<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">AM</journal-id>
      <journal-title-group>
        <journal-title>Applied Mathematics</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2152-7385</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/am.2021.127038</article-id>
      <article-id pub-id-type="publisher-id">AM-110356</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Articles</subject>
        </subj-group>
        <subj-group subj-group-type="Discipline-v2">
          <subject>Physics&amp;Mathematics</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>


          Times Series Applied to Study Vitamin D Seasonality in Argentina

        </article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>José</surname>
            <given-names>Bavio</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
          <xref ref-type="corresp" rid="cor1">
            <sup>*</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>Carina</surname>
            <given-names>Fernández</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>Patricia</surname>
            <given-names>Fernández</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">
            <sup>2</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>Beatriz</surname>
            <given-names>Marrón</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">
            <sup>1</sup>
          </xref>
        </contrib>
      </contrib-group>
      <aff id="aff1">
        <addr-line>Depto. de Matemática Universidad Nacional del Sur, Bahía Blanca, Buenos Aires, Argentina</addr-line>
      </aff>
      <aff id="aff2">
        <addr-line>IACA Laboratiorios, Bahía Blanca, Buenos Aires, Argentina</addr-line>
      </aff>
      <pub-date pub-type="epub">
        <day>05</day>
        <month>07</month>
        <year>2021</year>
      </pub-date>
      <volume>12</volume>
      <issue>07</issue>
      <fpage>546</fpage>
      <lpage>555</lpage>
      <history>
        <date date-type="received">
          <day>23,</day>
          <month>April</month>
          <year>2021</year>
        </date>
        <date date-type="rev-recd">
          <day>3,</day>
          <month>July</month>
          <year>2021</year>
        </date>
        <date date-type="accepted">
          <day>6,</day>
          <month>July</month>
          <year>2021</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement>
        <copyright-year>2014</copyright-year>
        <license>
          <license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p>
        </license>
      </permissions>
      <abstract>
        <p>


          In this study, we analyze how vitamin D (VD) serum levels flow with latitude and throughout seasons of the year within a population sample over three years, taking into account that VD is mainly photosynthesized in the skin from sun exposure. Vitamin D levels have been measured in 80,763 patients during 2013, 2014, and 2015. To accomplish the objectives, we first perform some inference tests like two-way Analysis of Variance (ANOVA) followed by post-hoc tests. Secondly, we develop time series techniques including cross correlation calculations. Least than 10% of the sample had healthy VD levels, which should be a fact of public health major concern. The effect of the interaction between the two factors, zones and seasons, was proved by ANOVA. The mean values which are significantly different were determined by post hoc test. Furthermore, we find that mean serum VD levels, measured as 25-hydroxy-VD, follow a seasonal lag pattern of 9 weeks, a delay for minimum and maximum values after the respective equinoxes and daily sunlight duration. Reliable estimates of the population are provided in the present study, since one of the strengths is its huge sample size. We have quantitatively characterized the seasonality of serum vitamin D levels in the Argentine and the seasonal lag pattern has been determined for the study region.

        </p>
      </abstract>
      <kwd-group>
        <kwd>Vitamin D Status</kwd>
        <kwd> Population Study</kwd>
        <kwd> Time Series Correlation</kwd>
        <kwd> Interaction Effects</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="s1">
      <title>1. Introduction</title><p>
        It has been known for decades that VD is involved in calcium homeostasis and metabolism, from its absorption in the intestine to bone remodeling. Nevertheless, osteopenia, osteoporosis [<xref ref-type="bibr" rid="scirp.110356-ref1">1</xref>] and sarcopenia [<xref ref-type="bibr" rid="scirp.110356-ref2">2</xref>] continue to grow as health disorders. No significant amounts of VD are found in food, and its main source is sun exposure on the skin. Although some foods are supplemented in Argentina, there have been no updates for years or in the area of international recommendations [<xref ref-type="bibr" rid="scirp.110356-ref3">3</xref>].
      </p><p>
        In recent years, many VD non-classic functions have been discovered [<xref ref-type="bibr" rid="scirp.110356-ref4">4</xref>]. It is known now that chronic VD deficiency increases the risk of infectious and autoimmune diseases, cancer, high blood pressure, hormonal, cardiovascular, skeletal, muscular, metabolic, and affective disorders, as well as autism [<xref ref-type="bibr" rid="scirp.110356-ref5">5</xref>], among others.
