Describing the status of reproductive ageing simply and precisely: A reproductive ageing score based on three questions and validated with hormone levels.

OBJECTIVE: Most women live to experience menopause and will spend 4-8 years transitioning from fertile age to full menstrual stop. Biologically, reproductive ageing is a continuous process, but by convention, it is defined categorically as pre-, peri- and postmenopause; categories that are sometimes supported by measurements of sex hormones in blood samples. We aimed to develop and validate a new tool, a reproductive ageing score (RAS), that could give a simple and yet precise description of the status of reproductive ageing, without hormone measurements, to be used by health professionals and researchers.
METHODS: Questionnaire data on age, menstrual regularity and menstrual frequency was provided by the large multicentre population-based RHINE cohort. A continuous reproductive ageing score was developed from these variables, using techniques of fuzzy mathematics, to generate a decimal number ranging from 0.00 (nonmenopausal) to 1.00 (postmenopausal). The RAS was then validated with sex hormone measurements (follicle stimulating hormone and 17β-estradiol) and interview-data provided by the large population-based ECRHS cohort, using receiver-operating characteristics (ROC).
RESULTS: The RAS, developed from questionnaire data of the RHINE cohort, defined with high precision and accuracy the menopausal status as confirmed by interview and hormone data in the ECRHS cohort. The area under the ROC curve was 0.91 (95% Confidence interval (CI): 0.90-0.93) to distinguish nonmenopausal women from peri- and postmenopausal women, and 0.85 (95% CI: 0.83-0.88) to distinguish postmenopausal women from nonmenopausal and perimenopausal women.
CONCLUSIONS: The RAS provides a useful and valid tool for describing the status of reproductive ageing accurately, on a continuous scale from 0.00 to 1.00, based on simple questions and without requiring blood sampling. The score allows for a more precise differentiation than the conventional categorisation in pre-, peri- and postmenopause. This is useful for epidemiological research and clinical trials.

1. Introduction

Menopause marks the cessation of menstruations and the end of the reproductive part of life [1]. This transition, which occurs in women around 50 years of age, takes on average five years and is a major part of reproductive ageing [2, 3]. It also implies profound hormonal changes: a woman’s estrogen levels start to decline, and her gonadotropin levels begin to rise. The result is that her body gradually changes into a non-reproductive state [4, 5]. Epidemiological research traditionally uses categories to describe the reproductive status of a woman, such as perimenopausal or postmenopausal. These categories are based on arbitrary thresholds; they may be rather heterogeneous and lead to an aggravated interpretation of research findings. As an example, the current consensus, the Stages of Reproductive Ageing Workshop (STRAW) defines late perimenopause as a stage lasting one to three years, during which women experience amenorrhea for 60 days or more [6]. This evidently conglomerates a range of women of different reproductive ages, who would then be jointly analysed in an epidemiological study. Categorization may facilitate communication between clinicians and the public, but it does not reflect the underlying biology and it introduces clear limitations, especially for epidemiological research on women undergoing the menopausal transition [7]. The frequent use of categories can however be understood, as there is to date no single biomarker sufficiently describing menopause [6, 8].

We aim to mathematically describe the status of reproductive ageing and create an easy to replicate reproductive ageing score based on the age of a woman and the number and regularity of menstruations she experiences.

2. Materials and methods

We used data from two population-based cohorts, the Respiratory Health in Northern Europe (RHINE) study and the European Community Respiratory Health Survey (ECRHS). Ethical approval was obtained for each centre of the RHINE study and the ECRHS from the appropriate institutional or regional ethics committee and each participant provided informed written consent prior to inclusion in the studies.

2.1 RHINE

Bergen: Regional Committee for Medical and Health Research Ethics in Western Norway (2010/759); Reykjavik: National Bioethics Committee of Iceland (VSN 11–121); Uppsala, Umeå, Göteborg: Ethics Committee of Uppsala University (2010/068); Aarhus: not required for questionnaire-only studies; Tartu: Research Ethics Committee of the University of Tartu (209/T-17);

