Prevalent cohort studies and unobserved heterogeneity

Approaches for Assessing Effects of Exposures on Human Fertility

BACKGROUND

Fecundability (conception rate per menstrual cycle) varies among non-contracepting couples. Time-to-pregnancy studies can identify exposures contributing to that variability, using three designs: incident cohort, prevalent cohort, and retrospective. Typically, researchers then apply semi-parametric, generalized linear time-to-pregnancy models to data, with either a log or a logit "link," to estimate either a fecundability ratio (FR) or a fecundability odds ratio (FOR). The ongoing-attempt study design can also be informative.

METHODS

We consider a different generalized linear model, based on an inverse link. It models the heterogeneity as beta distributed and enables estimation of both the FR and FOR, defined based on population mean fecundabilities, without requiring constancy across attempt time. Under an ongoing-attempt design, the parameter associated with a dichotomous exposure has no clear meaning with a log or a logit link, but under the proposed approach estimates the ratio of the two average times to pregnancy. Basing simulations on conception rates from a large study, we compare the three analytic approaches for confidence interval coverage and power. We also assess the performance of a commonly used method for verifying the constancy of FOR or FR across time.

RESULTS

The inverse-link approach had slightly less power than the others, but its estimates maintained nominal confidence interval coverage under nonconstancy. A popular method for testing constancy across time for the FR and FOR had poor power.

CONCLUSIONS

The inverse-link analysis offers a useful alternative to the usual methods, with estimation performance that generalizes to the ongoing-attempt design and does not require hard-to-verify constancy assumptions.

New Measures for Family Planning and Exposure to Risk of Pregnancy Based on Sexual Activity and Contraceptive Use Data

Family planning measures for unmarried women are based on contraceptive demand and use among sexually active women. Sexual activity status is commonly defined based on comparing reported time-since-last-sex to a cutoff time, with women defined to be sexually active if their most recent sex was within the last four weeks. While easy to understand and compute, this approach to constructing family planning measures results in a limited understanding of family planning and exposure to unintended pregnancy because it cannot comprehensively capture the frequency of sex at the population level. We propose a new statistical approach to quantify sexual activity, using reported time-since-last-sex data. Based on estimated frequencies of sex among users and nonusers in need of family planning, we propose new family planning measures, including the ratio of protected exposure over all women's exposure to risk of unintended pregnancy.

In a Stationary Population, the Average Lifespan of the Living Is a Length-Biased Life Expectancy

What is the average lifespan in a stationary population viewed at a single moment in time? Even though periods and cohorts are identical in a stationary population, we show that the answer to this question is not life expectancy but a length-biased version of life expectancy. That is, the distribution of lifespans of the people alive at a single moment is a self-weighted distribution of cohort lifespans, such that longer lifespans have proportionally greater representation. One implication is that if death rates are unchanging, the average lifespan of the current population always exceeds period life expectancy. This result connects stationary population lifespan measures to a well-developed body of statistical results; provides new intuition for established demographic results; generates new insights into the relationship between periods, cohorts, and prevalent cohorts; and offers a framework for thinking about mortality selection more broadly than the concept of demographic frailty.

Flexible extension of the accelerated failure time model to account for nonlinear and time-dependent effects of covariates on the hazard

The accelerated failure time model is an alternative to the Cox proportional hazards model in survival analysis. However, conclusions regarding the associations of prognostic factors with event times are valid only if the underlying modeling assumptions are met. In contrast to several flexible methods for relaxing the proportional hazards and linearity assumptions in the Cox model, formal investigation of the constant-over-time time ratio and linearity assumptions in the accelerated failure time model has been limited. Yet, in practice, prognostic factors may have time-dependent and/or nonlinear effects. Furthermore, parametric accelerated failure time models require correct specification of the baseline hazard function, which is treated as a nuisance parameter in the Cox proportional hazards model, and is rarely known in practice. To address these challenges, we propose a flexible extension of the accelerated failure time model where unpenalized regression B-splines are used to model (i) the baseline hazard function of arbitrary shape, (ii) the time-dependent covariate effects on the hazard, and (iii) nonlinear effects for continuous covariates. Simulations evaluate the accuracy of the time-dependent and/or nonlinear estimates, and of the resulting survival functions, in multivariable settings. The proposed flexible extension of the accelerated failure time model is applied to re-assess the effects of prognostic factors on mortality after septic shock.