      </p><p>
        VD is photosynthesized in skin by sun exposure and is therefore fluctuating, as it depends on the individual, environmental and sociocultural factors, such as season of the year, latitude, cloudiness, smog, skin pigmentation, age, lifestyle: body mass index, clothing, indoors time, use of sunscreen, etc. [<xref ref-type="bibr" rid="scirp.110356-ref6">6</xref>].
      </p><p>Although there is great interest in studying the influence of VD on health, there is little information based on seasonality of VD serum levels. The cyclical nature of serum VD levels flows with B ultraviolet (UVB) sunlight exposure. However, there is little research on large samples that address detailed empirical data on when the population reaches the maximum and minimum serum 25-OH vitamin D levels throughout the year.</p><p>The above mentioned variables determine that the data of a nation cannot be applied to others so that motivated us to carry out this study specifically within our country. This research has been developed in years in which there was practically no medical VD supplementation.</p><p>We aimed to assess baseline serum levels of 25-OH vitamin D in the population sample, relate it to its location, evaluate differences and similarities between areas and seasons in order to provide estimates of optimal values of the delay between solar light hours available and the moment when maximum VD level is reached.</p>Vitamin D Levels<p>
        25-hydroxy-vitamin D is a biomarker that better reflects a person’s VD status, measured in ng/mL [<xref ref-type="bibr" rid="scirp.110356-ref7">7</xref>].
      </p><p>
        According to the Endocrine Society recommendations [<xref ref-type="bibr" rid="scirp.110356-ref3">3</xref>], VD serum levels are stratified as follows:
      </p><p>&#183; deficiency, below 20 ng/mL,</p><p>&#183; insufficiency, between 20 and 30 ng/mL,</p><p>&#183; optimal, above 30 ng/mL.</p>
    </sec>
    <sec id="s2">
      <title>2. Subjects and Methods</title>
      <p>Vitamin D levels have been measured in 80,763 patients during 2013, 2014, and 2015, as total 25-OH Vitamin (D2 + D3) by chemiluminescence, Liaison, Diasorin. It is worth mentioning that during these years people were hardly supplemented with VD in Argentina.</p>
      <p>
        According to quality control standards, this analyte has allowable limits of performance (ALP) of plus or minus (&#177;) 15%, as stated by the Royal College of Pathologists of Australasia (RCPA), Allowable Limits of Performance for Biochemistry [<xref ref-type="bibr" rid="scirp.110356-ref8">8</xref>]. Therefore we took an optimal serum vitamin D level of 40 ng/mL or more so that we are sure it is always preferably above 30 ng/mL, as recommended by the Endocrine Society.
      </p>
      <p>Additional information collected: date, age, gender, residence location, and clinical history. The homogeneity of the sample was monitored and divided into groups of interest.</p>
      <sec id="s2_1">
        <title>2.1. Definitions of the Variables</title>
        <p>The variables and their categorization are presented below:</p>
        <p>1) Gender: Male (M) and Female (F);</p>
        <p>2) Season: Winter (I), Autumn (O), Spring (P) and Summer (V);</p>
        <p>3) Age: the age of each individual has been categorized into the following groups, up to 13 years, from 13 to 20 years, from 20 to 40 years, from 40 to 60 years and older than 60 years;</p>
        <p>
          4) Location: this variable has been categorized into four zones according with the corresponding south latitude value: Z<sub>1</sub> = more than 45˚ south latitude, Z<sub>2</sub> = between 45˚ and 40˚ south latitude, Z<sub>3</sub> = between 40˚ and 35˚ south latitude and Z<sub>4</sub> = Less than 35˚ south latitude. The geographical distribution of the zones can be seen in <xref ref-type="fig" rid="fig1">Figure 1</xref>.
        </p>
      </sec>
      <sec id="s2_2">
        <title>2.2. Statistics and Data Analysis</title>
        <p>
          Statistical analysis was performed using InfoStat [<xref ref-type="bibr" rid="scirp.110356-ref9">9</xref>]. Chi square test was used to compare the proportion of people with healthy level of Vitamin D, this is serum 25-(OH) D concentration of at least 40 ng/mL, separately in each variable. The result showed that there was no significant difference in this proportion between the different age groups; however there was a significant difference between genders, zones and seasons, p &lt; 0.001 (<xref ref-type="table" rid="table1">Table 1</xref>).