2.2 ECRHS

Aarhus: Scientific ethical committee for Region Midtlylland; Albacete: Comité Ético de Investigación Clínica del Hospital Universitario de Albacete; Galdakao: Comité Ético de Investigación Clínica del Hospital de Galdakao-Usansolo; Huelva: Comisión de Ética de Investigación Sanitarias del Hospital Juan Ramón Jiménez de Huelva; Bergen: Regional Committee for Medical and Health Research Ethics in Western Norway (2010/759); Bordeaux, Grenoble, Montpellier, Paris: Comite De Protection Des Personnes (2011-A00013-38); Erfurt, Hamburg: Ethikkommission der Bayerischen Landesärztekammer (Reg Nr. 10015); Uppsala, Umeå, Göteborg: Ethics Committee of Uppsala University (2010/068); Reykjavik: National Bioethics Committee of Iceland (VSN 11–121); Tartu: Research Ethics Committee of the University of Tartu (209/T-17);

2.3 Development and validation population

The reproductive ageing score (RAS) was developed using data of subjects participating in the questionnaire-based RHINE study and it was validated in the population of the ECRHS where objective sex hormone measurements were available.

The RHINE study is a longitudinal, international, multi-centre study (www.rhine.nu), which includes seven Northern European centres (Bergen in Norway; Reykjavik in Iceland; Umeå, Uppsala and Göteborg in Sweden; Aarhus in Denmark and Tartu in Estonia). For the current paper, we used data from the most recent wave, carried out between 2010 and 2012 with a response rate of 63% [9]. We used data from 3107 women with a mean age of 52 years (range: 38–66 years) to develop the RAS.

The ECRHS also is a longitudinal, international, multicentre study (www.ecrhs.org) [10, 11]. The validation population includes women from 16 centres in nine countries who participated during 2010 to 2012 (Aarhus in Denmark; Albacete, Galdakao and Huelva in Spain; Bergen in Norway; Bordeaux, Grenoble, Montpellier and Paris in France; Erfurt and Hamburg in Germany; Göteborg, Umeå and Uppsala in Sweden; Reykjavik in Iceland and Tartu in Estonia). The available serum samples were analysed for concentrations of follicle stimulating hormone (FSH) and 17β-estradiol. The database contained 1056 women with a mean age of 55 years (range: 40–67 years). For the seven Northern European centres in ECRHS, participants were also a subsample of the RHINE study. Women who participated in both surveys were included into the validation population but not the development population. We further excluded women from both populations who currently used exogenous sex hormones like contraceptives or hormone replacement therapy (including intermittent progestin therapy), women being pregnant or breastfeeding at the time of the surveys and women reporting irregular menstruation unrelated to menopause (Fig 1) [6, 12, 13].

Fig 1

Flow chart of the development population (left) and validation population (right) with inclusion criteria.

RHINE: Respiratory Health in Northern Europe study, ECRHS: European Community Respiratory Health Survey.

2.4 Score development

To develop the score we used techniques of fuzzy set theory, a mathematical concept to depict the biology of physiological processes [14, 15]. It was created in 1964 and successfully implemented in biology, artificial intelligence, and linguistics [14, 16, 17]. Unlike conventional mathematics, which does not allow vague expressions and demands that an object either is a member of a set or not, fuzzy sets are defined by a function (μ) assigning a value between 0.00 and 1.00 to an observation, representing the degree of belonging to a fuzzy set. The value 1.00 means that an object completely belongs to the set and the value 0.00 means the object does not at all belong to the set.

We first defined a function μ based on the number of periods per year and the menstrual regularity. The function requires the proportion P(period) of regularly menstruating women for every single number of reported periods as answers to the question: “How may periods did you have in the last twelve months?”. A cross-tabulation (Table 1) of the menstrual regularity (answers to the question: “Do you have regular periods?”, possible answers: “Yes”, “No, they have been irregular for a few months”, “No, my periods have stopped”) and the number of periods, illustrates the entirety of all values for P(period) calculated with Eq 1.

Table 1

Pattern and number of menstruations in the last year among 3107 women (RHINE).

