Distribution of age and apnea-hypopnea index in diagnostic sleep tests in West Texas

Abstract

Obstructive sleep apnea (OSA) is a disease characterized by the collapse of the upper airway during sleep. It is debated whether increasing age is associated with an increased severity based on the apnea-hypopnea index (AHI) in OSA patients. To better characterize the distribution of age and AHI in OSA patients, a large, retrospective analysis of diagnostic sleep test results in West Texas was performed. This study analyzed 3993 adult patients (aged ≥18 years) who had either a full or a split night sleep study performed at Alpha Sleep Labs between July 1, 2009, and September 1, 2020. The distribution of age approximates a normal distribution with a mean age of 52.6 and standard deviation of 14.4 years. Compared to the US population, the study population is overrepresented by those 40 to 60 years of age and underrepresented by those 20 to 40 and ≥60 years. The degree of underrepresentation was greater for young patients than the elderly. The number of subjects vs. AHI approximated an exponential decay. Although prevalence probably contributes to the observed distributions of age and AHI, we cannot conclude that our data represent either the prevalence of OSA or AHI. The population of people undergoing diagnostic sleep testing is not representative of the total population. Interdependencies are observed between age and AHI, but the basis for these interdependencies is unclear. Future studies will need to examine these effects in greater detail.

Obstructive sleep apnea (OSA) is a disease characterized by collapse of the upper airway during sleep.¹ The severity of OSA is classified according to the apnea-hypopnea index (AHI), which counts the total apnea and hypopnea events divided by the total sleep time; an AHI <5 is considered normal.^2,3 In the general population, clinical studies estimate the prevalence of OSA at 4%.⁴ Previous reports have estimated that patients >65 years have an OSA incidence between 5.6% and 13%.^2,3 Further data reported in the elderly population showed that 88% of men aged 65 to 69 years had 5 or more events per hour, while the incidence increased to 90% in men aged 70 to 85 years.⁵ However, it remains debated whether increasing age is associated with an increased severity (AHI) in OSA patients.⁶ A study by Peppard et al showed that the apparent increase in AHI with age previously reported was strongly correlated with weight gain.⁷ Another study found that AHI only increased with age among patients with moderate to severe OSA.⁸ In contrast, a recent meta-analysis found that there was no difference in baseline AHI between those aged <65 years and those aged >65 years.⁶ To better characterize the distribution of age and AHI, a large, retrospective analysis of diagnostic sleep test results in West Texas was performed.

METHODS

Adult patients (≥18 years) who had either full night laboratory diagnostic sleep studies or split night sleep studies performed at Alpha Sleep Labs and interpreted by one of the authors (G.B.) between July 1, 2009, and September 1, 2020, were included. Age and AHI information were extracted from the sleep study reports on the 3993 patients who were entered into the study. The average AHI for full night diagnostic studies was used. The average AHI for the diagnostic portion of the split night studies was used. Age was calculated as the date of study minus the date of birth rounded down to years.

Linear and exponential regression analyses as well as the Q-Q plot (using the Kolmogorov-Smirnov test and Shapiro-Wilk test) were performed using GraphPad PRISM software (GraphPad Prism, San Diego, CA).^9,10 Statistical significance was determined using conservative multiplicity adjustments with the Bonferroni test, where the P value must meet a more conservative threshold of 0.05/number of comparisons.

RESULTS

There were 3993 subjects in the study population. Figure 1 is a histogram of the number of people of each age. The distribution of age approximates a normal distribution. The calculated mean age was 52.6 years, and the calculated standard deviation was 14.4 years. Figure 2 shows the age distribution of the study population overlaid with the normal distribution having an equal mean and standard deviation to those of the study population. A normal distribution with total area under the curve equal to 1 has the following equation:

$$f\left(x\right)=\mathrm{ }\frac{1}{\sqrt{2\pi {\sigma }^2}}\mathrm{ }{e}^{\frac{{-(x-\mu )}^2}{2{\sigma }^2}}$$

where f(x) = probability density function (PDF), σ = standard deviation, and μ = mean. The cumulative distribution function (CDF) is related to the PDF but represents the area under the PDF from -∞ to x. Data points for each age group were calculated as the CDF for the upper age minus the CDF for the lower age. The data point for the age group 85 and older was calculated as 1 minus the CDF for age 85.

Figure 1.

The distribution of age of all subjects in the study. The x axis is the age group. The y axis is the number of subjects in each age group.

Figure 2.

A comparison between distribution of age group for study subjects and a normal distribution. See text for details on how the normal distribution was computed.

