# Fecundability and Sterility by Age: Estimates Using Time to Pregnancy Data of Japanese Couples Trying to Conceive Their First Child with and without Fertility Treatment

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Statistical Analyses

#### 2.3. Maximum Likelihood Method

#### 2.4. Sensitivity Analysis

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Detailed Description About the Maximum Likelihood Method

#### Appendix A.1. One-Parameter Model

#### Appendix A.2. Two-Parameter Model

#### Appendix A.3. Three-Parameter Model

#### Appendix A.4. Maximum Likelihood Estimate

#### Appendix A.4.1. Two-Parameter Models

#### Appendix A.4.2. Three-Parameter Models

**Table A1.**Maximum log-likelihood and the mean (variance) of fecundability from one- and two-parameter models for all ages and by age group based on TTP-all or TTP-natural. p-values were obtained from chi-square distribution with one degree of freedom.

TTP-All | |||||
---|---|---|---|---|---|

Fecundability, Mean (Variance) | |||||

Age (y) Group | n | Two-Parameter Models | One-Parameter Models | ||

All | 1264 | 0.13 (0.01) | 0.07 (0.00) | ||

24 or younger | 91 | 0.21 (0.03) | 0.11 (0.00) | ||

25–29 | 561 | 0.14 (0.01) | 0.09 (0.00) | ||

30–34 | 417 | 0.12 (0.01) | 0.06 (0.00) | ||

35–39 | 174 | 0.09 (0.01) | 0.04 (0.00) | ||

40+ | 21 | 0.02 (0.00) | 0.01 (0.00) | ||

Maximum Log-Likelihood | |||||

Age (y) Group | n | Two-Parameter Models (a) | One-Parameter Models (b) | 2{(a)–(b)} | p-Value |

All | 1264 | −3350.67 | −3498.01 | 294.69 | 0.000 |

24 or younger | 91 | −239.40 | −252.39 | 25.98 | 0.000 |

25–29 | 561 | −1507.31 | −1555.25 | 95.88 | 0.000 |

30–34 | 417 | −1111.52 | −1162.00 | 100.96 | 0.000 |

35–39 | 174 | −427.49 | −444.62 | 34.26 | 0.000 |

40+ | 21 | −22.62 | −22.73 | 0.21 | 0.646 |

TTP-Natural | |||||

Fecundability, Mean (Variance) | |||||

Age (y) Group | n | Two-Parameter Models | One-Parameter Models | ||

All | 1264 | 0.13 (0.02) | 0.07 (0.00) | ||

24 or younger | 91 | 0.21 (0.02) | 0.12 (0.00) | ||

25–29 | 561 | 0.14 (0.01) | 0.09 (0.00) | ||

30–34 | 417 | 0.13 (0.02) | 0.06 (0.00) | ||

35–39 | 174 | 0.10 (0.02) | 0.04 (0.00) | ||

40+ | 21 | 0.02 (0.00) | 0.01 (0.00) | ||

Maximum Log-Likelihood | |||||

Age (y) Group | n | Two-Parameter Models (c) | One-Parameter Models (d) | 2{(c)–(d)} | p-Value |

All | 1264 | −2870.59 | −3000.66 | 260.14 | 0.000 |

24 or younger | 91 | −234.63 | −246.43 | 23.61 | 0.000 |

25–29 | 561 | −1346.07 | −1382.87 | 73.60 | 0.000 |

30–34 | 417 | −907.64 | −966.84 | 118.39 | 0.000 |

35–39 | 174 | −323.91 | −339.84 | 31.86 | 0.000 |

40+ | 21 | −15.67 | −15.70 | 0.06 | 0.813 |

**Table A2.**Maximum log-likelihood of two- and three-parameter models by age group, based on TTP-all or TTP-natural. p-values were obtained from chi-square distribution with one degree of freedom.

