Lung function reference equations and lower limit of normal for Cree First Nations Children and adolescents living in rural Saskatchewan,Canada

Abstract

BACKGROUND:

Spirometric prediction equations are used to evaluate lung function in the clinical setting. However, such equations are not yet available for First Nations populations. The purpose of this study is to derive appropriate spirometric reference equations for a group of Cree First Nations school-aged children and adolescents living in rural Saskatchewan, Canada.

METHODS:

Spirometric data was collected from Cree First Nations cohort living in rural Saskatchewan, Canada. In the baseline survey, 351 children and adolescents participated and of these 134 were identified as healthy non-smoking individuals. The predicted values and Lower Limit of Normal (LLN) of spirometric indices were calculated for school-going children and adolescents (ages 6–17 years for males and 6–14 years for females). The spirometric indices were assumed to follow a Box-Cox-Cole-Green (BCCG) distribution with median, $\mu$ , coefficient of variation, $\sigma_{L}$ and skewness, $\nu$ . Akaike Information Criteria (AIC) approach was used to obtain the reference models. The LLN was calculated by taking the fifth percentile of the prediction equations of the lung function variables.

RESULTS:

Two-sample $t$ -test revealed significant differences in the means of lung function and demographic measurements between both boys and girls. Therefore, separate equations were fitted for both boys and girls.

CONCLUSION:

This study provides the baseline lung function reference equations for Cree First Nations children and adolescents. This baseline study provides a platform for future studies, which can be conducted to improve the accuracy of the predicted lung function indices for such study cohort.

Keywords

Aboriginal BCCG GAMLSS LLN lung function reference equations spiromtery

1. Introduction

Respiratory diseases are one of the leading causes of morbidity for children (Bulkow et al., 2012). The prevalence of pulmonary diseases is unusually high in indigenous children (McCuskee et al., 2014), and a large number of them require repeated hospitalization and admission to pediatric intensive care unit (ICU) (Banerji et al., 2001). Childhood respiratory problems are associated with chronic lung diseases in adulthood (Singleton et al., 2000). Spirometric data along with age, height, weight and ethnicity are used to develop reference equations, based on statistical methods involving regression analyses (Veale et al., 1997). Such equations are then used to predict lung function values for an individual given his/her age, sex, height, weight and ethnicity.

The ethnicity of the children has an effect on lung function and has been examined by several authors (Azizi & Henry, 1994). For example, the predicted lung function values for African-American children are lower than those for Mexican-American and Caucasian children (Hsu et al., 1979; Hsi et al., 1983; Kirkby et al., 2013). In Australia, Caucasians children have been shown to have higher lung function values compared to Aboriginal children (Watson et al., 1986), and children of European regions tend to have higher lung function values compared to children of Asian origin (Wesley et al., 1989; Johnston et al., 1987). Differences in lung function were also observed between Caucasian, Chinese and Indian populations (Yang et al., 1991). It is evident that ethnic differences in lung function begin in childhood due to different physical stature between different ethnic groups (Yang et al., 1991).

Quanjer et al. (2012) provided all-age multi-ethnic spirometric reference equations that can be used globally for different ethnic groups including Caucasian, African-American, North-East Asian, South-East Asian and Others (people with mixed-ethnicity). The authors considered for an adjustment for ethnicity while modeling lung function indices.

Some studies (Gutierrez et al., 2004; Tan et al., 2011; Karunanayake et al., 2015) on developing spirometric reference equations for Canadians have been conducted. However, these studies were aimed at deriving lung function prediction equations for Caucasian adults living in Canada. Sin et al. (2004) conducted a pilot study to provide lung function values for school-going First Nations children living in Northern Alberta. The spirometric reference equations calculated from Caucasian population living in the United States provided by Hankinson et al. (1999) were used for First Nations children in this study. Observed lung function values were compared with the LLN values for the assessment of airflow obstruction. The authors found that 25% of the First Nations children showed evidence of airflow obstruction. Sin et al. (2004) suggested that asthma is under-diagnosed and under-recognized for First Nations children. Therefore, spirometric reference equations for non-First Nations people may not be appropriate for First Nations people, as the equations may be influenced by ethnicity. Moreover, adult equations cannot be used for children, as lung function increases with age until adulthood and starts to decline with age (Chen et al., 2005). At present, there are no specific spirometric reference equations available for First Nations people in Canada, including children. Coates et al. (2016) provided reference equations for Canadian population which considered including North American Indians, Inuits or Métis, but not First Nations people.

This analysis is focused on deriving appropriate reference equations for Cree First Nations children and adolescents to improve diagnostic accuracy in the assessment of respiratory disease. The results from this study will be compared with the equations provided by Hankinson et al. (1999) to see if the application of reference equations calculated from Caucasian children and adolescents is appropriate for Cree First Nations people.

