# Age- and Sex-Adjusted Reference Intervals in Tear Cytokine Levels in Healthy Subjects
## 3 Results
\begin{tabular}{c c c c c c c c} \hline \hline
**Age Range** & **EGF** & **Fractalkine** & **IL-1 RA** & **IL-7** & **IL-8** & **IP-10** & **MCP-1** & **VEGF** \\ \cline{2-8}
**(n)** & **(pg/mL)** & **(pg/mL)** & **(pg/mL)** & **(pg/mL)** & **(pg/mL)** & **(pg/mL)** & **(pg/mL)** \\ \hline
**18–31 years** & \(866.9\) & \(352.8\) & \(1752.18\) & \  
as not having DED. Fractalkine and VEGF tear levels were also increased in the DED sample; in these cases, the percentages of values over the upper RIs were 72.7% and 75% versus 5.6% and 6.3% of the validation sample, respectively. On the other hand, EGF and IP-10 showed lower concentrations in the utility sample, finding that 23.1% and 38.5% of the DED patients had levels below the corresponding lower RI. These percentages are significantly higher than those found in the validation sample (0% and 2.9%, respectively). Interestingly, all the patients of severe DED sample had tear cytokine concentrations that fell outside the RIs in at least two of the cytokines evaluated (see Table 12 in Appendix C).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Normal**} & \multicolumn{2}{c}{**Box-Cox Cole and Green**} & \multicolumn{2}{c}{**Power Exponential**} & \multicolumn{2}{c}{**Box-Cox Power**} \\ \cline{2-9}  & \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Application**} & \multicolumn{1}{c}{**AIC**} & \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Specification**} & \multicolumn{1}{c}{**AIC**} & \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Specification**} & \multicolumn{1}{c}{**AIC**} \\ \hline
**EGF** & \(\mu\) - age \(\sigma\sim 1\) & 628.43 & \(\mu\) - age \(\sigma\sim 1\) & 629.3 & \(\sigma\sim 1\) & 629.9 & \(\sigma\sim 1\) & **627.38** \\  & \(\sigma\sim 1\) & & \(\
u\sim\) age & & \(\
u\sim 1\) & & \(\tau\sim 1\) & \\ \hline
**Fractalkine** & \(\mu\) - sex \(\sigma\sim 1\) & **576.18** & \(\mu\) - 1 \(\sigma\sim 1\) & 579.37 & \(\mu\) - sex \(\sigma\sim 1\) & 577.73 & \(\sigma\sim 1\) & 580.88 \\  & \(\sigma\sim 1\) & & \(\
u\sim 1\) & & \(\
u\sim 1\) & & \(\tau\sim 1\) & \\ \hline
**IL-IRA** & \(\mu\) - cs(age) \(\sigma\sim 1\) & 690 & \(\mu\) - cs(age) \(\sigma\sim 1\) & 687.66 & \(\mu\) - cs(age) \(\sigma\sim 1\) & 687.71 & \(\sigma\sim 1\) & **687.59** \\  & \(\sigma\sim 1\) & & \(\
u\sim 1\) & & \(\
u\sim\) cs(age) & & \(\tau\sim 1\) & \\ \hline
