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From the * Animal Reproduction and Biotechnology
Laboratory and the Department of Statistics,
Colorado State University, Fort Collins, Colorado.
| Correspondence to: Dr Rupert P. Amann, 909 Centre Ave, #123, Ft Collins, CO 80526-2091 (e-mail: rpalra62{at}comcast.net). |
| Received for publication September 10, 2008; accepted for publication April 1, 2009. |
We retrospectively mined and modeled data to answer 3 questions. 1)
Relative to an estimate based on
20 semen samples, how imprecise is an
estimate of an individual's total sperm per ejaculate (TSperm) based on 1
sample? 2) What is the impact of abstinence interval on TSperm and TSperm/h?
3) How many samples are needed to provide a meaningful estimate of an
individual's mean TSperm or TSperm/h? Data were for 18–20 consecutive
masturbation samples from each of 48 semen donors. Modeling exploited the
gamma distribution of values for TSperm and a unique approach to project to
future samples. Answers: 1) Within-individual coefficients of variation were
similar for TSperm or TSperm/h abstinence and ranged from 17% to 51%; average
34%. TSperm or TSperm/h in any individual sample from a given donor was
between –20% and +20% of the mean value in 48% of 18–20 samples
per individual. 2) For a majority of individuals, TSperm increased in a nearly
linear manner through 72 hours of abstinence. TSperm and TSperm/h after
18–36 hours' abstinence are high. To obtain meaningful values for
diagnostic purposes and maximize distinction of individuals with relatively
low or high sperm production, the requested abstinence should be 42–54
hours with an upper limit of 64 hours. For individuals producing few sperm, 7
days or more of abstinence might be appropriate to obtain sperm for
insemination. 3) At least 3 samples from a hypothetical future subject are
recommended for most applications. Assuming 60 hours' abstinence, 80%
confidence limits for TSperm/h for 1, 3, or 6 samples would be 70%–163%,
80%–130%, or 85%–120% of the mean for observed values. In only
50% of cases would TSperm/h for a single sample be within –16% and
+30% of the true mean value for that subject. Conclusions: Pooling values for
TSperm in samples obtained after 18–36 or 72–168 hours' abstinence
with values for TSperm obtained after 42–64 hours is inappropriate.
Reliance on TSperm for a single sample per subject is unwise.
Key words: Imprecision of total sperm per ejaculate, abstinence interval, meaningful semen data, noninvasive evaluation of spermatogenesis
It generally is accepted that there is substantial within-individual variation in seminal volume or total number of sperm per ejaculate (TSperm, as 106/ejaculate). Obviously, results for a single sample will be imprecise and this could hamper correct detection of testicular illness or nonillness by an epidemiologist-andrologist team. We found no report considering the impact of within-individual variation in TSperm on detection of decreased sperm production in a subject and noted that most reports of coefficients of variation for TSperm were limited by number of samples per subject, number of subjects, or other factors.
Available data (reviewed in Amann, 2009a) show that TSperm increases for only 2–3 days of abstinence in many men and increases for 6–7 days in other men. In epidemiologic studies it is common to adjust TSperm or sperm concentration after abstinence intervals of 2–9 days to standardized values (eg, to 96 hours; Jørgensen et al, 2001). Does this ignore the dynamics of sperm accumulation in the excurrent ducts? We had the perception that studying normalcy of spermatogenesis in an individual on the basis of 1 or 2 samples of semen obtained after an abstinence interval ranging from 2 to more than 7 days might result in flawed conclusions. New information was needed for evidence-based recommendations on appropriate number of samples and especially abstinence interval.
By retrospective data mining and modeling we sought answers to 3 questions.
1) Relative to an estimate based on 20 semen samples, how imprecise is an
estimate of an individual's TSperm based on 1 sample? 2) What is the impact of
abstinence interval on TSperm and TSperm/h? 3) How many samples are needed to
provide a meaningful estimate of an individual's mean TSperm or TSperm/h?