        </p>
        <p>A study was carried out to test the effect of the zone, the season and the interaction between these two factors using two-way ANOVA.</p>
        <p>
          The two-way ANOVA was highly significant (p &lt; 0.0001), that is, there is sufficient evidence to affirm that the mean value of VD is not the same in each combination of both factors. Furthermore, the interaction is highly significant (p &lt; 0.0001), which means that the effect of the stations on the mean VD level is not the same for each zone, this can be seen in the graphs that are presented in <xref ref-type="fig" rid="fig2">Figure 2</xref> where some of the curves are not parallel and even more there are crosses between some profiles.
        </p>
        <p>
          Bonferroni post hoc tests were used to test which mean values are significantly different and which are not. The results are shown in <xref ref-type="table" rid="table2">Table 2</xref>, same letter means no differences were found (p &gt; 0.05).
        </p>
        <table-wrap id="table1" >
          <label>
            <xref ref-type="table" rid="table1">Table 1</xref>
          </label>
          <caption>
            <title> Number of individuals with healthy level of Vitamin D and their corresponding proportions</title>
          </caption>
          <table>
            <tbody>
              <thead>
                <tr>
                  <th align="center" valign="middle" ></th>
                  <th align="center" valign="middle" >n</th>
                  <th align="center" valign="middle" >%</th>
                  <th align="center" valign="middle" >p</th>
                </tr>
              </thead>
              <tr>
                <td align="center" valign="middle" >Gender</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Male (M)</td>
                <td align="center" valign="middle" >366</td>
                <td align="center" valign="middle" >3.38</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Female (F)</td>
                <td align="center" valign="middle" >2939</td>
                <td align="center" valign="middle" >4.20</td>
                <td align="center" valign="middle" >&lt;0.0001</td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Age</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >(0; 13)</td>
                <td align="center" valign="middle" >1310</td>
                <td align="center" valign="middle" >5.32</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >(13; 20)</td>
                <td align="center" valign="middle" >50</td>
                <td align="center" valign="middle" >8.14</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >(20; 40)</td>
                <td align="center" valign="middle" >334</td>
                <td align="center" valign="middle" >5.01</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >(40; 60)</td>
                <td align="center" valign="middle" >805</td>
                <td align="center" valign="middle" >5.75</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >&gt;60</td>
                <td align="center" valign="middle" >606</td>
                <td align="center" valign="middle" >4.77</td>
                <td align="center" valign="middle" >0.3278</td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Season</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Winter (I)</td>
                <td align="center" valign="middle" >472</td>
                <td align="center" valign="middle" >2.14</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Autumn (O)</td>
                <td align="center" valign="middle" >833</td>
                <td align="center" valign="middle" >4.17</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Spring (P)</td>
                <td align="center" valign="middle" >660</td>
                <td align="center" valign="middle" >2.79</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Summer (V)</td>
                <td align="center" valign="middle" >1340</td>
                <td align="center" valign="middle" >8.85</td>
                <td align="center" valign="middle" >&lt;0.0001</td>
              </tr>
              <tr>
                <td align="center" valign="middle" >Zone</td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Z<sub>1</sub>
                </td>
                <td align="center" valign="middle" >341</td>
                <td align="center" valign="middle" >2.18</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Z<sub>2</sub>
                </td>
                <td align="center" valign="middle" >733</td>
                <td align="center" valign="middle" >4.19</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Z<sub>3</sub>
                </td>
                <td align="center" valign="middle" >1766</td>
                <td align="center" valign="middle" >4.78</td>
                <td align="center" valign="middle" ></td>