**IL-7** & \(\mu\) - cs(age) + \(\sigma\sim 1\) & **442.84** & \(\mu\) - age + sex \(\sigma\sim 1\) & 445.65 & \(\mu\) - cs(age) + sex \(\sigma\sim 1\) & 444.98 & \(\sigma\sim 1\) & 442.20 \\  & \(\sigma\sim 1\) & & \(\
u\sim 1\) & & \(\
u\sim 1\) & & \(\tau\sim \text{age}+\text{sex}\) & \\ \hline
**IL-8** & \(\mu\) - cs(age) + \(\text{sex}\) & 541.76 & \(\mu\) - cs(age) + \(\text{sex}\) & 538.11 & \(\mu\) - cs(age) + \(\text{sex}\) & \(\mu\) - cs(age) + \(\text{sex}\) & \(\mu\) - cs(age) + \(\text{sex}\) & \\  & \(\sigma\sim\text{cs(age)}\) & & \(\sigma\sim 1\) & & \(\sigma\sim 1\) & 533.83 & \(\sigma\sim 1\) & 533.83 \\  & \(\sigma\sim\text{cs(age)}\) & & \(\
u\sim\text{cs(age)}\) & & \(\
u\sim 1\) & & \(\
u\sim 1\) & \\ \hline
**IP-10** & \(\mu\) - age + sex \(\sigma\sim\text{age}+\text{sex}\) & 567.61 & \(\mu\) - \(\text{sex}\) \(\sigma\sim 1\) & 562.86 & \(\mu\) - age + sex \(\sigma\sim\text{age}+\text{sex}\) & \(\mu\) - sex \(\sigma\sim 1\) & 556.26 \\  & \(\sigma\sim\text{age}+\text{sex}\) & & \(\
u\sim\text{cs(age)}\) & & \(\
u\sim 1\) & & \(\tau\sim 1\) & \\ \hline
**MCP-1** & \(\mu\) - age \(\sigma\sim 1\) & **672.06** & \(\mu\) - age \(\sigma\sim 1\) & 674.46 & \(\mu\) - age \(\sigma\sim 1\) & & \(\mu\) - age \(\sigma\sim 1\) & \\  & \(\sigma\sim 1\) & & \(\
u\sim\text{cs(age)}\) & & \(\sigma\sim 1\) & 672.32 & \(\
u\) - cs(age) + \(\text{sex}\) & 673.6 \\  & & & \(\
u\sim\text{cs(age)}\) & & \(\
u\sim\text{cs(age)}\) & & \(\tau\sim\text{cs(age)}+\text{sex}\) & \\ \hline
**VEGF** & \(\mu\) - cs(age) \(\sigma\sim 1\) & 524.07 & \(\mu\) - \(\text{cs(age)}\) & & \(\mu\) - cs(age) \(\sigma\sim 1\) & & \(\mu\) - cs(age) \(\sigma\sim 1\) & \\  & \(\sigma\sim 1\) & & \(\
u\sim 1\) & & \(\
u\sim\text{age}\) & & \(\tau\sim 1\) & \\ \hline \multicolumn{9}{c}{Four different distribution families: Normal, Box-Cox Cole and Green, Power Exponential and Box-Cox power exponential were tested. Potential explicative variables are sex and age. The age influence on each distributional parameter (location: \(\mu\); scale: \(\sigma\); skewness: \(\
u\); kurtosis: \(\tau\)) can be modelled as a constant (-1), as a linear function (-age) or as a cubic spline (-cs(age)). Sex can be added as qualitative variable (-es). The best model for a particular molecule, in bold, is the one that minimizes the Akaike Information Criterion (AIC). EGF = Epidermal Growth Factor; IL = Interleukin; RA = Receptor Antagonist; IP = Induced Protein; MCP = Monocyte Chemotactic Protein; VEGF = Vascular Endothelial Growth Factor.} \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons of fitted GAMLSS models.  