Materials and Methods
Semen Data
To access data appropriate for study of intraindividual variation in
TSperm, we approached commercial semen banks. Personnel associated with
Fairfax Cryobank, Fairfax, Virginia, and Cryogenic Laboratories Inc,
Roseville, Minnesota, reviewed records for 2000–2005 to identify 50
donors who had provided 20 or more semen samples. A given donor provided
samples to only 1 center. All donors had signed documents allowing research
use of information derived from their samples; no provided data could be
traced to a specific individual. Information for each sample included code
number, collection date, abstinence interval (hours, as stated by donor),
seminal volume (mL), and sperm concentration (106 sperm/mL).
All semen specimens were evaluated using standardized procedures, with quality control meeting World Health Organization guidelines (World Health Organization, 1999). Each semen specimen was evaluated by a technician who had passed an annual proficiency test after formal internal training or retraining. A given semen sample was evaluated by 1 technician, but different technicians likely evaluated samples from a given donor.
All semen specimens were collected on site into a prelabeled 150-mL sterile cup, in a private room with literature to help sexual arousal if a donor examined it. Both sperm banks requested correct information on abstinence interval, but had no quality assurance procedure for this attribute. In the laboratory, after allowing 30 minutes for liquefaction, semen was transferred into a graduated, conical, 15-mL centrifuge tube (Falcon 352097) using a 5- or 10-mL serological pipette. Seminal volume was recorded to the nearest 0.1 mL, as read from the tube.
When measuring sperm concentration, the same site-specific counting device was used for semen from a given donor. Neat semen was mixed and 10 µL was diluted with 190 or 40 µL of diluent (tap water) for placement into a hemocytometer or 20-µm MicroCell counting device (Bright-Line; Hausser Scientific, Horsham, Pennsylvania; Conception Technologies, San Diego, California) then in use, respectively, at Fairfax Cryobank and Cryogenic Laboratories Inc. Sperm within the demarked volume were counted using phase-contrast optics at 200x total magnification. Calculations were based on the mean for counts from 2 chambers of the counting device. If counts between 2 chambers did not agree within 10%, a recount was performed and only the last 2 counts were used to calculate the mean.
Data for 48 donors were transmitted electronically; there were 20 samples
for 40 donors and 18 or 19 samples for 8 donors. After the first sample in a
series, the interval between successive samples (not abstinence interval) was
less than or equal to 14 days for 90% of samples and less than or equal
to 8 days for 75% of samples. Days rather than weeks between samples was
desirable for study of intraindividual variation, but precluded meaningful
study of seasonal variation. For each sample, we calculated TSperm as
(volume)(sperm concentration) and then TSperm per hour of abstinence
(TSperm/h) was calculated. TSperm/h sometimes is termed sperm accumulation
rate.
Data Mining and Modeling
Statistical analyses focused on the relationship between TSperm and
abstinence interval, as well as within-donor and among-donor variation in
TSperm and TSperm/h. We did not model seminal volume or sperm concentration
because neither attribute informs about potential illness of the testes
(Amann, 2009b). TSperm was
plotted as a linear function of abstinence interval without restriction on the
intercept. Also, individual straight lines were calculated for each donor with
the intercept set equal to zero. Finally, data for TSperm and TSperm/h at
abstinence intervals common to many donors (ie, 24, 36, 48, 60, 84, 96, and
120 hours) were log10-transformed and compared by abstinence
interval using a mixed model with donor as the random effect.
Preliminary least squares analysis revealed that the standard deviation of
TSperm was approximately proportional to its mean and that the distribution of
deviations from the mean was right-skewed rather than bell-shaped. To match
those properties TSperm was assumed to have a gamma distribution, which is a
common model for measurements that have large coefficients of variation (CVs)
and long right tails and are constrained to nonnegative values. The family of
gamma distributions includes 
2 distributions and is flexible
in that with a high CV the gamma distribution is highly skewed, but with lower
CVs it becomes nearly symmetric and normal (see Supplemental Figure 1,
available online at
www.andrologyjournal.org).
This choice allowed modeling of the nontransformed response of TSperm with
increasing abstinence interval using generalized linear model methods
described in the Supplemental Material. In this model an outcome value
βi can be interpreted as mean sperm accumulation rate
(106 sperm/h) for the ith donor with a
dispersion parameter 
, which is the square of the CV.