              </tr>
              <tr>
                <td align="center" valign="middle" >
                  Z<sub>4</sub>
                </td>
                <td align="center" valign="middle" >465</td>
                <td align="center" valign="middle" >4.30</td>
                <td align="center" valign="middle" >&lt;0.0001</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        
           </sec>
            </sec>
      </body>
        <back>
          <ref-list>
            <title>References</title>
            <ref id="scirp.110356-ref1">
              <label>1</label>
              <mixed-citation publication-type="other" xlink:type="simple">Joo, N.-S., Dawson-Hughes, B., Kim, Y., Oh, K. and Yeum, K. (2013) Impact of Calcium and Vitamin D Insufficiencies on Serum Parathyroid Hormone and Bone Mineral Density: Analysis of the Fourth and Fifth Korea National Health and Nutrition Examination Survey (KNHANES IV-3, 2009 and KNHANES V-1, 2010). Journal of Bone and Mineral Research: The Official Journal of the American Society for Bone and Mineral Research, 28, 764-770. https://doi.org/10.1002/jbmr.1790</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref2">
              <label>2</label>
              <mixed-citation publication-type="other" xlink:type="simple">NHANES Survey (2013) Centers for Disease Control and Prevention US Government. http://www.cdc.gov/nchs/nhanes/nh3data.html</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref3">
              <label>3</label>
              <mixed-citation publication-type="other" xlink:type="simple">Holick, M., et al. (2011) Evaluation, Treatment, and Prevention of Vitamin D Deficiency: An Endocrine Society Clinical Practice Guideline. Journal of Clinical Endocrinology &amp; Metabolism, 96, 1911-1930. https://doi.org/10.1210/jc.2011-0385</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref4">
              <label>4</label>
              <mixed-citation publication-type="other" xlink:type="simple">Hollis, B.W., Wagner, C.L., Howard, C.R., Ebeling, M., Shary, J.R., Smith, P.G., Taylor, S.N., Morella, K., Lawrence, R.A. and Hulsey, T.C. (2015) Maternal versus Infant Vitamin D Supplementation during Lactation: A Randomized Controlled Trial. Pediatrics, 136, 625-634. https://doi.org/10.1542/peds.2015-1669</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref5">
              <label>5</label>
              <mixed-citation publication-type="other" xlink:type="simple">Patrick, R.P. and Ames, B.N. (2014) Vitamin D Hormone Regulates Serotonin Synthesis. Part 1: Relevance for Autism. FASEB Journal: Official Publication of the Federation of American Societies for Experimental Biology, 28, 2398-2413. https://doi.org/10.1096/fj.13-246546</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref6">
              <label>6</label>
              <mixed-citation publication-type="other" xlink:type="simple">Wacker, M. and Holick, M.F. (2013) Sunlight and Vitamin D. A Global Perspective for Health. Dermato Endocrinology, 5, 51-108. https://doi.org/10.4161/derm.24494</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref7">
              <label>7</label>
              <mixed-citation publication-type="other" xlink:type="simple">Oler&amp;#246;d, G., Hultén, L.M., Hammarsten, O. and Klingberg, E. (2017) The Variation in Free 25-Hydroxy Vitamin D and Vitamin D-Binding Protein with Season and Vitamin D Status. Endocrine Connections, 6, 111-120. https://doi.org/10.1530/EC-16-0078</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref8">
              <label>8</label>
              <mixed-citation publication-type="other" xlink:type="simple">Australasia, R.C. (2014) Allowable Limits of Performance (alp). http://www.rcpaqap.com.au/docs/2014/chempath/ALP.pdf</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref9">
              <label>9</label>
              <mixed-citation publication-type="other" xlink:type="simple">Di Rienzo, J., Casanoves, F., Balzarini, M., Gonzalez, L., Tablada, M. and Robledo, C. (2016) Grupo Infostat. http://www.infostat.com.ar</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref10">
              <label>10</label>
              <mixed-citation publication-type="other" xlink:type="simple">Hodrick, R. and Prescott, E. (1997) Postwar U.S. Business Cycles: An Empirical Investigation. Journal of Money, Credit, and Banking, 29, 1-16. https://doi.org/10.2307/2953682</mixed-citation>
            </ref>
            <ref id="scirp.110356-ref11">
              <label>11</label>
              <mixed-citation publication-type="other" xlink:type="simple">Forsythe, W., Rykiel, E., Stahl, R., Wu, H. and Schoolfield, R. (1995) A Model Comparison for Daylength as a Function of Latitude and Day of Year. Ecological Modelling, 80, 87-95. https://doi.org/10.1016/0304-3800(94)00034-F</mixed-citation>
            </ref>
          </ref-list>
        </back>
</article>