2. Materials and methods

2.1 Data source and variables

Lung function data for children and adolescents (ages between 6 to 17 years) from Saskatchewan First Nations Lung Health Project (FNLHP) were used to derive reference equations.

There were a total of 351 children and adolescents (47% males and 53% females), who completed a baseline survey. The survey questionnaire included questions regarding their past and current health conditions, lifestyles, personal and family history of chronic diseases. The clinical component of the study assessed anthropometric measurements (standing height, weight, and waist circumference), blood pressure, pulmonary function testing (FVC, FEV ${}_{1}$ , FEV ${}_{1}$ /FVC and FEF ${}_{\text{25\%--75\%}}$ ) and allergy skin status through skin prick testing. Parental report on the date of birth of a child was used to calculate the age. Standing height of the individuals were measured using a fixed tape with a participant standing on a hard surface without wearing shoes (Chen et al., 2005). Sensormedics (Anaheim, CA, USA) dry rolling seal spirometer was used to measure lung function values. Lung function testing was conducted according to criteria set by American Thoracic Society (ATS) (Miller et al., 2005). All lung function testing was conducted by a registered nurse certified in Spirometry. The spirometer was calibrated twice daily and lung function testing results were reviewed by a respirologist. Results from children who did not have acceptable curves on the first testing were retested and the best curves were retained in the study for further analysis. A consent form was completed by the parent and assent form by the study participants who were of 16 years of age or over, who were not living with a parent or guardian were emancipated and able to complete the consents for themselves.

Literature (Hsu et al., 1979; Burity et al., 2013; Dickman et al., 1971; Miller et al., 1977; Roizin et al., 1993; Wall et al., 1982) suggests that the most important covariates to predict lung function values are height and age. The general recommendation is to calculate prediction equations based on the healthy individuals. Therefore, a reduced dataset of healthy individuals was considered to calculate reference equations for FVC, FEV ${}_{1}$ , FEV ${}_{1}$ /FVC and FEF ${}_{\text{25\%--75\%}}$ . Participants with missing observations or extreme values for any of the lung function values or age and height were excluded from the analysis. Individuals with past or current history of dry cough, tightness in the chest, wheeze, doctor diagnosed asthma, tonsillitis, bronchitis, pneumonia, croup, sleep apnea were removed from the study. Also, participants with a smoking history of more than a year were excluded from the study, leading to a sample of 134 (64 males, 70 females) children and adolescents.

2.2 Statistical methods

Statistical methods to calulate lung function prediction equations are primarily based on regression models. Lung function values often exhibit a curved relationship with age. For skewed lung function data, the Generalized Additive Models for Location, Shape and Scale (GAMLSS) method is more appropriate to develop prediction equations, as this method does not require a specific distributional assumption for the response. Several authors (Quanjer et al., 2012; Wypij et al., 1993; Stanojevic et al., 2008; Koopman et al., 2011; Rochat et al., 2013) have used Generalized Additive Models (GAM) (Hastie & Tibshirani, 1986, 1990) or the extended version, GAMLSS for the derivation of lung function prediction equations.

GAMLSS is a framework for modelling the response variable (e.g., FVC, $\mathrm{FEV_{1}}$ or $\mathrm{FEV_{1}/FVC}$ ) following a wide range of family of distributions, which may depend non-linearly on covariates (e.g., age, height, weight, abdominal girth, etc.).

Let us consider the following matrices,

$\displaystyle\bm{Y}=\begin{pmatrix}y_{1}\\ y_{2}\\ \vdots\\ y_{n}\end{pmatrix},\quad\bm{X}=(x_{1},x_{2},\ldots,x_{n}),\quad\bm{\theta}=(% \theta_{1},\theta_{2},\theta_{3},\theta_{4})$

Let $(x_{i},y_{i})$ , for $i=1,2,\ldots,n$ be the covariate and response for individual $i$ . We can assume that the distribution of $\bm{Y}$ depends on parameters $\bm{\theta}$ , such that $\bm{\theta}$ can be modeled as a function of covariate and the response variable. The first two parameters of $\bm{\theta}$ are the location and scale. The remaining parameters are shape parameters, i.e., skewness and kurtosis. Here we are emphasizing on a popular special case of GAMLSS, the LMS model (Cole & Green, 1992). For $\bm{Y}>0$ , $\bm{Y}|\bm{X}$ follows a Box-Cox Cole and Green (BCCG) distribution (Box & Cox, 1964) with parameters $[\theta_{1}(x),\theta_{2}(x),\theta_{3}(x)]=[\mu(x),\sigma_{L}(x),\nu(x)]$ . Which means,

