### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 113-128 |

Number of pages | 16 |

Journal | Biostatistics |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2015 |

### Fingerprint

### Keywords

- Backward recurrence time
- Length-bias
- Menstrual cycle length
- Renewal process
- Selection effects
- Survival analysis

### ASJC Scopus subject areas

- Statistics and Probability
- Medicine(all)
- Statistics, Probability and Uncertainty

### Cite this

*Biostatistics*,

*16*(1), 113-128. https://doi.org/10.1093/biostatistics/kxu035

**Accounting for length-bias and selection effects in estimating the distribution of menstrual cycle length.** / Lum, Kirsten J.; Sundaram, Rajeshwari; Louis, Thomas.

Research output: Contribution to journal › Article

*Biostatistics*, vol. 16, no. 1, pp. 113-128. https://doi.org/10.1093/biostatistics/kxu035

}

TY - JOUR

T1 - Accounting for length-bias and selection effects in estimating the distribution of menstrual cycle length

AU - Lum, Kirsten J.

AU - Sundaram, Rajeshwari

AU - Louis, Thomas

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - Backward recurrence time

KW - Length-bias

KW - Menstrual cycle length

KW - Renewal process

KW - Selection effects

KW - Survival analysis

UR - http://www.scopus.com/inward/record.url?scp=84922548440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922548440&partnerID=8YFLogxK

U2 - 10.1093/biostatistics/kxu035

DO - 10.1093/biostatistics/kxu035

M3 - Article

C2 - 25027273

AN - SCOPUS:84922548440

VL - 16

SP - 113

EP - 128

JO - Biostatistics

JF - Biostatistics

SN - 1465-4644

IS - 1

ER -