title: Accounting for length-bias and selection effects in estimating the distribution of menstrual cycle length.
abstract: Prospective pregnancy studies are a valuable source of longitudinal data on menstrual cycle length. However, care is needed when making inferences of such renewal processes. For example, accounting for the sampling plan is necessary for unbiased estimation of the menstrual cycle length distribution for the study population. If couples can enroll when they learn of the study as opposed to waiting for the start of a new menstrual cycle, then due to length-bias, the enrollment cycle will be stochastically larger than the general run of cycles, a typical property of prevalent cohort studies. Furthermore, the probability of enrollment can depend on the length of time since a woman's last menstrual period (a backward recurrence time), resulting in selection effects. We focus on accounting for length-bias and selection effects in the likelihood for enrollment menstrual cycle length, using a recursive two-stage approach wherein we first estimate the probability of enrollment as a function of the backward recurrence time and then use it in a likelihood with sampling weights that account for length-bias and selection effects. To broaden the applicability of our methods, we augment our model to incorporate a couple-specific random effect and time-independent covariate. A simulation study quantifies performance for two scenarios of enrollment probability when proper account is taken of sampling plan features. In addition, we estimate the probability of enrollment and the distribution of menstrual cycle length for the study population of the Longitudinal Investigation of Fertility and the Environment Study.
authors.affiliation: Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, NIH, DHHS, Rockville, MD 20852, USA and Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA.
authors.forename: Kirsten J
authors.initials: KJ
authors.lastname: Lum
authors.affiliation: Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, NIH, DHHS, Rockville, MD 20852, USA.
authors.forename: Rajeshwari
authors.initials: R
authors.lastname: Sundaram
authors.affiliation: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA and U.S. Census Bureau, Suitland, MD 20746, USA tlouis@jhu.edu.
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Louis
mesh_terms: D000328:Adult; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008597:Menstrual Cycle / Q000502:physiology*; D012107:Research Design / Q000706:statistics & numerical data*; D015983:Selection Bias; D013997:Time Factors
keywords: Backward recurrence time; Length-bias; Menstrual cycle length; Renewal process; Selection effects; Survival analysis