$\displaystyle\bm{Y|X}\sim\textit{BCCG}\hskip 5.690551pt[\mu(x),\sigma_{L}(x),% \nu(x)]$

with the transformed response

$\displaystyle Z=\begin{cases}{\displaystyle\frac{\left[{\displaystyle\frac{Y}{% \mu(x)}}\right]^{\nu(x)}-1}{\sigma_{L}(x)\nu(x)}},&\nu(x)\neq 0\\ {\displaystyle\frac{1}{\sigma_{L}(x)}}\log\left[{\displaystyle\frac{Y}{\mu(x)}% }\right],&\nu(x)=0\end{cases}$ (1)

for $0<\bm{Y}<\infty$ , where $\mu(x)>0,\sigma_{L}(x)>0$ and $-\infty<\nu(x)<\infty$ $. Z$ is assumed to follow a truncated standard normal distribution with $-\frac{1}{\sigma_{L}(x)\nu(x)}<Z<\infty$ , if $\nu(x)>0$ and $-\infty<Z<-\frac{1}{\sigma_{L}(x)\nu(x)}$ , if $\nu(x)<0$ . Hence the probability density function (pdf) of $\bm{Y}$ is given by

$\displaystyle f_{Y}(y)=\frac{y^{\nu(x)-1}\exp(-\frac{1}{2}z^{2})}{\left[\mu(x)% \right]^{\nu(x)}\sigma_{L}(x)\sqrt{2\pi}\phi(\frac{1}{\sigma_{L}(x)|\nu(x)|})}$ (2)

where $z$ is given by Eq. (1) and $\phi(\cdot)$ is the distribution function of a standard normal distribution. Cole and Green (1992) assumed that $Z$ follows a normal distribution; therefore, the truncation probability $\phi(\frac{1}{\sigma_{L}(x)|\nu(x)|})$ is negligible. Here $\mu(x)$ is the median of $\bm{Y}$ for covariate $x$ (e.g., age), which can be modeled with log-link as follows:

$\displaystyle\log[\mu(x)]=\left[b_{\mu}(x)\right]^{T}\beta_{\mu}=\sum_{j=0}^{p% }b_{\mu_{j}}(x)\beta_{\mu_{j}}=\beta_{\mu_{0}}+\beta_{\mu_{1}}x_{i}+\beta_{\mu% _{2}}x_{i}^{2}+\ldots+\beta_{\mu_{p}}x_{i}^{p}.$

Hence, as a simple example, we have assumed that $\mu$ is believed to have a $p^{\rm th}$ order polynomial basis. Thus the space of polynomial of order $p$ and below contains $\mu$ . A basis for this space is, $b_{\mu_{0}}(x)=1,b_{\mu_{1}}(x)=x_{i},b_{\mu_{2}}(x)=x_{i}^{2}\ldots,b_{\mu_{p% }}(x)=x^{p}$ . Similarly, the scale (coefficient of variation) with log-link can be modeled as follows:

$\displaystyle\log\left[\sigma_{L}(x)\right]=\left[b_{\sigma_{L}}(x)\right]^{T}% \beta_{\sigma}=\sum_{j=0}^{p}b_{\sigma_{Lj}}(x)\beta_{\sigma_{Lj}}=\beta_{% \sigma_{L0}}+\beta_{\sigma_{L1}}x_{i}+\beta_{\sigma_{L2}}x_{i}^{2}+\ldots+% \beta_{\sigma_{Lp}}x_{i}^{p}.$

The shape (skewness) parameter with identity link can be modeled as follows:

$\displaystyle\nu(x)=\left[b_{\nu}(x)\right]^{T}\beta_{\nu}=\sum_{j=0}^{p}b_{% \nu_{j}}(x)\beta_{\nu_{j}}=\beta_{\nu_{0}}+\beta_{\nu_{1}}x_{i}+\beta_{\nu_{2}% }x_{i}^{2}+\ldots+\beta_{\nu_{p}}x_{i}^{p},$

where $\beta_{\mu},\beta_{\sigma_{L}},\beta_{\nu}\in\mathbb{R}$ are vectors of polynomial coefficients. This type of likelihood function was first proposed by Green (1987) in a general semi-parametric regression setting, and then further used by Cole and Green (1992) for LMS method. The log-likelihood function, $l$ derived from Eq. (1) for $n$ independent cases for $(y_{i},x_{i})$ is given by,

$\displaystyle l=l(\mu,\sigma_{L},\nu)=\log\left(\prod_{i=1}^{n}\frac{[\frac{y_% {i}}{\mu(x_{i})}]^{\nu(x_{i})}-1}{\sigma_{L}(x_{i})\nu(x_{i})}\right)=\sum_{i=% 1}^{n}\left(\nu(x_{i})\log\left(\frac{y_{i}}{\mu(x_{i})}\right)-\log(\sigma_{L% }(x_{i}))-\frac{1}{2}z_{i}^{2}\right)$

The GAMLSS package of R was proposed by Rigby and Stasinopoulos (2010), where the Rigby and Statsinopoulos (RS) algorithm can carry out the iterative procedure to maximize the log-likelihood function to obtain the estimate of the models of median, coefficient of variation and skewness of the data.