Maximum likelihood estimates of the model parameters were obtained using SAS PROC GENMOD (SAS Institute, 2003). The data were restricted to samples for which abstinence interval was between 13 and 84 hours, the range over which the response was most linear; this excluded 125 samples for which abstinence interval was 85–100 hours and 20 samples with an abstinence interval of 102–240 hours. As described in the Supplemental Material, 2-sided confidence intervals for loge(βi) were produced by the program using the likelihood-ratio method, and endpoints of the intervals were exponentiated to obtain confidence limits (CLs) for βi for each of the 48 donors in our data set. For hypothetical future subjects, CLs for accumulation rates (β) were calculated using method 1 described in the Supplemental Material.
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Results
Base Data and Imprecision of 1 Sample
Table 1 presents summary
data, with emphasis on variation within and among the 48 donors. Median values
were slightly lower than the respective mean, reflecting moderate skewness to
larger values. The range for volume or TSperm in individual samples was wide
(eg, 46–1290 x 106 sperm/ejaculate). Reported
abstinence interval ranged widely, but for 97% of samples was between 13 and
100 hours. Across donors, the means and standard deviations were correlated
(r = 0.84). Although within-donor CVs for TSperm ranged up to 50%,
the 95% CLs around the mean were 33%–37%. Among-donor CVs for TSperm, or
other seminal attributes, were not substantially greater than mean
within-donor CVs (Table 1).
Log10 transformation of raw values reduced CVs (see Supplemental
Material). As anticipated for seminal donors, the among-donor CLs were narrow,
with 90% of donor means between 2.9 and 3.4 mL or 309 and 368 x
106 sperm/ejaculate. Calculation of TSperm/h, to correct for
abstinence interval, did not substantially reduce CVs. They averaged 33%
within donors and 39% among donors.
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Considering all 946 samples, most correlations among seminal volume, sperm concentration, TSperm, and abstinence interval were low (Supplemental Table 1). TSperm had a greater association with sperm concentration than seminal volume (r2 of 0.41 vs 0.28). For all samples, the correlation between TSperm and abstinence interval was 0.27, and for samples provided after 13 to 84 hours' abstinence it was 0.24 (n = 791).
We had asked, how imprecise is a single sample as an estimate of an individual's TSperm? For this data set and relative to a mean value based on 18–20 samples, the value for TSperm in any individual sample from a given donor was between –20% and +20% of the mean value in 46% of the 18–20 possible cases. TSperm for an individual sample was between –30% and +30% of the mean value in 63% of cases. The situation was similar for TSperm/h. Individual values were between –20% and +20% of the mean value in 49% of possible cases.
Impact of Abstinence Interval on TSperm
To understand the relationship between TSperm and abstinence interval, we
examined plots of data for individual donors
(Figure 1 shows representative
data). Three features were obvious. 1) For a majority of donors TSperm
increased in a more or less linear manner from the shortest abstinence
interval through near 72 hours, after which the change in TSperm/h sometimes
leveled off. Panels M–P in Figure
1 present obvious exceptions to this generalization. 2) TSperm
ranged widely for samples provided by a donor after the same reported
abstinence interval (see array of data points on the Y-axis for a given
abstinence interval (X-axis) in panels A, C, F, H, K, M, or N in
Figure 1). 3) The slope of the
linear plot (value for a in upper left corner of each panel; describes the
dotted line), TSperm/h abstinence, ranged from 0 to 11 x 106
sperm/h (including plots not in Figure
1). Correlation coefficients (value for r in top center
of each panel) between TSperm and abstinence interval for individual donors
generally were greater than 0.55 and occasionally were greater than 0.80. This
means that, based on r2, abstinence interval usually was
associated with less than 45% of the variation in TSperm. For most donors a
linear plot provided a better fit than a second- or third-order polynomial
(panel G in Figure 1
illustrates an exception, when the donor's full range of abstinence intervals
was considered).
