Seasonality of Birth and Conception to Teenagers in Texas

Seasonality of Birth and Conception to Teenagers in Texas

Scafetta, N

ABSTRACT:

We study the births to teenagers during the years 1964-2000 and analyze separately the three main racial/ethnic groups in Texas (White, Hispanic, and African American), as well as married and unmarried teens during the years 1994-2000. By using traditional statistical methods of analysis and a filter based on the multiresolution wavelet analysis, we draw inferences about the times of the year when adolescent females of different racial/ethnic and marital groups have the highest probability for pregnancy ending in live birth. Multiple factors influencing teen pregnancy are identified and associated with temporal features of social, cultural, educational, and familial processes. In particular, we detect links between unmarried teen conception times and school terms, and weekly birth patterns associated with scheduled c-sections that differ according to racial/ethnic groups.

INTRODUCTION

Teenage pregnancy rates vary from country to country, but the extent of the problem in the United States, and in Texas particularly, remains significant. The United States has one of the highest teenage pregnancy rates among the industrialized nations (Darroch, Singh, and Frost, 2001; Singh and Darroch, 2000). Even though the United States has observed a drop in the rates of birth to teens of all ages and racial/ethnic groups since 1990 (Ventura, Curtis, and Matthews, 2000), 35 percent of U.S. teenage girls become pregnant at least once before they reach age 20, resulting in more than 850,000 teen pregnancies per year (Henshaw, 2003). In 1996 the rate of pregnancy in the U.S. for young women aged 15 to 19 years was 98.7 per 1,000 women of that age group (Ventura, Curtis, and Matthews, 2000). The Texas teenage pregnancy rate was 113 per 1,000 women aged 15 to 19 in 1996 and, today, Texas ranks 5th in the U.S. (Nevada has the highest rate) (The Allan Guttmacher Institute, 2003). Of the almost 80,000 teen pregnancies each year in Texas, 65 percent result in live births, 20 percent result in induced abortions, and 15 percent result in miscarriages (The Allan Guttmacher Institute, 2003).

The problem of teenagers giving birth has important socioeconomic consequences (Grogger and Bronars, 1993) and both policy makers and health care providers are greatly interested in determining the personal, social, and political costs (Huffman, Foster, and Furstenberg, 1993). Herein, we analyze the births to girls aged 15 to 19 in Texas during the years 1964-2000 and, in particular, the count of daily births to the three main racial/ethnic groups (White, Hispanic, and African American), as well as, to married and unmarried teens during the years 1994-2000. Finally, we analyze influences associated with social, cultural, educational, and familial processes (Brewster, 1994; Geronimus and Korenman, 1992; Geronimus, 1996; Rich and Kirn, 1999).

General patterns in birth seasonality have usually been detected via traditional methods of analysis, such as spectral analysis, least-squares fitting functions, autoregressive integrated moving average (ARIMA) models, and linear or trigonometric regression models (Fellman and Eriksoon, 2001). To draw inferences about the times of the year when adolescent females have the highest probability for pregnancy, there is the need to handle the large error associated with the uncertainty of the date of conception. Herein, we suggest the adoption of a filter based on the multiresolution wavelet analysis (MWA) (Percival and Waiden, 2000). This technique optimizes the analysis by decomposing the time series into a sequence of smooth and detail hierarchical scaling curves that are localized in both time and frequency.

We estimate the seasonality of adolescent reproductive behavior by using only daily birth data. Therefore, the findings are restricted to those conceptions related to pregnancies ending in live birth. It could be argued that conception seasonality estimates would be more accurate if birth, abortion, and miscarriage data are all used together (Rodgers and Parnell, 1999). However, we observe that while birth data are accurate, abortion and miscarriage data are usually inaccurate and incomplete. For example, there might be a significant number of errors in the gestational age at the time of the abortion or miscarriage. In addition, the official records may not contain any information concerning illegal abortions and miscarriages occurring during the first weeks of gestation. All these interrupted pregnancies are not usefully recorded or, simply, are not recorded at all. Therefore, official abortion and miscarriage data would not necessarily eliminate inaccuracies in the estimation of seasonal patterns of conception. In any case, we observe that studies about the monthly seasonality of recorded induced abortions and miscarriages in North Carolina (Parnell and Rodgers, 1998; Rodgers and Parnell, 1999) determined that these patterns correspond sufficiently well to the implicit seasonality of conceptions associated with the seasonality of birth patterns. Both types of estimations present similar peaks and valleys for several groups of women: adults and teenagers, married and unmarried, Whites and African Americans. These findings suggest that the number of abortions and miscarriages occurring during a particular period is likely to be proportional to, or monotonie in, the total number of pregnancies during the same period. Therefore, abortion and miscarriage data would stress the conception patterns from birth data alone, not alter them. In the present study we assume that the seasonality patterns of births are indicative of the seasonality patterns of conceptions, at least sufficiently for our purposes here.