2.3 Lower limit of normal (LLN) for lung function

This section focuses on calculating the Lower Limit of Normal (LLN) of the lung function indices. As described in Quanjer et al. (2012), for spirometric tests, the suggestion is to use 90% (NOT 95%), and two-sided (NOT one-sided) for calculating the LLN. Thus the remaining 10% are equally distributed in the two tails with 5% each side. Use of 90% lead to the fact that 5% of the population are considered to have too low values as opposed to 2.5%, that is, a larger portion of the population (5%) have too low values.

The formula for calculating the LLN (i.e., $5^{\rm th}$ percentile of BCCG distribution) involves the predicted values of median, skewness and coefficient of variation. For $\nu(x)\neq 0$ ,

$\displaystyle z=\frac{\left[\frac{y}{\mu(x)}\right]^{\nu(x)}-1}{\sigma_{L}(x)% \nu(x)}\geqslant y=\mu(x)[1+z\sigma_{L}(x)\nu(x)]^{\frac{1}{\nu(x)}}$

For $\nu(x)=0$ , the formula for calculating LLN involves the pdf of $z$ without the component for skewness, as described in Eq. (1).

$\displaystyle z=\frac{1}{\sigma_{L}(x)}\log\left[\frac{y}{\mu(x)}\right]% \geqslant y=\mu(x)\left[\exp(z\sigma_{L}(x))\right]$

Therefore, the formula for calculating lower $5^{\rm th}$ percentile becomes

$\displaystyle y_{0.05}=\begin{cases}\mu(x)\big{(}1-\sigma_{L}(x)\nu(x)z_{0.05}% \big{)}^{\frac{1}{\nu(x)}},&\nu(x)\neq 0\\ \mu(x)\exp(-\sigma_{L}(x)z_{0.05}),&\nu(x)=0\end{cases}$ (3)

Using this formula, the LLN can be calculated for spirometric indices based on the reference model.

The Akaike information criterion (AIC), which was proposed by Akaike (1974) is used for model selection.

3. Results

The summary statistics of the study variables (age, height, FVC, FEV ${}_{1}$ , FEV ${}_{1}$ /FVC and FEF ${}_{25\%-75\%}$ ) are displayed in Table 1. The measurement of skewness justified the use of GAMLSS to analyze the data. The $t$ -tests comparing the means of each of the study variables for boys and girls resulted in significant differences between groups (except for FEV ${}_{1}$ /FVC), indicating the need for separate reference equations for both males and females.

Table 1
Summary statistics of the study variables for a sample of 134 Cree First Nations healthy children and adolescents

Variables	Boys ( $n=$ 47)				Girls ( $n=$ 60)				Two sample $t$ -test
	Mean	SD	Skewness	Range	Mean	SD	Skewness	Range	$t$	$p$ -value
Age (years)	11.43	2.95	0.26	6.33–17.31	9.78	2.14	0.01	6.35–13.67	3.72	$<$ 0.01
Standing height (cm)	150.87	17.51	0.31	122–191	143.38	17.51	$-$ 0.04	113–171	2.68	$<$ 0.01
FVC (L)	3.12	1.15	0.94	1.51–6.73	2.49	0.75	0.39	1.33–4.34	3.75	$<$ 0.01
FEV ${}_{1}$ (L)	2.72	1.04	1.09	1.38–5.78	2.18	0.64	0.34	0.96–3.68	3.54	$<$ 0.01
FEV ${}_{1}$ /FVC	0.87	0.05	$-$ 0.30	0.70–0.98	0.88	0.05	$-$ 0.78	0.67–1.00	$-$ 1.26	0.21
FEF ${}_{\text{25\%--75\%}}$	3.23	1.31	1.27	1.62–7.28	2.66	0.84	0.20	0.68–4.44	2.96	$<$ 0.01

Suppose that the distribution of the response (lung function) variable $y$ is defined by three parameters $\mu$ , $\sigma_{L}$ and $\nu$ such that the transformed variable

$z=\frac{\left(\frac{y}{\mu}\right)^{\nu}-1}{\nu\times\sigma_{L}}$

is a $z$ score with distribution close to standard normal $N(0,1)$ . Here $\mu$ , $\sigma_{L}$ and $\nu$ are the location (median), scale (coefficient of variation) and shape (skewness) parameters, respectively. Any skewness in $y$ can be removed by a suitable choice of $\nu$ . The distribution of $z$ is called Box-Cox-Cole-Green (BCCG) distribution (Box & Cox, 1964). Following Quanjer, Stanojevic, et al. (2012), we consider GAM based on the BCCG distribution (i.e., GAMLSS) to derive prediction equations for FVC, FEV ${}_{1}$ , FEV ${}_{1}$ /FVC and FEF ${}_{25\%-75\%}$ . We apply log-links for $\mu$ and $\sigma_{L}$ and an identity link for $\nu$ , so that the models can be expressed as