Analysis of all available data for abstinence intervals with many samples (Figure 2) showed that TSperm increased through 72 hours. Although the numerical value for 84 hours was larger than that for 72 hours, the difference was not significant (P = .34) and means for 72, 84, and 120 hours were not significantly different from each other. TSperm after 24 or 36 hours of abstinence was greater than would be expected based on linear extrapolation (dotted line) from the origin to TSperm after 48, 60, or 72 hours of abstinence. TSperm/h was similar at 24 and 36 hours of abstinence, and obviously different from values after 48–84 hours of abstinence. There seemed to be "extra sperm." The back-transformed value for mean TSperm/h after 24 hours of abstinence was 6.88 x 106 sperm/h, compared with a value of 4.66 x 106 sperm/h for abstinence intervals of 48–84 hours (back-transformed from the weighted average of the least squares means of the log values). For both TSperm and TSperm/h, the interaction of abstinence interval and donor was significant (P < .01). In other words, for certain donors the temporal change in TSperm differed from that for other donors; not a surprise.
The finding of "extra sperm" after a short abstinence interval led to a within-individual comparison. We identified donors who had provided 4 or more samples after 18–40 hours of abstinence and also after 41–72 hours (7 donors; 4–16 samples per interval). On average, TSperm/h was 22% greater after 18–40 hours of abstinence (7.07 vs 5.81 x 106; P = .01). Also see Supplemental Material, page 3. We concluded that TSperm/h was atypically high in samples provided after less than or equal to 40 hours of abstinence compared to samples from the same individual provided after 41–72 hours of abstinence.
Precision of Estimated TSperm/H
Based on the generalized linear model, mean sperm accumulation rates
(βi) were estimated for the 48 donors using samples
with an abstinence interval of 13–84 hours. Estimated values ranged from
2.36 to 10.0 x 106 sperm/hour and averaged 5.40 x
106 sperm/hour. These model-based estimates usually were identical
with mean TSperm/h abstinence calculated from each sample from a given donor,
but the latter is not equal to the sometimes used (
TSperm)/(all
abstinence intervals). The model estimate for 
was 9.4212 (standard error
= 0.4662), which implied a CV of 32%, nearly matching the CV of 33% calculated
for TSperm/h using all values of abstinence interval. Lower and upper 90% CLs
for the individual donor sperm accumulation rates averaged –2.6% and
+15.4% of the estimated value. For individuals with 20 samples, the lower and
upper 90% CLs were –11% and +13%, respectively. On the other hand, for
an individual having only 2 samples with an abstinence interval between 13 and
84 hours, lower and upper 90% CLs were –30% and +50%, respectively.
To calculate CLs for 1 or more samples from a hypothetical future
individual we used the gamma model and the estimated from the donor data
set. The results (Table 2)
demonstrated the desirable asymmetry of the gamma model and the high degree of
uncertainty when mean TSperm/h was based on only a few samples. Both features
were especially evident if the mean was based on fewer than 6 samples (see
Supplemental Figure 2). An estimated upper CL based on a single sample from a
future individual is almost twice as far from the recorded value as an
estimated lower CL. We calculated a probability of 0.76 that a single sample
will not provide a value for TSperm/h within ±10% of a future
individual's true value.
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Discussion
Caveats to Our Study
Readers should consider caveats detailed in the Supplemental Material. Data
therein support correctness of the model for low values of TSperm, such as
15–60 x 106 after 48 hours of abstinence. Hence,
factors in Table 2 and CLs in
Supplemental Table 3 should be applicable for most samples encountered by a
clinician or epidemiologist-andrologist team.
Comparison of Statistical Approaches
It is common to use a logarithmic, square-root, or cube-root transformation
to normalize values for TSperm. Handelsman
(2002) evaluated several
normalizing transformations, using data for semen from nonoligozoospermic men,
and suggested that the cube root was easiest to use. The cube-root
transformation also is used to normalize 2 data
(Wilson and Hilferty, 1931),
which are a special case of the gamma distribution. The gamma model is
advantageous compared to normalization via cube roots for 2 reasons: 1) it
avoids transformation of data, so the linear relationship between TSperm and
abstinence interval is preserved; and 2) it eliminates negative statistical
bias that occurs when estimated TSperm is back-transformed from averages of
cube roots or logarithms (Lindgren,
1993).
TSperm per Hour Abstinence
Our model fitted a single linear function to each donor based on his
TSperm. For our donors, mean sperm accumulation rate (average of individual
β values) was 5.40 x 106 sperm/h. This value is
comparable with values calculated from the literature when abstinence interval
was 1–3 days (see Amann,
2009a).