BIRTHS TO TEENAGERS

Time series analysis in the social sciences is traditionally accomplished using linear models that assume the stationarity of the phenomena of interest (Rodgers, Rowe, and Buster, 1998). However, sociologie data are usually non-stationary (Doblhammer, Rodgers, and Rau, 2000) and certain precautions must be adopted to properly take the effects of these non-stationaritics into account. Figure 1 shows that the number of births to teens is seen to have both an annual cycle and an anomalous trend that reflects the dependency of the teen birth phenomenon on demographic, political, and social changes that have occurred in Texas during those years. The annual cycle seems to be mainly due to the fact that human fertility is higher in cold rather than hot months (Lam and Miron, 1996; Rojansky, Brzesinski, and Schenker, 1992). More precisely, sperm quality and quantity decrease in hot months (Levine et al., 1988; Saint Pol et al., 1989). After removing the annual periodicity and the long trend, the residual signals present patterns that depend upon the marital status of the teens (Scafetta, Hamilton, and Grigolini, 2001; Scafetta et al., 2003). Therefore, the teen birth phenomenon depends on social institutions and cultural backgrounds more than on mere biological factors.

Figure 1 depicts the daily number of births to 15 to 19 year old mothers in Texas from 1964 through 2000, representing 37 years (13,515 days). These data, as well as seven years of data concerning married and unmarried teens in the three racial/ ethnic groups, were obtained from the Bureau of Vital Statistics at the Texas Department of Health. These data represent all birth records available electronically at the time of the present study. By simply fitting the data, using a least-squares procedure, with the straight line f(t) = a + b(t – 1964), we evaluate a = 114 births per day and b = 1 daily birth per year. The slope, b = 1, indicates that the number of daily births from 1964 through 2000 increases on average by one per year. At the beginning of 1964 the average is 114 births per day and at the end of 2000 the average is 151 births per day. Over the entire period, the average count of births is 133 births per day, the maximum is 228 births per day, the minimum is 73 births per day, and the standard deviation is 21 births per day. Figure 1 also shows a continuous increase in the spread of the number of births over the period 1990 to 2000 that will be discussed later.

Figure 2 shows the daily number of births to married and unmarried teen mothers in Texas from 1994 through 2000 (2,557 days). During these 7 years, both counts of births are characterized by annual cycles that fluctuate around an apparent linear bias. The bias increases for unmarried teens, and decreases for married teens. Moreover, the spectral analysis of the teen birth time series shown in Figure 3 suggests that the teen birth data are characterized by three main periodicities: the annual (365 days), the ½-year (183 days), and the weekly (7 days) periodicity. The annual cycle is most likely related to the one-year, seasonal, temperature/light cycle to which human fertility is related (Lam and Miron, 1996; Rojansky et al., 1992). Figure 3 shows that the birth pattern of unmarried teens, contrary to that of married teens, is strongly influenced by the ‘/2-year cycle. We will see that this ‘/2-year harmonic is likely to be related to the fall and spring school semesters that, together with the Christmas and summer vacations, divide the year into two semesters. Finally, the weekly periodicity is associated with scheduled c-sections.

The coefficient a gives the approximate mean value of daily births at the beginning of 1994; b is the slope of the linear trend that gives the annual mean increase (positive value) or decrease (negative value) of daily births per year; C^sub 1^ and C^sub 1/2^ are the amplitudes of the 1-year and ½-year periodicities; τ^sub 1^ and τ^sub 1/2^ measure the temporal shift of the two sinusoidal functions. The time t is measured in years. The analysis of the period 1994-2000 shows that the 99 daily mean births to unmarried teens is almost double that to married teens, 50 daily mean births. The number of births to unmarried teens increases at b = 1.92 daily births per year, whereas the number of births to married teens decreases at b = 0.62 daily births per year. Finally, the two smooth black curves of Figure 2 clearly show that the ½-year harmonic has a much more prominent influence on the unmarried than it does on the married teens.