\begin{table}
\begin{tabular}{c} **High** \\ **\% (CI95\%)** \\ \end{tabular} \\ \hline
**EGF** & 40 & \begin{tabular}{c} 0\% \\ (0\%,10.9\%) \\ \end{tabular} & \begin{tabular}{c} 100\% \\ (89.1\%,100\%) \\ \end{tabular} & \begin{tabular}{c} 0\% \\ (0\% 10.9\%) \\ \end{tabular} & \begin{tabular}{c} 13 \\ (0\% 10.9\%) \\ \end{tabular} & \begin{tabular}{c} 23.1\% \\ (6.2\%,54\%) \\ \end{tabular} & \
\begin{tabular}{c} 76.9\% \\ (46\%,93.8\%) \\ \end{tabular} &
\begin{tabular}{c} 0\% \\ (0\% 28.3\%) \\ \end{tabular} \\ \hline
**Fractalkine** & 36 & \begin{tabular}{c} 0\% \\ (0\%,12\%) \\ \end{tabular} & \begin{tabular}{c} 94.4\% \\ (0\%,9\%) \\ \end{tabular} & \begin{tabular}{c} 5.6\% \\ (1\%,20\%) \\ \end{tabular} & \begin{tabular}{c} 11 \\ (1\%,20\%) \\ \end{tabular} & \begin{tabular}{c} 0\% \\ (0\%,32.1\%) \\ \end{tabular} & \
\begin{tabular}{c} 27.3\% \\ (7.3\%,60.7\%) \\ \end{tabular} &
\begin{tabular}{c} 0\% \\ (99.3\%) \\ \end{tabular} \\ \hline
**IL-IRA** & 39 & \begin{tabular}{c} 0\% \\ (0\%,11.2\%) \\ \end{tabular} & \begin{tabular}{c} 92.3\% \\ (78\%,98\%) \\ \end{tabular} & \begin{tabular}{c} 7.7\% \\ (2\%,22\%) \\ \end{tabular} & \begin{tabular}{c} 13 \\ (2\%,28.3\%) \\ \end{tabular} & \begin{tabular}{c} 0\% \\ (0\%,32.8\%) \\ \end{tabular} & \
\begin{tabular}{c} 7.7\% \\ (0.4\%,37.9\%) \\ \end{tabular} &
\begin{tabular}{c} 92.3\% \\ (62.1\%,59.6\%) \\ \end{tabular} \\ \hline
**IL-8** & 40 & \begin{tabular}{c} 0\% \\ (0\%,10.9\%) \\ \end{tabular} & \begin{tabular}{c} 95\% \\ (81.8\%,9\%) \\ \end{tabular} & \begin{tabular}{c} 5\% \\ (0.9\%,18.2\%) \\ \end{tabular} & \begin{tabular}{c} 13 \\ (0\%,9\%) \\ \end{tabular} & \
\begin{tabular}{c} 0\% \\ (0.4\%,37.9\%) \\ \end{tabular} &
\begin{tabular}{c} 7.7\% \\ (62.1\%,59.6\%) \\ \end{tabular} \\ \hline
**IP-10** & 35 & \begin{tabular}{c} 2.9\% \\ (0.2\%,16.6\%) \\ \end{tabular} & \begin{tabular}{c} 97.1\% \\ (83.4\%,9\%) \\ \end{tabular} & \begin{tabular}{c} 0\% \\ (0\% 12.3\%) \\ \end{tabular} & \begin{tabular}{c} 13 \\ (0\%,15\%) \\ \end{tabular} & \
\begin{tabular}{c} 61.5\% \\ (67.7\%) \\ \end{tabular} &
\begin{tabular}{c} 0\% \\ (0\%,32.3\%) \\ \end{tabular} \\ \hline
**MCP-1 \({}^{*}\)** & 8 & \begin{tabular}{c} 0\% \\ (0\%,40.2\%) \\ \end{tabular} & \begin{tabular}{c} 100\% \\ (59.8\%,100\%) \\ \end{tabular} & \begin{tabular}{c} 0\% \\ (0\%,40.2\%) \\ \end{tabular} & \begin{tabular}{c} 1 \\ (0\%,30.1\%) \\ \end{tabular} & \begin{tabular}{c} 100\% \\ (0\%,32.2\%) \\ \end{tabular} & \begin{tabular}{c} 0\% \\ (0\%,30.1\%) \\ \end{tabular} & \
\begin{tabular}{c} 0\% \\ (6.7\%,57.2\%) \\ \end{tabular} &
\begin{tabular}{c} 0\% \\ (42.8\%,9\%) \\ \end{tabular} \\ \hline
**VEGF** & 32 & \begin{tabular}{c} 0\% \\ (0\%,13.3\%) \\ \end{tabular} & \begin{tabular}{c} 93.8\% \\ (77.8\%,9\%) \\ \end{tabular} & \begin{tabular}{c} 6.3\% \\ (1.1\%,22.2\%) \\ \end{tabular} & \begin{tabular}{c} 6.3\% \\ (0\%,30.1\%) \\ \end{tabular} & \
\begin{tabular}{c} 6.3\% \\ (6.7\%,57.2\%) \\ \end{tabular} &
\begin{tabular}{c} 6.3\% \\ (42.8\%,9\%) \\ \end{tabular} \\ \hline \hline \end{tabular}