Abstinence Interval
For this data set, the rate of increase in TSperm slowed after 60
hours of abstinence (Figure 2),
and the rate of sperm accumulation in the excurrent ducts must have approached
zero near 84 hours of abstinence because TSperm in ejaculated semen remained
stable. These data, together with information in the literature
(Amann, 2009a), led to
emphasizing the need for an abstinence interval shorter than often
accepted.
Also obvious in Figure 2 is that TSperm/h was higher for abstinence intervals of 24 or 36 hours than after abstinence intervals of 48–84 hours. This difference has a biological basis that was evident as "extra sperm" when the plot for TSperm and the dotted line in Figure 2 were compared. It was estimated that 34–78 x 106 sperm (95% CLs) were moved distally in the excurrent ducts during 0–18 hours after the preceding ejaculation, and this estimate was in reasonable agreement with number of sperm in the first ejaculate after vasectomy (see Amann, 2009a). The impact of these extra sperm on TSperm was diminished when abstinence interval was 36 rather than 24 hours, and negligible by 48 hours. This postejaculation movement of sperm typically is not considered when thinking about TSperm as a function of abstinence interval and especially distorts calculations of TSperm/h if abstinence interval is less than 42 hours.
For clinicians, if the goal is to obtain a representative sample of semen
for diagnostic use, then an abstinence interval of 48 hours (uniform as
42–54 hours or more leeway with 42–60 hours) will provide the most
meaningful value for TSperm, especially if the patient had ejaculated during
the previous week once every 42–60 hours. Samples produced after
42–60 hours' abstinence also should allow meaningful evaluation of sperm
motion and morphology. This recommendation is shorter than the 2–3 days
of abstinence often recommended (eg,
Sharlip et al, 2002;
McLachlan et al, 2003) for an
initial clinical evaluation.
For epidemiologists, the recommended abstinence interval also is 42–60 hours (exclude all samples with abstinence intervals >64 hours). A stringent range of abstinence intervals provides the best separation of individuals with a high, normal, or low sperm production rate and, hence, the best chance to detect if agent X affected testes function.
Why is a short abstinence interval important? If abstinence intervals greater than 64 hours are accepted for routine clinical evaluations or epidemiologic studies, resulting calculations will underestimate true TSperm/h abstinence for men with a reasonable rate of sperm production and overestimate true TSperm/h for individuals with moderately reduced sperm production. In other words, acceptance of an abstinence interval of 3 days or more might hamper detection of individuals with moderately reduced sperm production or borderline oligozoospermia, because the excurrent ducts could accommodate all sperm produced over far longer than 42–60 hours before any loss. See "Stabilize Number of Sperm in the Excurrent Ducts" in Amann (2009a). However, when it is known that an individual produces relatively few sperm, capability of the epididymides to accumulate sperm for 7 days or more can be exploited by use of a long abstinence interval before obtaining a sample for artificial insemination.
Adjustment of TSperm for abstinence interval (ie, expression as TSperm/h)
usually would have little impact on any clinical conclusion based on number of
sperm ejaculated, if abstinence interval was 42–60 hours. This is
because for each hour of deviation from 48 hours of abstinence, TSperm would
decrease or increase by 2%. Our conclusion that correction for abstinence
interval has little clinical utility when abstinence interval is relatively
short confirms Baker et al
(1981). For an
epidemiologist-andrologist team, however, an unadjusted 12-hour difference in
abstinence would result in a 25% error in TSperm for a given subject,
which might hamper correct placement of that subject with others having
diseased or nondiseased testes.
For donations to a sperm bank, an abstinence interval greater than 64 hours is appropriate because one wishes to maximize the number of good-quality sperm available to process as 1 batch rather than obtain a reasonably precise value for TSperm/h. For nonoligozoospermic donors an abstinence interval of 72–96 hours might be appropriate, although samples after an abstinence interval of 42–72 hours often would have a similar TSperm.
How Many Samples Are Needed?