RACIAL/ETHNIC AND MARITAL GROUPS

Figure 4 shows the number of births to teens in Texas during the period 1994-2000 for all racial/ethnic and marital groups. Table 1 records the fitting parameter values by using Eq. (1). By plotting Eq. (1) with the coefficients C^sub 1^, C^sub 1/2^, τ^sub 1^ and τ^sub 1/2^ recorded in Table 1 and using a = 0 and b = 0 it is possible to get approximate birth seasonality patterns for each group. Unmarried groups always present two peaks, while married groups present only one peak. Among the three racial/ ethnic groups, the mean number of daily births to Hispanic teen mothers is the highest with a mean of 80 births per day. The White group is second with a mean of 44 births per day, and the African American is last with a mean of 25 births per day. Moreover, for all racial/ethnic groups, the mean number of births to unmarried teens is almost double that for the married teens. For Whites and Hispanics, the ratio between the births to unmarried and married young women is almost the same (27/17 = 1.59 for White and 49/31 = 1.58 for Hispanic). By contrast, for African American teens, the mean is 23 births to unmarried mothers versus only 2 births to married mothers. The ratio is 23/2 = 11.5 and is almost seven times higher than that for the other two racial/ethnic groups. Therefore, pregnant African American teens are much less likely to be married than are their White and Hispanic counterparts (Unger and Cooley, 1992).

The detailed numerical analysis of the least-square fitting curves of Table 1 stresses further differences among the groups. The number of births to unmarried Hispanic teens grows at b = 2.06 daily births per year. In contrast, there is only a slight increase of births to unmarried White teens (b = 0.35), and a slight decrease in the number of births to unmarried African American teens (b = 0.50). Within the married group, the number of births to Hispanic teens is increasing slightly (b = 0.07), while the number of births to the other two groups is decreasing slightly (Whites, b = 0.65; African Americans, b = 0.04). For all three racial/ethnic groups, the unmarried teen’s behavior is always influenced by a relatively strong ½-year periodicity. The strength of a periodicity is estimated by the intensity of the amplitudes C^sub 1^ and C^sub 1/2^. For the unmanned groups, the two amplitudes are quite similar, whereas for married groups, the annual amplitude C^sub 1^ is always much stronger than the ½-annual amplitude C^sub 1/2^. We have already obtained this effect via the spectral analysis of the teen birth time series shown in Figure 3.

Table 2 and Figure 5 show the rates of births per 1,000 teenagers for the three racial/ethnic groups. We observe that rates (births/population at risk) require reliable population counts. However, because population counts are most often made using projections and only occasionally using census, rates may be slightly misleading depending on the reliability of the projections. In particular, we notice the sudden increase by 20 percent of the Hispanic teenager population between the projection of 1999 and the census of 2000. This means that projections and, therefore birth rates, are not very reliable for Hispanics. In any case, Hispanic and African American groups present a rate of teen births much higher than that for the White group. These differences may be due to earlier physical maturity, greater likelihood of initiating sexual activity in the teen years, more frequent sexual activity, older sexual partners, less likelihood of using contraception, greater acceptance of pregnancy as a normal and desirable event in the teen years, and/or less likelihood of seeking abortion for unintended pregnancies. These births represent only 65 percent of all pregnancies. Moreover, Table 2 and Figure 5 also show that the rate of births to Whites and, in particular, to African American teens, decreased during the last few years, whereas the rate of births to Hispanic teens is more uncertain and looks stationary.

Table 3 records the percentage of births to teens for each day of the week. The weekly periodicity is due to the separation of the week into weekdays when a higher number of births is recorded and weekends when a lower number of births is recorded. In fact, the weekly periodicity has been recognized to be due to the tendency of health care providers to induce delivery on particular days, primarily Monday through Friday, in order to avoid weekends and holidays (Rindfuss et al., 1979). Table 3 shows that the likelihood of a weekday birth is greatest for Whites (the amplitude of the weekly cycle can be estimated by the standard deviation of the seven daily probabilities, sd = 2.71) followed by Hispanics (sd = 1.60), and greater for married (sd = 2.09) than for unmarried (sd = 1.76) teens. Among the three racial/ethnic groups, African Americans show the smallest weekday preference (sd = 1.34) that is almost one half of that of the White group. This fact may increase the African American’s odds of a neonatal death, because this preference may mean that African American teens, for a variety of reasons, have a looser connection to the Texas medical system than do Whites and Hispanics and, therefore, African American teens more often deliver their babies on an emergency basis. The issue of births on holidays and weekends is of critical importance. Recent research has shown that the odds of a neonatal death, attributable to a condition arising in the perinatal period (from 20 weeks gestation through 27 days after birth), are 42 percent greater among weekend births than among weekday births (Hamilton and Restrepo, 2003). While decreased staffing levels and emergency deliveries likely play a role in risk for neonatal mortality, the exact mechanism responsible for this increased mortality is not yet certain and is under study.