		"Do you have regular periods?"
		Yes	Irregulara	Nob	Total	P (period) c
Number of periods per year	0	0	0	1742	1742	0.000
	1	1	1	34	36	0.028
	2	2	10	26	38	0.053
	3	3	9	11	23	0.130
	4	5	18	10	33	0.152
	5	3	15	7	25	0.120
	6	6	14	5	25	0.240
	7	6	24	5	35	0.171
	8	13	17	6	36	0.361
	9	13	23	3	39	0.333
	10	24	28	1	53	0.453
	11	66	22	1	89	0.742
	12	779	31	1	811	0.961
	13	61	6	0	67	0.910
	14	23	8	0	31	0.742
	15	12	12	0	24	0.500
	Total	1017	238	1852	3107

a“No, they have been irregular for a few months”,

b“No, my periods have stopped”,

cProportion of women with regular menstruation (calculated with Eq 1)

Equation 1. Proportion of women who have regular menstruation for each number of reported menstruations in the last year (with period = number of periods per year, x = number of women answering “Yes” to the question: “Do you have regular periods?”, y = number of women answering “No, they have been irregular for a few months” and z = number of women answering “No, my periods have stopped”, e.g. x(11) = number of women reporting regular menstruation among those who report 11 menstruations in the last 12 months).

For women reporting zero menstruations per year this proportion is expected to be zero, as those women are most likely menopausal, while for women reporting twelve menstruations per year it is expected to approach one, as those women are most likely nonmenopausal. For women who report more than twelve menstruations per year it is expected to decline again, as shortening as well as lengthening cycles are an indicator of the beginning menopausal transition [18]. Plotting the complementary proportion 1-P(period) versus the corresponding number of periods per year, depicts a discrete function, from which the continuous function μ can be approximated using the least squares function approximation.

A second function μ was defined based on age. The construction of μ requires the proportion P(age) of women whose menstruations have already stopped for every single reported age. A cross-tabulation of the menstrual status with the reported ages illustrates the entirety of all values for P(age) calculated with Eq 2 (Table 2).

Table 2

Presence of menstruations by age among 3107 women (RHINE).

		"Do you have regular periods?"
		Yes	Irregular1	No2	Total	P(age)3
Age [y]	38	5	0	0	5	0.000
	39	33	2	2	37	0.054
	40	86	6	5	97	0.052
	41	79	10	2	91	0.022
	42	87	7	5	99	0.051
	43	99	8	9	116	0.078
	44	98	14	14	126	0.111
	45	78	19	19	116	0.164
	46	86	13	23	122	0.189
	47	83	17	24	124	0.194
	48	58	19	28	105	0.267
	49	47	26	45	118	0.381
	50	32	27	52	111	0.468
	51	32	20	77	129	0.597
	52	27	23	93	143	0.650
	53	13	14	101	128	0.789
	54	8	8	122	138	0.884
	55	9	0	135	144	0.938
	56	3	3	116	122	0.951
	57	2	1	131	134	0.978
	58	6	0	129	135	0.956
	59	7	0	120	127	0.945
	60	12	0	115	127	0.906
	61	8	1	131	140	0.936
	62	9	0	158	167	0.946
	63	6	0	96	102	0.941
	64	4	0	86	90	0.956
	65	0	0	13	13	1.000
	66	0	0	1	1	1.000
	Total	1017	238	1852	3107

1 “No, they have been irregular for a few months”

2 “No, my periods have stopped”

3 Proportion of women without menstruation (calculated with Eq 2)

Equation 2. Proportion of women whose menstruations have already stopped, for each reported year of age (with age = age in years, x = number of women answering “Yes” to the question: “Do you have regular periods?”, y = number of women answering “No, they have been irregular for a few months”, z = number of women answering “No, my periods have stopped”, e.g. x(40) = number of women reporting regular menstruations among those who are 40 years old).

This proportion increases with age and for younger women this proportion is expected to be low. Plotting the proportion P(age) versus the corresponding age depicts a discrete function, from which the continuous function μ can be approximated using the least squares function approximation.

Additionally, two optional modifiers were introduced to μ: smoking and unilateral oophorectomy. According to recent literature, current smoking is associated with two years [19] and unilateral oophorectomy with one year [20] younger age at menopause. Therefore, two years were added to the age of current smokers and one year was added to the age of women reporting unilateral oophorectomy, defining the new variable m (modified age) (Eq 3).

Equation 3. Age modification by smoking and oophorectomy.

Subsequently, the value for the function μ is defined from P(m).

The calculated probability of being not regularly menstruating or without menses, according to the number of periods within the last twelve months (μ), does not depend on the woman’s age, thus allowing to calculate the probability for each year of being either amenorrheic or not regularly menstruating. Thus, the RAS can be calculated as the union of μ and μ by adding the two sets (μ + μ) and subtracting the overlap, i.e. the repeated elements of the intersection (μμ):

Equation 4. The reproductive ageing score as an aggregation function of μ and μ.

