Estimating menarcheal age distribution from partially recalled data.

In a cross-sectional study, adolescent and young adult females were asked to recall the time of menarche, if experienced. Some respondents recalled the date exactly, some recalled only the month or the year of the event, and some were unable to recall anything. We consider estimation of the menarcheal age distribution from this interval-censored data. A complicated interplay between age-at-event and calendar time, together with the evident fact of memory fading with time, makes the censoring informative. We propose a model where the probabilities of various types of recall would depend on the time since menarche. For parametric estimation, we model these probabilities using multinomial regression function. Establishing consistency and asymptotic normality of the parametric maximum likelihood estimator requires a bit of tweaking of the standard asymptotic theory, as the data format varies from case to case. We also provide a non-parametric maximum likelihood estimator, propose a computationally simpler approximation, and establish the consistency of both these estimators under mild conditions. We study the small sample performance of the parametric and non-parametric estimators through Monte Carlo simulations. Moreover, we provide a graphical check of the assumption of the multinomial model for the recall probabilities, which appears to hold for the menarcheal data set. Our analysis shows that the use of the partially recalled part of the data indeed leads to smaller confidence intervals of the survival function.

Ferromagnetic Cr2Te3 nanorods with ultrahigh coercivity.

Ferromagnetic Cr2Te3 nanorods were synthesized by a one-pot high-temperature organic-solution-phase method. The crystalline phases and magnetic properties can be systematically tuned by varying the molar ratio of the Cr and Te precursors. A magnetically hard phase, identified as chemically ordered Cr2Te3, is the dominating one at the precursor ratio between Cr : Te = 1 : 1.2 and 1 : 1.8. A magnetically soft phase, attributed to chemical disorder due to composition inhomogeneity and stacking faults, is present under either Cr-rich or Te-rich synthesis conditions. A large coercivity of 9.6 kOe is obtained for a Cr : Te precursor ratio of 1 : 1.8, which is attributed to the large magnetocrystalline anisotropy of ordered Cr2Te3 nanorods, and verified by density-functional theory calculations. The hard and soft phases sharing coherent interfaces co-exist in a seemingly single-crystalline nanorod, showing an unusual transition from exchange-coupled behavior at higher temperatures to two-phase behavior as the temperature is lowered.

Submarine groundwater discharge derived strontium from the Bengal Basin traced in Bay of Bengal water samples.

Evaluating the submarine groundwater discharge (SGD) derived strontium (Sr) flux from the Bengal Basin to the Bay of Bengal (BoB) and determining its isotopic composition is crucial for understanding the marine Sr isotopic evolution over time. Measurements of spatially and temporally distributed water samples collected from the BoB show radiogenic 87Sr/86Sr, high Sr, calcium (Ca) concentrations and high salinity in samples collected dominantly from 100-120 m depth, which can be explained only by the contribution of saline groundwater from the Bengal Basin. These results provide a direct evidence of the SGD-Sr flux to the BoB. This SGD-Sr flux is however, spatially heterogeneous and using conservative hydrological estimates of the SGD flux to the BoB, we suggest a SGD Sr flux of 13.5-40.5 × 105 mol/yr to the BoB. Mass balance calculations using Sr concentrations and 87Sr/86Sr suggest up to 7% contribution of SGD to the 100-120 m BoB water samples. The identification of SGD at 100-120 m depth also provides an explanation for the anomalous variations in barium (Ba) concentrations and the δ18O-salinity relationship in intermediate depths of the BoB.

On graphical tests for proportionality of hazards in two samples.

In this paper, we present a class of graphical tests of the proportional hazards hypothesis for two-sample censored survival data. The proposed tests are improvements over some existing tests based on asymptotic confidence bands of certain functions of the estimated cumulative hazard functions. The new methods are based on the comparison of unrestricted estimates of the said functions and their restricted versions under the hypothesis. They combine the rigour of analytical tests with the descriptive value of plots. Monte Carlo simulations suggest that the proposed asymptotic procedures have reasonable small sample properties. The power is much higher than existing graphical tests and comparable with existing analytical tests. The method is then illustrated through the analysis of a data set on bone marrow transplantation for Leukemia patients.

Nonparametric estimation of time-to-event distribution based on recall data in observational studies.

In a cross-sectional observational study, time-to-event distribution can be estimated from data on current status or from recalled data on the time of occurrence. In either case, one can treat the data as having been interval censored, and use the nonparametric maximum likelihood estimator proposed by Turnbull (J R Stat Soc Ser B 38:290-295, 1976). However, the chance of recall may depend on the time span between the occurrence of the event and the time of interview. In such a case, the underlying censoring would be informative, rendering the Turnbull estimator inappropriate. In this article, we provide a nonparametric maximum likelihood estimator of the distribution of interest, by using a model adapted to the special nature of the data at hand. We also provide a computationally simple approximation of this estimator, and establish the consistency of both the original and the approximate versions, under mild conditions. Monte Carlo simulations indicate that the proposed estimators have smaller bias than the Turnbull estimator based on incomplete recall data, smaller variance than the Turnbull estimator based on current status data, and smaller mean squared error than both of them. The method is applied to menarcheal data from a recent Anthropometric study of adolescent and young adult females in Kolkata, India.

Estimation of competing risks with general missing pattern in failure types.

In competing risks data, missing failure types (causes) is a very common phenomenon. In this work, we consider a general missing pattern in which, if a failure type is not observed, one observes a set of possible types containing the true type, along with the failure time. We first consider maximum likelihood estimation with missing-at-random assumption via the expectation maximization (EM) algorithm. We then propose a Nelson-Aalen type estimator for situations when certain information on the conditional probability of the true type given a set of possible failure types is available from the experimentalists. This is based on a least-squares type method using the relationships between hazards for different types and hazards for different combinations of missing types. We conduct a simulation study to investigate the performance of this method, which indicates that bias may be small, even for high proportion of missing data, for sufficiently large number of observations. The estimates are somewhat sensitive to misspecification of the conditional probabilities of the true types when the missing proportion is high. We also consider an example from an animal experiment to illustrate our methodology.