BIRTH AND CONCEPTION SEASONALITY THROUGH WAVELET ANALYSIS

Herein, we estimate birth and conception seasonal patterns within the year. As we anticipated earlier, the birth data shown in Figures 1 and 4 presents non-stationary trends and a weekly cycle plus some anomalous behavior such as artificial drops in the number of births on weekends and holidays. Seasonal patterns have to be independent as much as possible from the supra-annual non-stationary increasing or decreasing trends as well as from the fast weekly cycle and artificial sudden drops. In fact, it is easy to realize that a persistent supra-annual increase in the number of births, if it is not removed from the data, would produce noncyclical seasonal patterns that depend on the way the data are analyzed. For example, if the original data set starts on January 1 and ends on December 31, in the presence of an increasing trend, the average seasonality trend would present a discontinuous jump between the end of December and the beginning of January. The same discontinuity would appear at a different time of the year if the data set started and ended in different months. Instead, a seasonal pattern should present a cyclical stationary behavior without such artificial discontinuities. One approach to analyzing this richer complexity might be to extract the supra-annual non-stationarities by fitting the time series with a high-order polynomial or by adopting a trigonometric regression model (Fellman and Eriksoon, 2001). However, such a procedure would be laborious and arbitrary because it implies the need to implement the model with several parameters whose meaning is often obscure. In an analogous way, the presence of artificial sudden drops in the data would induce an artificial depression in an ARIMA generated smooth curve. A better resolution might be to ignore, as much as possible, those sudden changes rather than trying to smooth them out.

Figures 6 and 7 suggest how to use the WMA to estimate the birth and conception seasonal patterns from the Texas teen birth data. As we explained above, first we have to identify and remove the non-stationary supra-annual slow bias from the data. This anomalous trend reflects the dependency of the teen birth phenomenon in Texas on demographic, political, and social changes that have occurred during those years. The wavelet that smoothes a period longer than one year is the smooth curve S^sub 9^(t) that captures the smooth variability of the signal with time scale larger than τ = 29 = 512 days. Therefore, we detrend the original data of the smooth curve S^sub 9^(t) and we get a stationary signal (dots at the bottom of Figure 7) that contains all fluctuations of the data captured by the first nine MWA detail curves. At this point we have a signal with a stationary mean and we can estimate the seasonal birth patterns by averaging the daily values using the 37 years from 1964-2000. The result is shown in Figure 8 (gray curve).

The months with the lowest daily number of births are April and May, with a rapid increase during June and July to the months with the highest count of births, August and September, with a peak between September 5 and 15. The number of births is nearly constant from October through February. Figure 8 also shows sharp depressions corresponding to days around national holidays, such as, January 1-2, July 4 (Independence day), the first week of September (Labor day) and December 25-26 (Christmas holidays). These drops in the number of births are further evidence of the long-standing tendency of health care providers to schedule inductions of labor and elective c- sections at times when staffing is high, such as weekdays, and to avoid times when staffing is low, such as weekends and holidays (Rindfuss et al., 1979).

Estimating the conception rate from birth certificates may be imprecise because in the U.S. only 51 percent of teen conceptions end in live birth; with 35 percent ending in induced abortion and 14 percent resulting in stillbirth or miscarriage (Committee on Adolescence of the American Academy of Pediatrics, 1999). In Texas the situation is relatively different from the U.S. average: 65 percent of teen pregnancies result in live births, 20 percent result in abortions and 15 percent result in miscarriages. Estimates of premature birth rates range from 4.4 percent to 21.5 percent of all births with even higher rates of premature births occurring among minorities and very young women (Petersen and Alexander, 1992; Savitz, Blackmore, and Thorp, 1991; Warren, Gwinn, and Rubin, 1986). However, as we explained in the Introduction, studies about the monthly seasonality of recorded induced abortions and miscarriages in North Carolina (Parnell and Rodgers, 1998; Rodgers and Parnell, 1999) determined that these patterns correspond sufficiently well to the implicit seasonality of conceptions associated with the seasonality of birth patterns. So, we assume that the seasonality patterns of birth are indicative of the seasonality patterns of conception.