$\displaystyle\log(\mu)=\beta_{0}+\beta_{1}\log\left(\mathrm{Height}\right)+% \beta_{2}\log\left(\mathrm{Age}\right)+\left\{\alpha_{0}+\alpha_{1}\left(\frac% {\mathrm{Age}}{20}\right)+\ldots+\alpha_{p}\left(\frac{\mathrm{Age}}{20}\right% )^{p}\right\}$ $\displaystyle\log\left(\sigma_{L}\right)=\beta_{0}+\beta_{1}\log\left(\mathrm{% Age}\right)+\left\{\alpha_{0}+\alpha_{1}\left(\frac{\mathrm{Age}}{20}\right)+% \alpha_{2}\left(\frac{\mathrm{Age}}{20}\right)^{2}+\ldots+\alpha_{p}\left(% \frac{\mathrm{Age}}{20}\right)^{p}\right\}$ $\displaystyle\nu=\beta_{0}+\beta_{1}\log\left(\mathrm{Height}\right)+\beta_{2}% \log\left(\mathrm{Age}\right)+\left\{\alpha_{0}+\alpha_{1}\left(\frac{\mathrm{% Age}}{20}\right)+\ldots+\alpha_{p}\left(\frac{\mathrm{Age}}{20}\right)^{p}\right\}$

where $p$ is the order of a polynomial. Note that age is divided by 20 to scale down the polynomial bases; since the ages of the participants range from about 6 to 18, age/20 $\in$ (0, 1).

Initially we considered several models based on the order $p$ of the polynomial $(p=1,2,\ldots,5)$ . Model selection procedure reveals that the smallest Akaike Information Criteria (AIC) (Akaike, 1974) values are achieved for models with $p^{\rm th}$ order polynomial as displayed in Table 2. Once the estimates of the regression coefficients for each of the $\mu$ , $\sigma_{L}$ , and $\nu$ models are obtained we estimated $\mu$ , $\sigma_{L}$ , and $\nu$ for different values of height and age. For a height-age combination, the estimates of $\mu$ , $\sigma_{L}$ , and $\nu$ then used to obtain the median reference value and LLN: given $\mu$ , $\sigma_{L}$ , and $\nu$ , the median reference value and the LLN were below the lower $50^{\rm th}$ and above the $5^{\rm th}$ percentiles of the BCCG distribution, respectively. The height-age adjusted median reference curve and the LLN curve were then constructed using the estimated median reference values and LLNs for different combinations of heights and ages. The GAMLSS package (Rigby & Stasinopoulos, 2005) in R (R Core Team, 2016) is used to fit the models.

Table 2

Order, $p$ , of polynomials for which the smallest AIC values are achieved here

Lung function	Males				Females
	$p$ for the	$p$ for the	$p$ for the	AIC	$p$ for the	$p$ for the	$p$ for the	AIC
	$\mu$ model	$\sigma_{L}$ model	$\nu$ model	Value	$\mu$ model	$\sigma_{L}$ model	$\nu$ model	Value
FVC	1	1	2	22.41	4	4	1	$-$ 11.41
$\mathrm{FEV_{1}}$	4	3	1	$-$ 14.62	3	4	4	$-$ 6.86
$\mathrm{FEV_{1}/FVC}$	2	1	4	$-$ 201.40	3	4	3	$-$ 229.93
$\mathrm{FEF_{\text{25\%--75\%}}}$	1	1	3	133.65	2	4	1	109.41

Figure 1.

Comparison of the fitted plots of lung function indices for males with other study; solid curves indicate predicted median lung function based on GAMLSS; dashed curves indicate predicted mean lung function based on the study of Hankinson et al. (1999).

As indicated by scatterplots of Figs 1 and 2, the observed values of the lung function indices increase with both age and standing height. However, the FEV ${}_{1}$ /FVC ratios exhibited an irregular shape for women and large variability for both sexes. Overall, there existed a curved relationship between each of the lung function values and anthropometric variables (i.e., age and height). The application of GAMLSS with polynomial bases was used to capture such curved relationships.

Figure 2.

Comparison of the fitted plots of lung function indices for females with other study; solid curves indicate predicted median lung function based on GAMLSS; dashed curves indicate predicted mean lung function based on the study of Hankinson et al. (1999).