A Shapiro-Wilk test was used to test for a normal distribution of age. The null hypothesis for this test is that the data are normally distributed. The statistic “W” was calculated to be 0.99298. This W statistic corresponds to a P value of 4.324e-13, which rejects the null hypothesis. Visual inspection of Figure 1 reveals a left bias; in other words, the tail to the left of the mean is larger or thicker than the tail to the right of the mean.

This left-right asymmetry of appearance can be quantitated as skew, which is the third power moment of the distribution. The skewness measurement of the age distribution was −0.144. Another type of deviation from the normal distribution is kurtosis.¹¹ Kurtosis is the fourth power moment of the distribution and measures whether subjects are more common near the mean or more common in the tails. Curves with positive excess kurtosis have higher peaks and thinner tails, while curves with negative excess kurtosis have shorter peaks and thicker tails. The excess kurtosis measurement of the study age distribution was −0.413.

A Q-Q plot of the study population age was also done to assess whether the age data modeled a normal distribution (Figure 3). Specifically, a Q-Q plot is a scatterplot created by plotting two sets of quantiles on the x and y axes. As shown in Figure 3, the age distribution of the sample population deviates from a normal distribution at both tails of the distribution (0–25 and 80–100). This was further supported by the Kolmogorov-Smirnov test, which showed a significant deviation from a normal distribution (KS value −0.1780; P < 0.0001). Our data approximated a normal distribution near the mean age but deviated from a normal distribution at both tails distant from the mean.

Figure 3.

A Q-Q plot of test on normal distribution for age. The x and y axes are the quartiles from the age distribution that are ordered compared to a normal distribution for analysis.

Figure 4 overlays the age distribution of the US population with that of our study population. The data for the US population was obtained from the Census Bureau (https://www.census.gov/topics/population/age-and-sex/data/tables.html). The study population was overrepresented by those 40 to 60 years of age but underrepresented by those 20 to 40 and <60 years of age.

Figure 4.

A comparison of age data with US Census data.

Figure 5 shows the distribution of AHI in our study population. AHI was grouped in increments of 5 events per hour. The precision for AHI was 0.1. The groups were 0–4.9, 5–9.9, 10–14.9, etc. The x axis is the lower bound for each AHI group. In other words, x = 0 corresponds to the AHI group 0–4.9. As AHI group increased, the number of subjects in that AHI group decreased. To determine whether this trend was consistent with exponential decay, a semi-log plot of AHI distribution was done, as shown in Figure 6.

Figure 5.

The distribution of AHI for our study population. The red curve is the regression equation.

Figure 6.

A semi-log plot of the distribution of AHI in our study subjects. The y axis is the natural logarithm of the number of subjects in each AHI group. The red line is the regression equation.

Table 1 contains the number of subjects stratified by age group and AHI group. The age groups are based on Figure 4. Subjects in age group 18–39 were underrepresented compared to the US population. Subjects in age group 40–69 were overrepresented compared to the US population. Subjects in age group ≥70 were underrepresented compared to the US population. AHI was stratified based on clinical grounds. AHI 0–4.9 is considered within normal limits. AHI 5–14.9 is consistent with a diagnosis of OSA but does not meet the criterion for automatic approval of continuous positive airway pressure therapy. AHI 5–14.9 can be considered mild OSA; AHI 15–44.9, moderate OSA; and AHI ≥45, severe OSA.

Table 1.

Study population stratified by age group and AHI group^a

	AHI group (n)					AHI (%) b
Age group	0–4.9	5–14.9	15–44.9	45+	Total	0–4.9	5–14.9	15–44.9	45+
18–39	200	230	174	181	785	0.255	0.293	0.222	0.231
40–69	457	799	862	641	2759	0.166	0.290	0.312	0.232
70+	56	151	151	91	449	0.125	0.336	0.336	0.203

^a See text for rationale of stratification. AHI indicates apnea-hypopnea index.

^b Fraction of number of subjects in each AHI group divided by the total number of subjects in that age group.

The proportions of all three age groups differed across the AHI groups (all P < 0.005). The proportions of the AHI 0–4.9 group (P < 0.001) and 15–44.9 group (P < 0.001) were not the same for each age group. The proportion of patients with normal AHI values (0–4.9) decreased with increasing age. The proportion of study population patients with moderate OSA (AHI 15–44.9) increased with increasing age. The proportions of the AHI 5–14.9 group (P = 0.130) and >45 group (P = 0.366) did not significantly differ across the three age groups. There was no consistent change in the proportion of subjects with an increase in age group for mild OSA (AHI 5–14.9) and severe OSA (AHI ≥45).