TTP-All | ||||
---|---|---|---|---|

Maximum Log-Likelihood | ||||

Age (y) Group | Three-Parameter Models (a) | Two-Parameter Models (b) | 2{(a)–(b)} | p-Value |

All | −3350.60 | −3350.67 | 0.14 | 0.710 |

24 or younger | −239.30 | −239.40 | 0.21 | 0.648 |

25–29 | −1507.04 | −1507.31 | 0.54 | 0.463 |

30–34 | −1111.52 | −1111.52 | −0.01 | 1.000 |

35–39 | −427.49 | −427.49 | 0.00 | 1.000 |

40+ | −22.63 | −22.62 | 0.00 | 1.000 |

TTP-Natural | ||||

Maximum Log-Likelihood | ||||

Age (y) Group | Three-Parameter Models (c) | Two-Parameter Models (d) | 2{(c)–(d)} | p-Value |

All | −2865.78 | −2870.59 | 9.64 | 0.002 |

24 or younger | −234.51 | −234.63 | 0.24 | 0.625 |

25–29 | −1344.58 | −1346.07 | 2.99 | 0.084 |

30–34 | −904.84 | −907.64 | 5.61 | 0.018 |

35–39 | −323.55 | −323.91 | 0.72 | 0.398 |

40+ | −15.67 | −15.67 | 0.00 | 1.000 |

**Table A3.**Estimated parameters of the two-parameter models and the median, the first and third quartiles, and the mean and variance of fecundability estimated using TTP-natural for all ages and by age group. The analytic sample was limited to those who discontinued contraception within 24 months before the survey (n = 525).

Parameters | Fecundability | |||||||
---|---|---|---|---|---|---|---|---|

Age (y) Group | n | $\alpha $ | $\beta $ | First Quartile | Median | Third Quartile | Mean | Variance |

All | 525 | 0.82 | 4.87 | 0.04 | 0.10 | 0.21 | 0.14 | 0.02 |

24 or younger | 31 | 0.93 | 2.16 | 0.11 | 0.25 | 0.45 | 0.30 | 0.05 |

25–29 | 223 | 1.65 | 10.25 | 0.06 | 0.12 | 0.19 | 0.14 | 0.01 |

30–34 | 183 | 0.77 | 4.44 | 0.04 | 0.10 | 0.22 | 0.15 | 0.02 |

35–39 | 76 | 0.26 | 1.87 | 0.00 | 0.03 | 0.17 | 0.12 | 0.03 |

40+ | 12 | 1.19 | 147.43 | 0.00 | 0.01 | 0.01 | 0.01 | 0.00 |

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**Figure 1.**Probability density function of fecundability for all ages, based on: (

**a**) two-parameter ($\alpha =0.84,\beta =5.44$); or (

**b**) three-parameter models ($\alpha =1.88,\beta =10.73,q=0.14$). Estimates were made using TTP-natural (n = 1264). In (

**b**), the probability mass of $q=0.14$ exists at zero-fecundability.

**Table 1.**Number of participants and all (including both assisted and natural) and natural conceptions resulted in a live birth or an ongoing pregnancy by ages at discontinuing contraception. The mean (SD) of TTP-all and TTP-natural by age at discontinuing contraception were calculated using both censored and non-censored TTPs.

Age (y) Group | Participants | All Conceptions | Natural Conceptions | TTP-All ${}^{\mathit{a}}$ (Month) | TTP-Natural ${}^{\mathit{b}}$ (Month) |
---|---|---|---|---|---|

All | 1264 | 952 | 834 | 10.3 (12.9) | 8.2 (10.4) |

24 or younger | 91 | 81 | 80 | 6.8 (9.7) | 6.5 (9.0) |

25–29 | 561 | 456 | 415 | 8.5 (11.2) | 7.0 (9.2) |

30–34 | 417 | 304 | 253 | 11.6 (14.0) | 9.5 (11.9) |

35–39 | 174 | 107 | 83 | 13.7 (15.0) | 9.8 (10.3) |

40+ | 21 | 4 | 3 | 19.7 (12.8) | 8.9 (7.9) |

**Table 2.**Parameters of the two-parameter models and the median, the first and third quartiles, and the mean and variance of fecundability estimated using TTP-all and TTP-natural for all ages and by age group (n = 1264).

TTP-All | ||||||||
---|---|---|---|---|---|---|---|---|

Parameters | Fecundability | |||||||

Age (y) Group | n | $\alpha $ | $\beta $ | First Quartile | Median | Third Quartile | Mean | Variance |

All ages | 1264 | 0.94 | 6.22 | 0.04 | 0.10 | 0.19 | 0.13 | 0.01 |

24 or younger | 91 | 1.21 | 4.48 | 0.09 | 0.18 | 0.31 | 0.21 | 0.03 |

25–29 | 561 | 1.44 | 8.76 | 0.06 | 0.12 | 0.20 | 0.14 | 0.01 |

30–34 | 417 | 0.82 | 5.91 | 0.03 | 0.09 | 0.18 | 0.12 | 0.01 |

35–39 | 174 | 0.61 | 5.98 | 0.02 | 0.05 | 0.13 | 0.09 | 0.01 |

40+ | 21 | 0.24 | 15.47 | 0.00 | 0.00 | 0.02 | 0.02 | 0.00 |

TTP-Natural | ||||||||

Parameters | Fecundability | |||||||

Age (y) Group | n | $\alpha $ | $\beta $ | First Quartile | Median | Third Quartile | Mean | Variance |