Imprecision of quantitative values based on 1 semen sample has long been
recognized, and standard texts emphasize that 2–3 samples should be
evaluated. What is the impact of imprecision on conclusions based on semen
data? Our approach and model for the first time allow facile calculation of
CLs showing the uncertainty around TSperm/h for a single future sample,
followed by refinement based on 2 or 3–6 samples from a future
individual. The 80% CLs would be –30% to +64% for a single value, but if
based on 3 samples the CLs would be –20% to +30% of mean TSperm/h
(Table 2). For a hypothetical
future individual, the CLs for TSperm narrow (Supplemental Figure 2) by
approximately 35%, 20%, and 15% as his data base is expanded from 1 to 2, 2 to
3, and 3 to 4 samples. Precision of a mean based on 3 samples is almost twice
as good as that of a mean based on 1 sample. A mean for TSperm/h based on 3
samples will be within –20% and +30% of the true value in 80% of
cases, whereas a single value would be within –16% and +30% of the true
value in only 50% of cases (Table
2).
A clinician seeks values for seminal attributes of an individual with sufficient precision to make a recommendation to a patient couple. This might not require precision represented by 90% CLs assuming a continuous variable (eg, TSperm), but simply sufficient precision to allow correct conclusions in a go/no-go (binomial) manner. For this reason, both 50% and 80% CLs are included in Table 2 and Supplemental Figure 2. Obviously, TSperm is only 1 of many factors to consider. For future samples, calculations based on TSperm, recorded abstinence interval, and Table 2 can be made almost instantaneously by any technician. For a single sample, the CLs are obtained by multiplying the product of the observed TSperm/h and recorded abstinence interval by the appropriate table entries. When multiple samples are available, the average of the sample values for TSperm/h and table entries are used. Appropriate calculations could be incorporated into computer programs for seminal records.
Width of the intervals in Table 2 draws attention to the difficulty of evaluating the effect of a change (eg, old or placebo vs new treatment) in the same or different individuals using small sample sizes. If the 2 confidence intervals do not overlap (examples in Supplemental Table 3), the 2 treatments would be significantly different (although the converse is not true). With increasing sample numbers CLs are narrower and detection of differences is easier. Not surprisingly, for an extreme test result (relative to an individual's true value) a second value is likely to be closer to the true value (Baker and Kovacs, 1985) and additional samples will bring the mean closer to the true value.
Large epidemiologic studies usually involve detailed evaluation of 1 or 2 ejaculates to characterize the number and quality of sperm then being produced by each subject's testes, with abstinence intervals ranging up to 7 days. Implicit in the intent of most studies is detection of illness vs nonillness of each individual's testes in respect to spermatogenesis. The weakness of the conventional approach is evident from information in this paper and Amann (2009a). There are 2 problems. First, pooling data for TSperm for samples with abstinence intervals greater than 64 hours with values for samples with abstinence intervals less than or equal to 60 hours inappropriately benefits individuals with impaired sperm production. Second, and assuming a short abstinence interval, evaluation of 1 semen sample per subject would be appropriate only if the hypothesis in a future study can be evaluated with a protocol whereby test results for 25% of the subjects are more than 16% below their true value for TSperm and test results for another 25% of subjects are more than 31% above their true value for TSperm. Note that a test result for TSperm based on a single sample is more likely to be far above an individual's true value (Supplemental Figure 2) than far below.
Conclusions
To obtain meaningful data on TSperm and maximize detection of individuals
with low sperm production, requested abstinence interval should be 42–54
hours with an upper limit of 64 hours. Accurately determine TSperm. For
individuals known to produce few sperm, 7 days or more of abstinence will
maximize number of sperm available for insemination or deposition during
intercourse. TSperm/h based on a single sample will be within –16% and
+30% of the true value in only 50% of cases, whereas a mean TSperm/h
based on 3 samples will be within –20% and +30% of the true value in
80% of cases.
Acknowledgments
Genetics & IVF Institute, Fairfax, Virginia, kindly allowed transfer of data for seminal donors at 2 of their facilities, making this study possible. David S. Karabinus and Stephen H. Pool, of the Genetics & IVF Institute, reviewed historic data, selected the sets of 20 samples used, corrected the semen data portion of the methods section of the manuscript, and read the manuscript. We greatly appreciate their enthusiasm about this study and willingness to provide semen data.
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