The union of μ and μ can be imagined within a three-dimensional Cartesian coordinate system, where μ is projected on the planes parallel to the one spanned by the x- and z-axis for each increment of μ and is projected on the planes parallel to the one spanned by the y- and z-axis for each increment of μ. Subsequently the function, representing the union of μ and μ is formed by the maximum value of either function (μ or μ) for any given coordinates of the plane spanned by the x- and y-axis. Thus, Eq 4 can be applied for any woman, knowing the following variables: age, number of periods in the last year, age, oophorectomy (“Never”, “One ovary”, “Both ovaries”) and the smoking status (“Yes” / “No”).

2.5 Validation of the developed score

We used receiver operating characteristics (ROC) to validate the calculated score against established hormone cut-offs in our validation population (ECRHS) [21] (nonmenopausal: FSH ≤20IU/L and 17β-estradiol ≥147pmol/L, postmenopausal: FSH ≥80IU/L and 17β-estradiol ≤73pmol/L [22]. ROC curves show the true positive rate (sensitivity) against the false positive rate (specificity) and compare to random guessing. An area under the curve (AUC) of one would indicate perfect performance. We validated two concepts. First, we tested how well the score separated nonmenopausal women from the remaining (perimenopausal and postmenopausal) women and second, how well the score separated postmenopausal women from the remaining (nonmenopausal and perimenopausal) women. As perimenopausal women score by definition intermediate values, they were evaluated by comparing intermediate cut-offs of the score to hormone levels and menstrual pattern. For the sake of completeness, this was also done for nonmenopausal and postmenopausal women. Additionally, in order to visualize the performance of the RAS, we include a boxplot of the RAS against three commonly used categories defined by hormonal measurements in the supporting information (S1 Fig).

The least square approximations to develop the RAS were performed using the Maxima CAS (Computer Algebra System) software [23]. All other calculations, including the validation of the RAS, were performed using the R statistical package [24].

3. Results

The cross-tabulated data to derive the first function μ based on P(period) is presented in Table 1. This function can be approximated by a biquadratic exponential function with a mean-squared error (MSE) of 0.011 (Eq 5). It shows, consistently with existing literature, that the transition to menopause is characterized by an increased frequency of both very long and very short cycles (Fig 2) [18].

Fig 2

Approximated function for menstrual regularity.

Data points: Inverse proportion of women with regular menstruation for every response to the number of periods during the last year, observed in the RHINE dataset 1-P(period); Line: biquadratic exponential function μ with best fit to observed values 1-P(period).

Equation 5. Biquadratic exponential function depending of the number of periods.

The tabulated data to derive the second function μ (Eq 6) based on P(age) is presented in Table 2.

The calculated proportion of women who indicate being menopausal by answering “No” to the question "Do you have regular periods?" of all women of the same age (μ) can be approximated by a quadratic logistic function (Fig 3) with a MSE for this approximation of 0.002.

Fig 3

Approximated function for age.

Data points: Proportion of women without menstruations according to age observed in the RHINE dataset P(age); Line: quadratic logistic function μ with best fit to observed values P(age).

Equation 6. Quadratic logistic function approximating the function (with age in years).

Finally, the function of the RAS (Eq 7) according to the aggregation expressed in Eq 4:

Equation 7. Final formula to calculate the reproductive ageing score (RAS) (with period being the number of periods per year and age as the age in years, modified according to smoking status and oophorectomy).

Graphically the RAS can be represented as a three-dimensional figure (Fig 4) using the variables period along the x-axis and age along the y-axis.

Fig 4

Unique function of the reproductive ageing score (RAS) (with menstruations per year on the x-axis, age on the y-axis and the RAS, expressed as percentage on the z-axis).

Both, older age and fewer menstruations contribute to a higher RAS and indicate progression into a postmenopausal state. Smoking and oophorectomy act as modifiers of the function μ and thus the RAS. We calculated the RAS for women within the validation population (ECRHS) with Eq 7, which was derived from the development population (RHINE).

The area under the ROC curve was 0.91 (95% CI: 0.90–0.93) to distinguish nonmenopausal women from the remaining perimenopausal and postmenopausal women (Fig 5, black curve) and 0.85 (95% CI: 0.83–0.88) to distinguish postmenopausal women from the remaining nonmenopausal and perimenopausal women (Fig 5, grey curve), as defined by concentrations of FSH and 17β-estradiol.