All ages | 1264 | 0.84 | 5.44 | 0.04 | 0.10 | 0.19 | 0.13 | 0.02 |

24 or younger | 91 | 1.24 | 4.60 | 0.09 | 0.18 | 0.30 | 0.21 | 0.02 |

25–29 | 561 | 1.46 | 8.87 | 0.06 | 0.12 | 0.20 | 0.14 | 0.01 |

30–34 | 417 | 0.58 | 3.90 | 0.02 | 0.08 | 0.19 | 0.13 | 0.02 |

35–39 | 174 | 0.42 | 3.87 | 0.01 | 0.04 | 0.14 | 0.10 | 0.02 |

40+ | 21 | 0.31 | 15.23 | 0.00 | 0.01 | 0.02 | 0.02 | 0.00 |

**Table 3.**Parameters of the three-parameter models and the median, the first and third quartiles of fecundability estimated using TTP-all and TTP-natural for all ages and by age group (n = 1264).

TTP-All | |||||||
---|---|---|---|---|---|---|---|

Parameters | Fecundability | ||||||

Age (y) Group | n | $\alpha $ | $\beta $ | q (Sterile) | First Quartile | Median | Third Quartile |

All ages | 1264 | 1.01 | 6.60 | 0.02 | 0.04 | 0.10 | 0.19 |

24 or younger | 91 | 1.60 | 5.92 | 0.03 | 0.10 | 0.18 | 0.29 |

25–29 | 561 | 1.74 | 10.47 | 0.02 | 0.07 | 0.12 | 0.19 |

30–34 | 417 | 0.82 | 5.90 | 0.00 | 0.03 | 0.09 | 0.18 |

35–39 | 174 | 0.61 | 5.97 | 0.00 | 0.02 | 0.05 | 0.13 |

40+ | 21 | 0.29 | 20.22 | 0.00 | 0.00 | 0.00 | 0.02 |

TTP-Natural | |||||||

Parameters | Fecundability | ||||||

Age (y) Group | n | $\alpha $ | $\beta $ | q (Sterile) | First Quartile | Median | Third Quartile |

All ages | 1264 | 1.88 | 10.73 | 0.14 | 0.05 | 0.11 | 0.19 |

24 or younger | 91 | 1.72 | 6.35 | 0.04 | 0.10 | 0.18 | 0.29 |

25–29 | 561 | 2.58 | 15.08 | 0.06 | 0.07 | 0.13 | 0.19 |

30–34 | 417 | 1.75 | 9.40 | 0.22 | 0.02 | 0.10 | 0.19 |

35–39 | 174 | 1.31 | 8.64 | 0.30 | 0.00 | 0.06 | 0.15 |

40+ | 21 | 0.31 | 15.21 | 0.00 | 0.00 | 0.01 | 0.02 |

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## Share and Cite

**MDPI and ACS Style**

Konishi, S.; Kariya, F.; Hamasaki, K.; Takayasu, L.; Ohtsuki, H. Fecundability and Sterility by Age: Estimates Using Time to Pregnancy Data of Japanese Couples Trying to Conceive Their First Child with and without Fertility Treatment. *Int. J. Environ. Res. Public Health* **2021**, *18*, 5486.
https://doi.org/10.3390/ijerph18105486

**AMA Style**

Konishi S, Kariya F, Hamasaki K, Takayasu L, Ohtsuki H. Fecundability and Sterility by Age: Estimates Using Time to Pregnancy Data of Japanese Couples Trying to Conceive Their First Child with and without Fertility Treatment. *International Journal of Environmental Research and Public Health*. 2021; 18(10):5486.
https://doi.org/10.3390/ijerph18105486

**Chicago/Turabian Style**

Konishi, Shoko, Fumiko Kariya, Kisuke Hamasaki, Lena Takayasu, and Hisashi Ohtsuki. 2021. "Fecundability and Sterility by Age: Estimates Using Time to Pregnancy Data of Japanese Couples Trying to Conceive Their First Child with and without Fertility Treatment" *International Journal of Environmental Research and Public Health* 18, no. 10: 5486.
https://doi.org/10.3390/ijerph18105486