3.1 Model fits and prediction equations

The predicted models for lung function indices of boys and girls are provided in Tables 3 and 4. From the parameter estimates, we can see that the polynomial order for the model of $\mu$ in females is higher compared to males. The reason behind this is that the plots of lung function data in terms of anthropometric measurements in females exhibited more curved patterns compared to males as seen in Figs 1 and 2. Furthermore, the signs of the polynomial are alternatively positive ( $+$ ) and negative ( $-$ ). This is because there were upward and downward peaks in the observed curves as shown in the scatterplots. Fitted curves overlaid with the observed data are displayed in Figs 1 and 2, and the estimates of the regression coefficients are provided in Tables 3 and 4. The estimated curves (Figs 1 and 2) show that the models fit the lung function data reasonably well for all the lung function indices.

Table 3
Prediction equations for log(FVC) and log(FEV ${}_{1}$ ) resulting from GAMLSS analyses

		Males			Females
		$\mu$ Model	$\sigma_{L}$ Model	$\nu$ Model	$\mu$ Model	$\sigma_{L}$ Model	$\nu$ Model
Lung		estimate	estimate	estimate	estimate	estimate	estimate
function	Parameters	( $p$ -value)	( $p$ -value)	( $p$ -value)	( $p$ -value)	( $p$ -value)	( $p$ -value)
$\log(\mathrm{FVC})$	Intercept	$-$ 12.74	13.95	$-$ 983.30	$-$ 220.7	5279.2	428.37
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	Log (height)	$3.04$			$2.21$
		$(<0.01)$			$(<0.01)$
	Log (age)	$-$ 0.93	$-$ 11.72	1088.59	1009	$-$ 29718.3	$-$ 349.17
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	Age/20	1.46	21.16	$-$ 3904.78	$-$ 8129	246566.7	745.14
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{2}$			1719.02	12170	$-$ 379664.6
				$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{3}$				$-$ 10700	342902.3
					$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{4}$				3936	$-$ 129323.3
					$(<0.01)$	$(<0.01)$
$\log(\mathrm{FEV_{1}})$	Intercept	0.68	$-$ 597.80	342.84	26.64	2293.5	$-$ 8944.7
		(0.8548)	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	Log (height)	3.32	1035.52		1.68
		$(<0.01)$	$(<0.01)$		$(<0.01)$
	log (Age)	$-$ 74.27	$-$ 5518.62	234.48	$-$ 93.79	$-$ 17675.6	31813.1
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	Age/20	585.70	4778.12	$-$ 398.50	617.05	153637.8	$-$ 233422.2
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{2}$	$-$ 838.86	$-$ 1791.86		$-$ 661.65	$-$ 247227.6	303746.6
		$(<0.01)$	$(<0.01)$		$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{3}$	686.79	309.03			232787.9	$-$ 218206.1
		$(<0.01)$	$(<0.01)$			$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{4}$	$-$ 228.78				$-$ 91305.1	$-$ 218206.1
		$(<0.01)$				$(<0.01)$	$(<0.01)$

Table 4

Prediction equations for $\log$ (FEV ${}_{1}$ /FVC) and $\log$ (FEF ${}_{\text{25\%--75\%}}$ ) resulting from GAMLSS analyses

		Males			Females
		$\mu$ Model	$\sigma_{L}$ Model	$\nu$ Model	$\mu$ Model	$\sigma_{L}$ Model	$\nu$ Model
Lung		estimate	estimate	estimate	estimate	estimate	estimate
function	Parameters	( $p$ -value)	( $p$ -value)	( $p$ -value)	( $p$ -value)	( $p$ -value)	( $p$ -value)
$\log(\mathrm{FEV_{1}/FVC})$	Intercept	$-$ 0.31	15.29	16499	$-$ 10.89	1266.8	3345
		(0.6695)	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	Log (height)	$-$ 0.39			$-$ 0.68
		$(<0.01)$			$(<0.01)$
	Log (age)	2.42	$-$ 14.46	$-$ 58454	36.72	$-$ 10344.1	$-$ 14831
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	Age/20	$-$ 9.02	29.27	432886	$-$ 238.58	90470.9	111794
		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{2}$	4.28		$-$ 584975	254.15	$-$ 146194.7	$-$ 135967
		$(<0.01)$		$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{3}$			456883	$-$ 117.50	137972.0	71114
				$(<0.01)$	$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{4}$			$-$ 147137		$-$ 54158.8
				$(<0.01)$		$(<0.01)$
$\log(\mathrm{FEF_{\text{25\%--75\%}}})$	Intercept	$-$ 7.51	$-$ 0.05	923.9	4.18	423.9	7.70
		$(<0.01)$	(0.9940)	$(<0.01)$	(0.2254)	(0.0383)	(0.7200)
	Log (height)	1.72			1.0
		$(<0.01)$			$(<0.01)$
	Log (age)	$-$ 0.22	$-$ 2.38	$-$ 1673.8	$-$ 12.04	$-$ 5502.6	$-$ 8.80
		(0.6843)	(0.6010)	$(<0.01)$	$(<0.01)$	$(<0.01)$	(0.9650)
	Age/20	0.93	7.35	9110.8	52.01	50417.9	$-$ 15.84
		(0.3313)	(0.3900)	$(<0.01)$	$(<0.01)$	$(<0.01)$	(0.6880)
	(Age/20) ${}^{2}$			$-$ 8045.1	$-$ 25.83	$-$ 85465.4
				$(<0.01)$	$(<0.01)$	$(<0.01)$
	(Age/20) ${}^{3}$			3085.3		84609.9
				$(<0.01)$		$(<0.01)$
	(Age/20) ${}^{4}$					$-$ 34794.7
						$(<0.01)$