Fig 5

Receiver operating characteristic for validation of the reproductive ageing score by combined FSH and 17β-estradiol cut-offs in the validation population (ECRHS).

Black curve: Nonmenopausal women versus perimenopausal and postmenopausal women; Grey curve: Postmenopausal women versus perimenopausal and nonmenopausal women.

Table 3 shows reproductive characteristics for quartiles of the RAS, to illustrate the reproductive characteristics of women with intermediate reproductive ageing scores (0.26–0.75), who are presumed to be in the menopausal transition.

Table 3

Quartiles of the reproductive ageing score versus age, menstrual and endocrine status in the validation population (ECRHS).

Reproductive ageing score (Quartiles)	0.00–0.25	0.26–0.50	0.51–0.75	0.76–1.00
Age, mean (SD1) [years]	43.6 (1.9)	47.5 (1.9)	50.2 (2.4)	56.7 (5.5)
Periods last 12 months, mean (SD1)	12.1 (0.3)	12.0 (0.7)	11.7 (1.4)	1.2 (3.2)
Regular menses [%]	93	97	75	2
Irregular menses [%]	7	3	25	11
Amenorrhea [%]	0	0	0	87
FSH, median (IQR2) [IU/L]	11 (7–16)	17 (9–27)	22 (11–48)	124 (83–166)
17β-estradiol, median (IQR2) [pmol/L]	264 (144–380)	241 (113–368)	217 (96–337)	12 (6–26)

1Standard deviation,

2Interquartile range

4. Discussion

We developed a continuous reproductive ageing score based on age and number of menstruations. Calculating this score for each woman in the validation population (ECRHS) showed that women with the lowest scores featured nonmenopausal characteristics [21, 25]. Women who scored intermediate values showed characteristics of advancing degrees of the menopausal transition and women who scored highest strongly resembled typical postmenopausal women [21, 25]. The RAS can be interpreted as an indicator of the progress of reproductive ageing. Women with a score of 0.00 can be considered premenopausal and women with a score of 1.00 can be considered postmenopausal, while the intermediate values can be considered advancing degrees of reproductive ageing in terms of decreasing fertility, respectively depletion of the ovarian reserve.

The validation with ROC curves and the practical example (supporting information) presented the RAS as a useful tool for epidemiologists. The performance of the RAS for women who were either nonmenopausal or postmenopausal was very good, with AUC values of 0.91 and 0.85, respectively. The ROC curve validation shows that the RAS discriminates nonmenopausal women slightly better than postmenopausal women. The score was able to quantify degrees of the menopausal transition, which has so far not been possible, resulting in women at different stages of reproductive ageing being defined as one heterogeneous group. This tool has great potential to offer new insights into health and disease, e.g. whether women are vulnerable to a certain health condition during a narrow time window within the perimenopausal phase.

In addition, the mean square deviation of the calculated functions reaches values very close to zero, implying a strong nonlinear correlation between the independent variables (number of periods in the last year and age) and the proportions, calculated within the development population. Concerning μ, possibly less precise data in the upper range of menstruations per year (>12), due to the lower number of data points, is largely being adjusted for by the relation with age (μ) after forming the final function (RAS). The RAS is based on the strong association between age and the changing number of menstrual periods and its major strength is to quantify reproductive ageing continuously and that it is based on answers to a few simple questions. Important factors influencing reproductive ageing are unilateral oophorectomy and current smoking behaviour, both related to a younger age at menopause, which we accounted for as modifiers. In the case that it is desirable to evaluate smoking behaviour and/or unilateral oophorectomy separately or in a different manner, these modifiers may be removed from the calculation of the RAS.

Another strength is that the RAS can be easily used with all common statistical software and spread sheets by applying the final formula (Eq 7) to a dataset. To replicate the development of the RAS (least square approximations) in other settings we recommend using the open-source software Maxima CAS (https://sourceforge.net/projects/maxima/files/), a specialized computer algebra system that yields high precision numerical results and is capable of including and evaluating complex operations, such as Taylor series and Laplace transforms as well as linear algebra tools like matrix operations, which have been used for the current calculations.