We observe that using the normal length of gestation can lead to inaccuracy in calculating conception rates because of the large error, which may be as great as one month, associated with the uncertainty of the date of conception. To handle this large error we suggest removing from the data all fast fluctuations that cannot be significantly correlated with the date of conception. We proceed as follows. The typical period of gestation dates from the first day of the last normal menstrual period, an average of 40 weeks before delivery (Gleicher et al., 1998; Gabbe et al., 2001). The pre-ovulatory or follicular phase of the ovarian cycle, which ends with the ovulation of an oocyte ready for conception, is approximately two weeks. Therefore, on average, the conception of a baby takes place about 38 weeks or 266 days prior to a full term delivery. Periods ranging from 36 to 40 weeks from conception to delivery are considered to be within normal limits. It has been estimated (Leridon, 1986) that 90 percent of the births occur between 243 and 294 days of gestation (± 25.5 days from the average); 85 percent of births occur between 247 aind 289 days (± 21 days); and 79 percent occur between 249 and 283 days (± 17 days). Consequently, by using only birth data, we cannot reliably correlate the variability of births occurring on a shorter time scale, than these estimates suggest, with the date of conception. This level of coarse-graining is taken into account by assuming that the fluctuations within a period below 64 days (or ± 32 days) from the average cannot be reliably correlated with the date of conception. These fast fluctuations are captured by the MWA detail curve Y^sub 1,5^(t) = D^sub 1^(t) + D^sub 2^(t) + D^sub 3^(t) + D^sub 4^(t) + D^sub 5^(t). We observe that the weekly cycle as well as the sudden sharp drops associated with weekends and holidays are contained in Y^sub 1,2^(t) = D^sub 1^(t) + D^sub 2^(t) curve. Therefore, together with the slow supra-annual non-stationary trend given by the smooth curve S^sub 9^(t), we need to remove these fast details as well. This leaves the detail curve Y^sub 6,9^(t) = D^sub 6^(t) + D^sub 7^(t) + D^sub 8^(t) + D^sub 9^(t) that is obtained, according to Eq. (2), by detrending the smooth curve S^sub 5^(t) of the smooth curve S^sub 9^(t). We suggest that the Y^sub 6,9^(t) curve is the best indicator of the birth seasonal variation that can be linked to the conceptions. In particular, D^sub 6^(t) + D^sub 7^(t) details capture the sub-annual variability of the signal within the time interval from 64 to 256 days, D^sub 9^(t) curve captures most of the annual variability and D^sub 9^(t) curve captures small variation of the annual variability up to almost 3 years.

Finally, we average the daily values of the Y^sub 6,9^(t) curve for the 37 years, shift back the time by 7 × 38 = 266 days and plot the result in the black curve of Figure 8. In fact, 38 weeks is the estimated mean duration of pregnancy and the mean is the only significant statistical value. In other words, we do not expect to obtain better results by using the actual length of the gestational period for each birth because for general theorems of statistics for a sufficiently large sample of data, the general behavior will regress to the average value. Concerning the fact that teenagers have a mean period of gestation slightly shorter than the adult mean value, due to a higher rate of premature deliveries among teenagers, we observe that for a sociological interpretation, the time of coitus is more important than the time of conception, and coitus ending in a conception precedes the conception itself up to a few days. This temporal shift may partially compensate the temporal shift in the opposite direction due to premature deliveries. Because of the above arguments, we suggest that the seasonal patterns obtained with the wavelet detail Y^sub 6,9^(t) curve are reliable for a sociological interpretation of the phenomenon herein under study with a probability above 90 percent (Leridon, 1986) with a weekly resolution.

Figure 8 shows that the lowest daily number of conceptions for all teenagers occurs during the hottest months in Texas, these being July and August. This drop in the number of conceptions may be related to the fact that human fertility drops during the hot months (Lam and Miron, 1996), but we also note that schools are closed during much of this period. The number of conceptions increases steadily through September and October and reaches a peak during the middle of December when schools close. The number of daily conceptions again decreases starting in the middle of December and proceeds through January, but increases again in February and remains relatively high from late February to May. In June the conception curve abruptly decreases. Figure 8 shows that the phenomenon of conception varies in parallel with the seasonal changes in temperature and light, and also with the annual school calendar.

Figure 9 compares the relative conception count for all groups of teens during the years 1994-2000. We plot the results obtained by using the Y^sub 6,9^(t) curve according to the procedure explained above. Figure 9A compares the daily counts of conceptions for married and unmarried teens. Figure 9B compares the same analysis for the three racial/ethnic groups (White, Hispanic, and African American). Figures 9C and 9D compare the married and unmarried teens for each racial/ethnic group. The pictures evidence differences between married and unmarried teens.