The slope parameters for males were significant ( $p<$ 0.01), indicating that both standing height and age have substantial effects in predicting lung functions. Moreover, significant slopes for the polynomial bases suggest a curved relationship between age and lung functions (except for FEF ${}_{\text{(25\%--75\%)}}$ ) while for both males and females, significant slopes in the $\mu$ and $\sigma_{L}$ models suggested a curved relationship as well as large variability in lung function. This is also evident in Figs 1 and 2.

A comparison among the fitted median curves for FVC and FEV ${}_{1}$ is shown in Fig. 3. The predicted FVC values for males are higher than those for females (solid red) for ages between 6 and 17.5. On the other hand, we see lower FEV ${}_{1}$ for females until around age 11, we see a sudden drop in FEV ${}_{1}$ for males at around age 11, followed by a transition until around age 15. During this transition phase, FEV ${}_{1}$ values are higher for females than those for males. There is a sharp increase in FEV ${}_{1}$ for males after around age 15, leading to higher FEV ${}_{1}$ values for males compared to females. As different age groups were used for males and females, we did not extrapolate data after approximately age 14 for females.

Figure 3.

Height-age adjusted median reference values for FVC and FEV ${}_{1}$ for both males and females.

3.2 Lower limit of normal (LLN)

The fitted curves for the lower $5^{\rm th}$ percentile of the BCCG distribution or the lower limit of normal (LLN) are given in Figs 4 and 5. One can easily find the predicted values and LLN values for lung function indices from the black and red curves, respectively. Only few observations were below the LLN curve, indicating that the LLN comprised of healthy individuals. In boys, there was only one observation at the age of 6 for all of the lung function indices; therefore, both the predicted curve and LLN curve intersect each other in FVC and FEV ${}_{1}$ . This means that the predicted lung function value and LLN were almost same for boy ages 6 years old. The same pattern was not observed in girls, as there was more than one observation in the data at the age of 6. At age 6 and 13 in girls, there were outlier in the plot of FEV ${}_{1}$ /FVC ratio. This outlier bends the curve towards it. As a result, girls’ LLN had a sudden decrease at the age of 6 and 13. The outliers are pulling the LLN curve towards them, which was not observed in the predicted median curve in Figs 1 and 2.

Figure 4.

Lower Limit of Normal (LLN) for the median of lung function indices (males); solid line represents the height and age-adjusted median curve, dashed line represents the height and age-adjusted LLN curve.

Figure 5.

Lower Limit of Normal (LLN) for the median of lung function indices (females); solid line represents the height and age-adjusted median curve, dashed line represents the height and age-adjusted LLN curve.

3.3 Comparison with the equations calculated for Caucasians

The results from this study are compared with the results from Hankinson et al. (1999). The equations proposed by Hankinson et al. (1999) is different than the results calculated in this study. The fitted plots of the lung function indices based on this study and the one by Hankinson et al. (1999) are given in Figs 1 and 2. Although the predicted curve calculated by Hankinson et al. (1999) fitted the data reasonably well, but it was not able to capture the non-linear relationship between anthropometric measurements and lung function.

4. Discussion

To the best of our knowledge, this is the first study to provide specific spirometric reference equations for Cree First Nations children and adolescents living in Canada. Well established reference equations provided by Hankinson et al. (1999) for Caucasians is not applicable to the studied population making specific equations necessary. They were calculated using an advanced statistical algorithm, GAMLSS (Rigby et al., 2019), where polynomial bases were considered to capture the non-linear relationship between lung function and anthropometric measurements. Increasing the order of the polynomial bases leads to over parametrization of the models, even though it captures more non-linearity of the data. Therefore, polynomial order ranging from one to five were examined to identify the most efficient model for the lung function indices. Akaike Information Criteria (AIC) showed that polynomial order ranging between one to four are more useful to model the spirometric indices for First Nations children and adolescents’ cohort. This is an advanced approach for modelling lung function indices, which was used to develop the GLI multi-ethnic reference equations by Stocks et al. (2012); Langhammer et al. (2016) and Cooper et al. (2017).