The proportions of women with regular menstruation for the various reported number of periods as well as ages correspond well to the general consensus and what has been described in other studies [6, 8, 22]. Both the development population and the validation population are representative for the women in the relevant age groups in Europe [9], thus the external validity is high for Caucasian populations. For other ethnicities, the functions might have to be slightly modified as age at menopause might differ.

A limitation of the RAS is that potential factors affecting reproductive ageing such as chronic disease, gynaecological disorders and the use of exogenous hormones, are not considered. These limitations are however also acknowledged in the STRAW +10 model [26], which, today, is considered to be the gold standard for assessing reproductive ageing.

It must also be noted that a continuous RAS, indicating how far along a woman is on her way from fertile age to menopause (0.00–1.00) should not be confused with menopause scores assessing women’s health after menopause or climacteric symptoms [27, 28].

5. Conclusion

The RAS provides a new, innovative and useful tool to describe the current status of reproductive ageing accurately, on a continuous scale from 0.00 to 1.00, based on simple questions and without a need for blood measurements. The score allows for a more precise differentiation between women during this period than the current, conventional categorisation into pre-, peri- and postmenopause. It thus is useful for epidemiological research and in the design of clinical trials, e.g. studies on hormone replacement therapy.

(DOCX)

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9 Mar 2020

PONE-D-20-00740

Defining menopausal status simply and precisely - A Reproductive Ageing Score for epidemiologists, clinicians and the general public, based on three questions and validated with hormone levels

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Reviewer #1: The authors aim to generate an objective score for menopausal status.

Overall, Im still struggling with the utility of this score. It essentially uses features of the diagnostic criteria for menopause to give a score indicating the likelihood of menopause.

However, the clinical features presented in table 3, suggest that it probably doesn't remove much heterogeneity to the diagnosis from the use of standard assessments or just asking the relevant information.

I appreciate it doesn't claim to have predictive capability, merely being descriptive of current menopausal status,

but is being validated against diagnostic criteria which have the flaws that the authors are trying to avoid.

However, Im unclear outside of the extremes of the range what knowing the score adds. I appreciate the example in research provided to try to demonstrate the utility in a continuous manner, but given that the validation step is arbitrary (and suspect that any number of similar scores using the information that form the diagnostic criteria for menopause could perform similarly), Im not sure how useful score would be for clinical practice nor how valid it is as an intermediary value for research.

Overall, Im supportive of the concept of trying to make an objective diagnosis of menopausal status, but remain sceptical of the score itself.

In any case, its technically fine, so it will be up to the community to see if the use of this score takes off.

It might be useful to add more detailed information about interpretation of the score beyond high and low,

as in what is the conversion from RAS to the chance of menopause. Can the RAS be converted into a probability of menopause, or is that what it already is supposed to denote ie does 0.86 mean an 86% chance of menopause?

If so, this can be clarified for the reader.

Why was the effect of smoking and oophorectomy not evaluated from the same dataset, but rather an arbitrary value from a different set just added ?

Were other potential modifiers assessed? Previous history of anovulatory disorders eg PCOS?

Line 131- Perhaps shortening of cycles in the lead up to menopausal transition might also contribute to this? Reassuring to see very short cycles in table 1 increase the score.

Line 169- despite the aim to move away from the arbitrary categorisations, the cut offs used to validate the score also seem like consensus categorisations without the possibility of nuance. The FSH threshold of >20 seemed to be one that indicated anovulation and need for contraception rather than nonmenopause per se from the reference. A lower level would identify a more pure non-menopausal group.

Furthermore, FSH levels are known to fluctuate- was there possibility of including repeated values over a threshold?

The ESHRE guidance for POI, uses two measurements of 25 on 2 occasions at least 4 weeks apart to diagnosis POI. An FSH of 15 would be considered high in the absence of raised LH, E2 which could suggest periovulatory value. Similarly not all women will have such a high FSH >80 post-menopause and gonadotropins can fall again after a number of years following menopause also.

Can you plot scatterplots of the RAS by the three categorisations non, peri and post to visualise the performance of the score ?

As it was a longitudinal data set, was it possible to assess 'change in the number of periods per year over more than one year' as a factor?

Table 3- the score seems similar until a score more than 0.75 is reached.

It seems that just asking how many periods in the last year would perform just as well as the RAS.