Figure 9A shows that married teens seem to follow the seasonal temperature/ light cycle more regularly with a uniform decrease in the number of conceptions from January to July, a minimum during the summer and, finally, a uniform increase during the autumn that reaches a maximum at the end of December. The behavior of unmarried teens, instead, is more complex. A peak is observed before the middle of December contrary to the peak observed at the end of December for the married teen group. A steady decrease in the number of conceptions starting in the middle of December and proceeding through January is followed by a sudden increase in February. Figures 9A and 9D show that the level of conceptions to unmarried teens grows slightly and remains above the average until May and June, when the schools close for summer vacation and temperatures begin to rise rapidly in Texas. The number of conceptions suddenly drops during July and August and increases rapidly during September when the schools are opened again and temperatures begin to decrease. Finally, at the end of the first half of December there is a maximum, and then the number of conceptions again decreases when the schools close for Christmas holidays. This particular seasonal pattern characterized by two peaks, one at the middle of December and the other during the spring, compared to the less variable seasonal pattern for married teens that presents only one peak during the end of December, supports the idea that the unmarried group is more at risk of pregnancy while school is in session and/or during school-related events. Therefore, it seems likely that unmarried teenagers in Texas may meet more easily their sexual partners at school; we discuss this issue again later.

Among the three ethnic groups, the seasonal conception patterns for White and African American teens look most similar. The amplitude of the seasonal pattern curve is higher for the Hispanic group which corresponds to the higher number of births to Hispanic teens. The general trend of the conception curve differs, in particular, in the case of unmarried Hispanic teens. In fact, Figure 9D shows that while the three curves have a similar shape during the period from July to April, the Hispanic trend looks different from the other two during May and June. The second strong peak that occurs in May (unmarried African American group) and in June (unmarried White group) seems to cause only a slight deviation in the decreasing trend of the unmarried Hispanic group that is present in the second peak in March. During May and June the relative daily conception count for unmarried Hispanic teens looks similar to that for married Hispanic teen mothers, as if the school term has only a minor influence upon the unmarried Hispanic group. Further research is required to establish what this variation implies; perhaps, the percentage of teenagers that do not frequent the last years of high school or the first years of college (age 15 to 19 years old) is higher among the Hispanic group than the other two groups.

Finally, Figure 10 shows the wavelet smooth curves S^sub 9^(t) for all groups of teens and indicates how the birth supraannual trends have changed during the years 1994-2000. This figure is complementary to Figure 5 that records the birth rate of the three groups. The curves in Figure 10 show anomalous behavior that the linear fitting of Eq. (1) to the data is not able to detect. We observe that the number of daily births to African American married teens is almost constant during these seven years. African American unmarried teens and White married teens show an almost monotonically decreasing number of daily births, whereas Hispanic unmarried teens are characterized by an almost monotonically increasing number of daily births. Finally, daily births to both White unmarried and Hispanic married teens show an anomalous non-monotonic behavior with a change of tendency that took place in 1998.

DISCUSSION AND CONCLUSION

In this work we have presented a statistical analysis of birth to teenagers in Texas. We have adopted several analysis techniques: least-square fits, spectral analysis, and wavelet filters. Because one of the purposes of the paper is to show the advantages of the wavelet methodology, we have discussed some of its more basic properties. We have also discussed some of those analysis problems that are well suited for wavelet analysis, such as those associated with non-stationary time series, pseudo-cycles, and the sudden sharp drops in birth data. Even if the MODWT algorithms are mathematically complicated, we believe that the MWA computer algorithm is relatively easy to interpret. The basic idea of the method is to decompose a time series into a sequence of hierarchical detail and smooth curves, capable of capturing local data patterns associated with the corresponding time scale; see Eq. (2) and Figure 6. This decomposition allows us to separately study those curves that correspond to the time scale of interest. MWA via MODWT is preferred to the other techniques because it mathematically optimizes the procedure of isolating the variations in the time series within a preselected time interval.

The United States has one of the highest teen pregnancy rates in the world (Darroch, Singh, and Frost, 2001; Singh and Darroch, 2000), and Texas has one of the highest teen pregnancy rates in the U.S. Of the almost 80,000 teen pregnancies each year in Texas, 65 percent result in live births, 20 percent result in abortions, and 15 percent result in miscarriages. Since 1964 the annual number of births has increased from almost 120 to almost 150 mean daily births. However, the birth rate decreased from 1994-2000, in particular for Whites and African Americans, but has remained almost unchanged or only slightly decreased for Hispanics. Moreover, as Table 2 and Figure 5 show, the birth rate to teen girls aged 15 to 19, for both Hispanics and African Americans is particularly high and more than double the rate for White teens.