The models of lung function in females had higher order of polynomial bases compared to males, since the observed values of spirometric indices for females exhibited a more curved nature compared to males. The predicted values for females and LLN for FVC and FEV1 were lower until the age of 9 when compared to males. Previous studies have shown that maternal smoking during pregnancy has an adverse effect on lung function (Balte et al., 2016; Zacharasiewicz, 2016; McEvoy & Spindel, 2017), which is more prevalent in female subjects compared to their male counterparts (Tager et al., 1995). In our study, 36.2% of the mothers reported to have smoked during their pregnancy, which may explain differences observed.

We speculate that the irregular shape of FEV ${}_{1}$ /FVC ratios exhibited for females and large variability for both sexes are secondary to the small sample size. According to the GLI, to calculate equations for the people of new ethnic group a minimum group size should be 150 males and 150 females (Stocks et al., 2012; Quanjer et al., 2011). As such it is premature to consider incorporating our data into the GLI equations and, equally as important, limits its use in the clinical setting.

Another factor that must be taken into consideration is that household smoking rates were high in the study sample. In this study, approximately 40% of households were exposed to second-hand smoking. Thus, obtaining a healthy sample with no smoke exposure was challenging in this population. As such, there is possibility that children included in this analysis, although non-smokers, were not indirectly exposed to significant amounts of second-hand smoke.

There is tremendous diversity among First Nations peoples in Canada. As such, the results from this study may not be generalizable to other First Nations groups in Canada.

5. Conclusions

We have provided a tentative baseline spirometric reference values (FVC, FEV ${}_{1}$ , FEV ${}_{1}$ /FVC and FEF ${}_{\text{25\%--75\%}}$ ), predicted values and LLN values for Cree First Nations children and adolescents living in rural Saskatchewan, Canada. This study provides the platform from which future studies can be conducted to improve the accuracy of the predicted values and LLN values for this population. Although this represents a unique data set specific to this population it is premature to recommend it be incorporated into clinical practice. Further studies with other Canadian First Nations communities should be conducted to expand the sample size and calculate more robust spirometric reference equations for children and adolescents.

Footnotes

Acknowledgments

Ms. Rifat Zahan takes responsibility for the integrity of the analysis and contents of the manuscript. The First Nations Lung Health Project was funded by a grant from the Canadian Institutes of Health Research “Assess, Redress, Re-assess: Addressing Disparities in Respiratory Health among First Nations People”, CIHR MOP-246983-ABH-CCAA-11829. The First Nations Lung Health Project Team consists of: James Dosman, MD (Designated Principal Investigator, University of Saskatchewan, Saskatoon, SK Canada); Dr. Punam Pahwa, PhD (Co-Principal Investigator, University of Saskatchewan, Saskatoon SK Canada); Jo-Ann Episkenew, PhD (Co-Principal Investigator (deceased), Former Faculty of Indigenous People’s Health Research Centre, University of Regina, SK Canada), Sylvia Abonyi, PhD (Co-Principal Investigator, University of Saskatchewan, Saskatoon, SK Canada); Co-Investigators: Mark Fenton, MD, John Gordon, PhD, Bonnie Janzen, PhD, Chandima Karunanayake, PhD, Malcolm King, PhD, Shelly Kirychuk, PhD, Niels Koehncke, MD, Joshua Lawson, PhD, Greg Marchildon, PhD, Lesley McBain, PhD, Donna Rennie, PhD, Vivian R Ramsden, RN, PhD, Ambikaipakan Senthilselvan, PhD; Collaborators: Amy Zarzeczny, BA, LLM; Louise Hagel, MSc, Breanna Davis, MD, John Dosman, MD, Roland Dyck, MD, Thomas Smith-Windsor, MD, William Albritton, MD, PhD; External Advisor: Janet Smylie, MD, MPH; Project Manager: Kathleen McMullin, MEd; Community Partners: Jeremy Seeseequasis, BA; Raina Henderson, RN; Arnold Naytowhow; Laurie Jimmy, RN. We are grateful for the contributions from Elders, community leaders, School Boards, School Principals, teachers that facilitated the engagement necessary for the study, and, all parents and children who donated their time to participate. Training support was also provided by Western Regional Training Center (WRTC) for Health Services Research (HSR).

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Lung function reference equations and lower limit of normal for Cree First Nations Children and adolescents living in rural Saskatchewan,Canada

Abstract

BACKGROUND:

METHODS:

RESULTS:

CONCLUSION:

Keywords

1. Introduction

2. Materials and methods

2.1 Data source and variables

2.2 Statistical methods

Table 1 Summary statistics of the study variables for a sample of 134 Cree First Nations healthy children and adolescents

Table 3 Prediction equations for log(FVC) and log(FEV 1 ) resulting from GAMLSS analyses

4. Discussion

5. Conclusions

Footnotes

Acknowledgments

References

Table 1
Summary statistics of the study variables for a sample of 134 Cree First Nations healthy children and adolescents

Table 3
Prediction equations for log(FVC) and log(FEV ${}_{1}$ ) resulting from GAMLSS analyses