And for a more subtle / nuanced assessment where there is not a clearcut diagnosis then a combination of inhibin B, AMH, E2, FSH, LH, would be more predictive ?

Can the methods add a paragraph or two explaining the concepts behind fuzzy mathematics for the non-expert reader?

Reviewer #2: The authors address a frequent issue when analysing epidemiological data dealing with age at menopause. The idea of a continuous quantitative score, the RAS, based of simple measurements in any field study is attractive. Age at Menopause has indeed a indirect restrospective definition. The cessation of menses for more than 12 months does not always imply menopause and both FSH and Estradiol level are just mimicking what the gynaecologist can observe directly.

Major Comment:

The developement of the composite score needs to be more carefully explained. Although the calculation of mu_A and mu_B seem easy to understand, allowing to replicate the figures in the last column in table 1 and 2, the merging of the two indices is very briefly noted as obvious like the probability of the union of two sets with a non- zero interception. Their is one basic assumption which may be obvious for the authors but absolutely not for the reader. My understanding is that for each year of age, the authors model the fraction of the women who were not regularly menstruating x times over the last 12 months....The later information is derived from all the women, whatever their ages are.

Minor comments:

- The authors propose a correction for smoking and unilateral oophorectomy based on 2 publications. It has the merit of simplicity but itcould have been compared with models integrating these two covariates into the modeling of the log(mu_A) or the logit(mu_B)

- The referee understands that the shape on figure 2 dictated a transformation that could cope with the strong non linearity with the constraints of staying within the range (0,1). Polynomial regression on the number of periods over the last year was an option, highly dependent on the data available in the range 12+, which are the less precise ones or may have different significances according tho the woman's age, although they profoundly influence the highest degree of the selected polynomes. Did the authors try to compare their model with other models? Some discussions could be added.

The study largely benefit of two large, partly overlaping sets of data from mainly caucasian women from the northern part of Europe. The authors indicate the exclusion of women either using contraceptive hormones, or being pregnant, or breastfeeding. How many women were exposed to intermittent progestin therapy, a common prescription at this period of life in European women? The two flowcharts seem to indicate that they have been also excluded?

Based on these two datasets, the validation study gives very good results at least for caucasian women as correctly pointed out by the authors. The appropriate use of the proposed RSA assumes the availability of similar datasets corresponding to different homogeneous groups of women. If m_B data appear rather easy to get by simple questionnaires, m_A data may be more difficult to obtain.

- The final example on the association between the RSA and the Odds ratio of developint new- onset asthma brings additional value to the proposed score. It is worth noting the large confidence intervals in the late post-menopausal on the figure displaying the results with the traditional approach as compared with the ones on the predicted probability of new- onset asthma in relation to RAS. The comparison is tricky as the abscissa and the ordinates concern different entities and the regression methods is totally different. The shape of the confidence envelope partly reflects the complexe non linearity of the transformation, but the rather "thin" right side remains intringuing. How was the confidence interval calculated?

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Reviewer #2: Yes: Jean-Christophe Thalabard

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14 Apr 2020

Please see the attached Rebuttal letter.

Submitted filename: Rebuttal letter.pdf

Click here for additional data file.

1 May 2020

PONE-D-20-00740R1

Describing the status of reproductive ageing simply and precisely - A reproductive ageing score based on three questions and validated with hormone levels

PLOS ONE

Dear Dr. Triebner,

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Reviewers' comments:

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Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

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Reviewer #2: Yes

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Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Comments addressed, very wide variety of scores for postmenopausal women even. Utility for epidemiological research noted.

Reviewer #2: The revised version adresses most of the comments. However the following suggestions could be taken into account to improve the readibility and the reproducibility of the manuscript

Major Comment:

Although the revised version adds substantial technical information, it does not fully address the basic assumption made by the authors which implies that the probability of either not regularly menstruating or being without menses according to the number of periods within the last 12 months (function mu_A(Period)) does not depend on the woman’s age, allowing to calculate for each year a probability of being either amenorrheic or not regularly menstruating by using the classical formula for the probability of the union of two sets with non null intersection. This is an important assumption which should be made more clear for the reader.

Minor comments:

Comment 12 : The authors propose a correction for smoking and unilateral oophorectomy based on 2 publications. It has the merit of simplicity but itcould have been compared with models integrating these two covariates into the modeling of the log(mu_A) or the logit(mu_B)

Comment on the response 12: We agree with the authors that the proposed score should be easy to calculate justifying their rather simple proposal, but it reincorporates a rather crude categorisation when the authors try to convince the reader to use a continuous variable for quantifying the reproductive aging status.