We determined that the weekly cycle increased over the decade beginning in 1990 by simply observing the wavelet detail D^sub 2^(t), see Figure 6. It is reasonable to expect that this pattern was caused by an increased tendency of health care providers to schedule more deliveries on weekdays when maximum services are available and to avoid weekends and holidays. This disparity between weekday and weekend births is important because it may be linked to risks for neonatal deaths that increase when teen mothers deliver on an emergency basis, or when staffing levels decrease, as during weekends and on holidays. Contrary to the White group, African Americans and unmarried teens should be at higher risk for negative birth outcomes as indicated by their higher likelihood of weekend deliveries, see Table 3. Poverty is probably a contributing factor to the African Americans being more weakly connected to the Texas medical system than is the White group. However, we cannot exclude important culturally-related causes for this weakness. In fact, the birth outcomes appear to be less dangerous for Hispanics whose socioeconomic characteristics are similar to African Americans. Possibly, Hispanics are buffered in some way against external risks of pregnancy by strong family, cultural, and religious ties (Sciarra and Ponterotto, 1998), which are known to be the strongest among the three racial/ethnic groups. These ties may result in more effective economic assistance and cooperation, as well as in protective behaviors toward women and children and, therefore, may help to prevent risks associated with pregnancy and birth outcomes despite poor sociocconomic conditions. The strong cultural difference between African Americans and Hispanics is also evident in the ratio of married to unmarried teen mothers, which for Hispanics, is seven times higher than the very low ratio for African American teen mothers.

September has the highest number of births with a peak observed during the first half of the month while April and May have the lowest number of births to teens. Therefore, December has the highest number of conceptions and July and August have the fewest conceptions. This is common to all groups and is likely to be due to the natural annual seasonal variation of human fertility, in particular to the sperm quality that lowers fertility during hot months (Lam and Miron, 1996; Levine et al., 1988; Rojansky et al., 1992; Saint Pol et al., 1989). However, the seasonal pattern of conception presents clear differences according to the marital status of the teens. The married teen group presents a regular annual cyclical pattern that closely follows the natural temperature/light annual cycle with only one peak at the end of December. The unmarried teen group presents a more complex pattern characterized by two peaks, one in the middle of December and the second during the late spring in contrast with the natural temperature/ light annual cycle. In addition there are two valleys, one in January-February and the second one in July-August. This particular shape suggests that unmarried teens are particularly at risk of pregnancy during the school term.

We notice that both peaks of conception for the unmarried teens correspond with the end of the fall and spring school semesters. In particular, the spring peak has been associated with the traditional end of the school year, when, in the United States, adolescents are involved in formal and informal celebrations including a formal dance referred to as “Prom (promenade) Night” (Petersen and Alexander, 1992). We also notice that the spring peaks shown in Figure 9D look less prominent than those found by Petersen and Alexander (1992). There may appear to be a slight inconsistency with the previous work by Petersen and Alexander (1992), but we do not think this is the case. The reason is that herein we study pregnancy to all teenagers (15 to 19 years old) together, while Petersen and Alexander (1992) separate teens younger than 18 years old that are strongly linked to high school and present a strong June peak, from the older teens that do not present such a June peak. Presumably, Petersen and Alexander, too, would have found a damped peak if they had considered the conceptions to all teenagers (aged 15 to 19) as we have done here.

We require a deeper interpretation to explain the apparent inconsistency with the comments made by Rodgers and Parnell (1999) and by Leridon (1986) who claimed that the winter peak occurs during the Christmas holidays and on New Year’s Day, respectively. In fact, we found the same result for married teens, but not for unmarried teens, which seem to have a peak of conceptions at least two weeks prior, in correspondence to the end of the fall school semester. To explain this slight inconsistency, we notice that Rodgers and Parnell (1999) used monthly intervals that do not allow the investigation of conception patterns within the shorter time interval of weeks, as we could do by using daily birth data. Consequently, the conclusions of Rodgers and Parnell (1999) are not sufficiently supported by the temporal resolution of their data, because on a monthly interval, the conceptions occurring at the beginning of the month are counted together with those occurring at the end of the month. Analogously, the New Year’s Day conception peak found by Leridon (1986) is comparable to our findings about married teens but is not comparable to our findings regarding unmarried teens. In fact, Leridon (1986) analyzed births to all women and not just to unmarried teens. The majority of women giving birth are adult and married and for this group the peak is at the end of December. Also, we observe that Leridon (1986) found a conception peak on New Year’s Day (perhaps because young adults, in particular, are involved in the New Year’s Day celebration that may precipitate sexual activity) because he found the peak of births occurring on the 24th of September, while for the Texas unmarried teen groups, we found a peak of birth during the first half of September that would link to conceptions in the first half of December.

