Parametric Estimation of Menarcheal Age Distribution Based on Recall Data

Statistical analysis of self-reported health conditions in cohort studies: handling of missing onset age

OBJECTIVES

This paper discusses methodological challenges in epidemiological association analysis of a time-to-event outcome and hypothesized risk factors, where age/time at the onset of the outcome may be missing in some cases, a condition commonly encountered when the outcome is self-reported.

STUDY DESIGN AND SETTING

A cohort study with long-term follow-up for outcome ascertainment such as the Childhood Cancer Survivor Study (CCSS), a large cohort study of 5-year survivors of childhood cancer diagnosed in 1970-1999 in which occurrences and age at onset of various chronic health conditions (CHCs) are self-reported in surveys. Simple methods for handling missing onset age and their potential bias in the exposure-outcome association inference are discussed. The interval-censored method is discussed as a remedy for handling this problem. The finite sample performance of these approaches is compared through Monte Carlo simulations. Examples from the CCSS include four CHCs (diabetes, myocardial infarction, osteoporosis/osteopenia, and growth hormone deficiency).

RESULTS

The interval-censored method is useable in practice using the standard statistical software. The simulation study showed that the regression coefficient estimates from the 'Interval censored' method consistently displayed reduced bias and, in most cases, smaller standard deviations, resulting in smaller mean square errors, compared to those from the simple approaches, regardless of the proportion of subjects with an event of interest, the proportion of missing onset age, and the sample size.

CONCLUSION

The interval-censored method is a statistically valid and practical approach to the association analysis of self-reported time-to-event data when onset age may be missing. While the simpler approaches that force such data into complete data may enable the standard analytic methods to be applicable, there is considerable loss in both accuracy and precision relative to the interval-censored method.

Two biases in incubation time estimation related to exposure

BACKGROUND

Estimation of the SARS-CoV-2 incubation time distribution is hampered by incomplete data about infection. We discuss two biases that may result from incorrect handling of such data. Notified cases may recall recent exposures more precisely (differential recall). This creates bias if the analysis is restricted to observations with well-defined exposures, as longer incubation times are more likely to be excluded. Another bias occurred in the initial estimates based on data concerning travellers from Wuhan. Only individuals who developed symptoms after their departure were included, leading to under-representation of cases with shorter incubation times (left truncation). This issue was not addressed in the analyses performed in the literature.

METHODS

We performed simulations and provide a literature review to investigate the amount of bias in estimated percentiles of the SARS-CoV-2 incubation time distribution.

RESULTS

Depending on the rate of differential recall, restricting the analysis to a subset of narrow exposure windows resulted in underestimation in the median and even more in the 95th percentile. Failing to account for left truncation led to an overestimation of multiple days in both the median and the 95th percentile.

CONCLUSION

We examined two overlooked sources of bias concerning exposure information that the researcher engaged in incubation time estimation needs to be aware of.

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.

The relationship among the age at menarche, anthropometric characteristics, and socio-economic factors in Bengali girls from Kolkata, India

OBJECTIVES

The aim of the study was to measure the causal effect of selected socio-economic factors and anthropometrical characteristics on the menarche occurrence.

METHODS

The sample consisted of 2195 Bengali girls (aged 7-21) from middle-class families, from Kolkata city, India. The age at menarche was recorded from the retrospective data and status quo method. The causal effect of anthropometric and socio-economic variables on menarche occurrence was estimated by the nonparametrical analysis of survival probability (survival random forest).

RESULTS

In the examined cohort menarche occurred, on average, at 11.8 years of age. The probability of menarche occurrence amplified with the increasing values of factors such as body mass index, height-for-age z-scores, number of family members, household rooms, and toilets, but decreased when expenditures increased. The relation maintained a similar pattern of causal effect with girls' age.

CONCLUSIONS

A complex pattern of relationship among sexual development, physique, and socio-economic characteristics was defined. The tendency toward early menarche, along with the observed causal relationships indicate that the analyzed sample is nearing the characteristics and standards of living noted in other middle and even high-income countries in the world.

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.