Comment 13 : The referee understands that the shape on figure 2 dictated a transformation that could cope with the strong non linearity with the constraints of staying within the range (0,1). Polynomial regression on the number of periods over the last year was an option, highly dependent on the data available in the range 12+, which are the less precise ones or may have different significances according tho the woman's age, although they profoundly influence the highest degree of the selected polynomes. Did the authors try to compare their model with other models? Some discussions could be added.

Comment on the response  13: the referee tried to replicate the observed results using the two tables provided in the manuscript. If the logit regression for the age- dependent frequencies gives rather similar results, but not exactly the same ones, for adjusting and graphing the mu_B curve, the adjustment of the mu_A part remains less straightforwards due to the right part of the curve, i.e. number of periods per year above 12. Various methods and selection of the non- linear transform could lead to rather good adjustments. The justification for the least square method as well the reference to the Gaussian Markov theorem has not evident theoretical basis for a regression which concerns either integer values or proportion, although it gives satisfactory results from the practical point of view. My suggestion is to suppress the corresponding sentence without entering into too much irrelevant detail.

Comment 14 : The study largely benefit of two large, partly overlaping sets of data from mainly caucasian women from the northern part of Europe. The authors indicate the exclusion of women either using contraceptive hormones, or being pregnant, or breastfeeding. How many women were exposed to intermittent progestin therapy, a common prescription at this period of life in European women? The two flowcharts seem to indicate that they have been also excluded?

Response 14: OK for the added sentence

Comment 14 bis: based on the two large available datasets, the validation study gives very good results at least for caucasian women as correctly pointed out by the authors. The appropriate use of the proposed RAS assumes the availability of similar datasets corresponding to different homogeneous groups of women. If m_B data appear rather easy to get by simple questionnaires, m_A data may be more difficult to obtain.

Comment on the absence of response to comment 14 bis: It is suggested to add in the supplementary material the R- code for adjusting the datasets, in order to allow epidemiologists to replicate the process in other settings. As an additional comment, it was not clear for the reader how the authors used the Maxima CAS software considering the absence of real theoretical development. A clear statement should be made about the only necessity of the R statistical package to replicate the results.

Comment 15 : The final example on the association between the RAS and the Odds ratio of developint new- onset asthma brings additional value to the proposed score. It is worth noting the large confidence intervals in the late post-menopausal on the figure displaying the results with the traditional approach as compared with the ones on the predicted probability of new- onset asthma in relation to RAS. The comparison is tricky as the abscissa and the ordinates concern different entities and the regression methods is totally different. The shape of the confidence envelope partly reflects the complex non linearity of the transformation, but the rather "thin" right side remains intringuing. How was the confidence interval calculated?

Comment on the response 15 :

The response remains rather vague for the reader. I understand that the authors performed in the previous published analysis a classical regression analysis of the occurrence of asthma episodes in relation to the menopausal status and perhaps age and here they are performing a second one of the same variable in relation to RAS and perhaps age. I assume that the second one was at least quadratic on RAS to take into account a possible more pronounced effect during the peri- menopausal period. Subsequently, I assume that the authors used some sort of delta method to calculate the confidence interval of the predicted probability from the variance of the regression variable taking into account the var/ cov matrix of the adjusted coefficients of the model. How it ends up with a very thin punctual confidence interval when RAS is 1 is not totally obvious. It could be useful to add more details in the appendix.

**********

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Reviewer #1: No

Reviewer #2: Yes: Jean- Christophe Thalabard

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

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13 Jun 2020

Please find attached a rebuttal letter with detailed point-to-point responses to the reviewer comments.

Submitted filename: 20200604_Rebuttal letter 2.pdf

Click here for additional data file.

17 Jun 2020

Describing the status of reproductive ageing simply and precisely - A reproductive ageing score based on three questions and validated with hormone levels

PONE-D-20-00740R2

Dear Dr. Triebner,

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19 Jun 2020

PONE-D-20-00740R2

Describing the status of reproductive ageing simply and precisely: A reproductive ageing score based on three questions and validated with hormone levels

Dear Dr. Triebner:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

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PLOS ONE