is difficult due to censoring and the fact that it may not be reasonable to assume patients are prognostically similar across all treatment strategies. We propose an estimator for mean response as a function of treatment-duration policy under these conditions. The method uses potential outcomes and embodies assumptions that allow consistent estimation of the mean response. The estimator is evaluated through simulation studies and demonstrated by application to the ESPRIT infusion trial coordinated at Duke University Medical Center.     

Serum Total Selenium Status in Greek Adults and Its Relation to Age. The ATTICA Study Cohort

The trace element selenium is an essential micronutrient for human health and its low levels in serum are implicated in the pathogenesis of several chronic diseases. Therefore, the determination of total selenium in serum may contribute to the assessment of the health and nutritional status of certain populations. The objective of the present work was to determine total selenium in the serum of 506 healthy volunteers that participated in the ATTICA study. Selenium was determined in serum by using the technique of inductively coupled plasma mass spectrometry. The mean serum selenium concentration was determined to be 91.8 ± 33.7 μg/L (N = 506); 87.6% of women and 88.5% of men had serum selenium concentration below 125 μg/L, the cutoff considered to be required for optimal glutathione peroxidase activity. No association was found between serum selenium levels and the gender of the participants while a significant decline of selenium with age (p < 0.0001) was observed. According to our results, no anthropometric, lifestyle, nutritional, or biochemical indices were able to affect the association between serum selenium and age. This result may indicate that other factors such as selenium distribution as well as retention may be affecting the relationship between serum selenium and age.     

Large-scale observational studies of hypericum extracts in patients with depressive disorders—a systematic review

We present a systematic review of observational studies of hypericum extracts in the treatment of depressive disorders. We included non-randomized studies with at least 100 patients suffering from depressive disorders treated with hypericum mono-preparations for at least 4 weeks, which reported clinical outcomes. Potentially relevant studies were identified through searches in electronic databases (Medline, PubMed), contacts with manufacturers, and handsearching of proceedings of phytomedicine congresses. Information on patients, interventions, methods an results were extracted by two reviewers. Sixteen studies including a total of 34,804 (range 101-11,296) patients met the inclusion criteria. Most studies investigated short-term effects (4-6 weeks) in patients with mild to moderate depression. Response rates (according to physician assessment) varied between 65% and 100%, the proportion of patients dropping out due to side effects varied between 0.0% and 2.8%. Two studies investigated long-term effects (52 weeks). Reponse rates were 60% and 69%, respectively, and the proportions of patients dropping out due to side effects were 3.4% and 5.7%, respectively. Serious side effects or interactions were not reported in any study. The quality of reporting was insufficient in the majority of publications. The available studies show that hypericum extract are well tolerated and seem to be effective in routine treatment of mild to moderate depressive disorders.     

The performance of random coefficient regression in accounting for residual confounding

Greenland (2000, Biometrics 56, 915-921) describes the use of random coefficient regression to adjust for residual confounding in a particular setting. We examine this setting further, giving theoretical and empirical results concerning the frequentist and Bayesian performance of random coefficient regression. Particularly, we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding. This devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model. The approach described by Gustafson (2005, Statistical Science 20, 111-140) is used to quantify the performance of a Bayesian estimator arising from a nonidentified model. From both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints. In terms of point-estimator bias this superiority arises when the extent of residual confounding is substantial, but the advantage is much broader in terms of interval estimation. The benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality, for the standard identifying constraints are equivalent to priors that typically correspond much worse.     

Socio-spatial levels in linearity analysis of dominance hierarchies: a case study on elephant seals

The analysis of linearity is a key aspect of the study of dominance hierarchies. To study the effect of the choice of socio-spatial level of analysis, we calculated linearity in a large set of southern elephant seal (Mirounga leonina) hierarchies from two populations (Valdés Peninsula and Falkland Islands). The socio-spatial level of analysis affects the observational effort, the completeness of matrices, and the frequency of unknown relationships. These factors, in turn, have a notable effect on linearity. We conclude that dominance should be studied at the local level, where the absence of structural zeros and the low incidence of observational zeros produce complete matrices, well rooted in the true spatial and social structure of the population. Depending on the specific social system, the extrapolation of dominance from the local level to higher levels may result in sparse matrices, and in biased estimates of linearity. The variation of the socio-spatial level of analysis may in part explain the contrasting results obtained in different studies of linearity of dominance hierarchies. Electronic Publication     

Estimating causal treatment effects from longitudinal HIV natural history studies using marginal structural models

Several recently completed and ongoing studies of the natural history of HIV infection have generated a wealth of information about its clinical progression and how this progression is altered by therepeutic interventions and environmental factors. Natural history studies typically follow prospective cohort designs, and enroll large numbers of participants for long-term prospective follow-up (up to several years). Using data from the HIV Epidemiology Research Study (HERS), a six-year natural history study that enrolled 871 HIV-infected women starting in 1993, we investigate the therapeutic effect of highly active antiretroviral therapy regimens (HAART) on CD4 cell count using the marginal structural modeling framework and associated estimation procedures based on inverse-probability weighting (developed by Robins and colleagues). To evaluate treatment effects from a natural history study, specialized methods are needed because treatments are not randomly prescribed and, in particular, the treatment-response relationship can be confounded by variables that are time-varying. Our analysis uses CD4 data on all follow-up visits over a two-year period, and includes sensitivity analyses to investigate potential biases attributable to unmeasured confounding. Strategies for selecting ranges of a sensitivity parameter are given, as are intervals for treatment effect that reflect uncertainty attributable both to sampling and to lack of knowledge about the nature and existence of unmeasured confounding. To our knowledge, this is the first use in "real data" of Robins's sensitivity analysis for unmeasured confounding (Robins, 1999a, Synthese 121, 151-179). The findings from our analysis are consistent with recent treatment guidelines set by the U.S. Panel of the International AIDS Society (Carpenter et al., 2000, Journal of the American Medical Association 280, 381-391).     

The Sign of the Unmeasured Confounding Bias under Various Standard Populations

Unmeasured confounders are a common problem in drawing causal inferences in observational studies. VanderWeele (Biometrics 2008, 64, 702–706) presented a theorem that allows researchers to determine the sign of the unmeasured confounding bias when monotonic relationships hold between the unmeasured confounder and the treatment, and between the unmeasured confounder and the outcome. He showed that his theorem can be applied to causal effects with the total group as the standard population, but he did not mention the causal effects with treated and untreated groups as the standard population. Here, we extend his results to these causal effects, and apply our theorems to an observational study. When researchers have a sense of what the unmeasured confounder may be, conclusions can be drawn about the sign of the bias.     

Causal inference on the difference of the restricted mean lifetime between two groups

When comparing survival times between two treatment groups, it may be more appropriate to compare the restricted mean lifetime, i.e., the expectation of lifetime restricted to a time L, rather than mean lifetime in order to accommodate censoring. When the treatments are not assigned to patients randomly, as in observational studies, we also need to account for treatment imbalances in confounding factors. In this article, we propose estimators for the difference of the restricted mean lifetime between two groups that account for treatment imbalances in prognostic factors assuming a proportional hazards relationship. Large-sample properties of our estimators based on martingale theory for counting processes are also derived. Simulation studies were conducted to compare these estimators and to assess the adequacy of the large-sample approximations. Our methods are also applied to an observational database of acute coronary syndrome patients from Duke University Medical Center to estimate the treatment effect on the restricted mean lifetime over 5 years.