Further remarks are also needed to explain the apparent contradiction that the seasonality of conceptions is at minimum during July and August, months in which other studies have determined that the coital activity seems to have a maximum. For example, Udry and Morris (1968) studied the seasonality of coitus restricted to the sexual behavior of 50 married, White, premenopausal, husband-present, and well-educated women and arrived at the conclusion that sexual interactions are slightly more frequent during summer. In a more recent work, Rodgers et al. (1992) found a peak in first intercourse among United States adolescents during June and July, coinciding with summer school vacation. These earlier findings supported the so-called “Summer Vacation Theory” according to which biological factors, such as the increase of libido in hot months, social mechanisms, such as more frequent parties and dating, and even media attention, can operate together to increase sexual activity in the summer, especially among adolescents.

To explain the apparent inconsistency between coital seasonality and conception seasonality we recall that hot weather reduces human fertility particularly because sperm quality decreases (Lam and Miron, 1996; Rojansky et al., 1992; Saint Pol et al., 1988). Therefore, the supposed increase of sexual activity during summer would not, in and of itself, necessarily lead to an increase in conceptions. We also observe that coital seasonality data may not be very reliable because the data about occurrences of coitus are based on a small number of interviews (Upchurch et al., 2002).

However, the fact that conceptions are more frequent for unmarried teens during the school term may also suggest an interpretation complementary to the “Summer Vacation Theory.” Perhaps there is a psychological and sociological mechanism that is not considered in such a theory. Vacation times have a short duration compared to school times and adolescents often follow parents to vacation localities that may be very far from their residence. The short duration of summer vacation and travel to new environments may not favor enduring sentimental relationships. Instead, the long duration of the school term and the stability of place might allow for more fraternization among adolescents, for example, at school itself. This situation may favor relations that can more easily precipitate more regular and, therefore, more risky sexual activity. If this assumption is true, the fact that conception rates drop markedly in the summer and drop again starting in the middle of December, when unmarried teenagers are on school holidays, and soar abruptly when school starts again in the autumn and again after January until through May and June, may reasonably suggest that unmarried adolescents in Texas not only are at higher risk of pregnancy when school is in session but also may more easily meet their sexual partners at school itself, or during school-related events.

In conclusion, we think that there are useful implications that can be drawn from our data analysis that can be more effectively addressed by policy makers and health care providers. In particular, the differences among the teen groups herein analyzed suggest that specific culturally-oriented programs may help to better link pregnant teenagers, in particular African American teens and unmarried teens, within the Texas medical system. secondly, programs directed toward sex education and pregnancy prevention should take into account the seasonal patterns of conception and, for example, could be intensified during the period of highest conception risk. Moreover, not all unmarried teenagers go to school and this seems particularly true among Hispanics. Therefore, sex education and pregnancy prevention programs should be advocated and advertised outside of school as well. In any case, the U.S. teenage pregnancy rate (rate R = 97.6 pregnancies per 1,000 adolescents in 1996; Texas, R = 113) is very high compared to that of other industrialized countries (England and Wales, R = 46.9; France, R = 20.2; Germany, R = 16.1; Spain, R = 12.3; Italy, R = 12; Japan, R = 10.1; Darroch et al., 2001; Singh and Darroch, 2000). Despite a recent decline in teen birth rates, teen pregnancy and, in particular, out-ofwedlock teen pregnancy, remain significant problems in the U.S. and impact nearly every community. Thus, the responsibility to solve these problems lies with all members of society, including families, communities, media, and young people themselves (U.S. Department of Health and Human Services, 2000).

ACKNOWLEDGMENTS

This work was supported in part by a grant from the National Institute for Child Health and Human Development (NICHD); N. S. gratefully acknowledges the support from Army Research Office. The authors thank Dr. Patty Hamilton for useful suggestions.

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N. Scafetta(a), E. Restrepo(b,c), and B. J. West(a,d)

a Department of Physics, Duke University, Durham, NC 27708; b Texas Health Resources, 611 Ryan Plaza Drive, Suite 1400, Arlington, Texas 76011; c College of Nursing, Texas Woman’s University, Denton, TX 76204-5498; d Mathematics Division, Army Research Office, Research Triangle Park, NC 27709

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