DISCUSSION

As noted previously, the distribution shown in Figure 1 does not necessarily reflect the prevalence of OSA or the prevalence of suspected OSA, as patients can have OSA for many years. The most common reason for obtaining a diagnostic sleep test is to establish or confirm a diagnosis of OSA. It is reasonable to think that the distribution of age in our study reflects the age of onset of OSA. Another plausible cause for a normal distribution would be that patients do not seek help for OSA specifically, but rather OSA is suspected as a comorbid condition for other medical problems that cause patients to enter the health care system.

The deviation from normality in the young tail of Figure 2 may be related to insurance issues. Sleep tests are expensive, so sleep testing may not be performed in young patients until the patient has employer-based health insurance. Furthermore, OSA may not be a high priority for the geriatric population, where many patients have very long problem lists by the time they reach age 85 (e.g., cancer, end-stage heart disease, or end-stage renal disease). Another possibility is that the first sleep test is a fairly constant percentage of people in each age group. The mechanism here would be that OSA is an uncommon problem that develops in a fairly random manner across all age groups. Under this hypothesis, one would expect the distribution of study age to be similar to the distribution of population age. However, the data in Figure 4 make this explanation seems unlikely.

Figure 5 shows the distribution of AHI for this study population using an exponential decay regression analysis, which yields the following expression:

$$\text{y}\left(\text{number of subjects}\right)=762.09*\exp \left(-0.05280*\mathrm{AHI}\right)+20.51);{\text{ r}}^2=0.9593$$

Figure 6 shows a semi-log plot of the distribution of AHI in the study subjects, which was modeled using a linear regression model. The analysis yielded the following expression:

$$\mathrm{y}\left(\ln \left(\text{number of subjects}\right)\right)=-0.0326*\left(\mathrm{AHI}\right)+6.369; {\mathrm{r}}^2=0.9429$$

Both figures demonstrate a strong exponential decay relationship between the number of subjects and AHI in the study sample. A decaying exponential is described by:

$$\frac{dN}{\mathit{dAHI}\mathrm{ }}=-k\mathrm{*}\left(\mathit{AHI}\right)$$

where −k is the decay rate constant. Systems that follow a decaying exponential dynamic are first-order linear systems. Examples include an electrical RC network, or the height of water in a container with a small hole in the bottom. When these first-order linear systems are driven by constant inputs, the system approaches an equilibrium between the fixed input supplying the system and the proportional output draining the system. One potential mechanism for this pattern in our study would be a defect that ramps up to a threshold before triggering an apnea event. A higher AHI requires either a higher rate of defect (ramp) or a lower threshold. Variation among normal people could reflect a normal rate of ramp and a variance of threshold. However, it becomes more difficult to have higher rates of ramp, so groups of people with higher mean AHI will have fewer people in the group.

Using Table 1 and Figure 7, several trends are apparent between age and AHI. As subjects get older, it is less likely for them to have a normal AHI. There was a significant reduction in the proportion of patients who had an AHI of 0–4.9 between the 18–39, 40–69, and 70+ age groups. The AHI values of 5–14.9 and 45+ remained relatively unchanged in all three age groups. In contrast, the proportion of participants with AHI values 15–44.9 increased between the age groups of 18–39 and 40–69; however, this trend did not continue for patients ≥70. This trend does not necessarily reflect the prevalence of OSA in these age groups. It could be that middle-aged patients are more likely to have sleep testing due to the appearance of other medical comorbidities (e.g., hypertension, diabetes, heart disease, and lung disease), or younger patients may have other causes of similar symptoms than middle-aged patients, so the younger patients do not have diagnostic sleep tests. As patients transition from middle age to elderly, other medical problems (heart disease, stroke, cancer) may take priority, causing sleep issues to be relatively ignored. It is unclear whether the interdependencies observed between age and AHI are due to changing severity of OSA with aging or are determined by other factors that influence who gets a sleep test.

Figure 7.

Proportion of patients in age groups stratified by AHI. The y axis is the proportion/percentage of study population in each group falling into four AHI groups: 0–4.9, 5–14.9, 15–44.9, and 45+.

In conclusion, this study investigated the distribution of age and AHI in patients undergoing diagnostic sleep testing using a large, retrospective study in West Texas. The age distribution of this study group closely resembled a normal distribution. In addition, the number of subjects vs. AHI approximates an exponential decay with a greater proportion of subjects having lower AHI values. Stratification of the population by age group and AHI group demonstrated that as subjects get older, they were less likely to have a normal AHI. This trend could be due to older patients being more likely to enter the health care system and have access to sleep testing. It is unclear whether the interdependencies observed between age and AHI are due to changing severity of OSA with aging or are determined by other factors that influence who gets a sleep test. This study is limited in that only age and AHI were examined. Other factors, such as gender and body mass index, would need to be included to gain further insight into other variables influencing AHI. Furthermore, this retrospective study was limited to West Texas. Additional data from other regions of the United States would provide a more representative sample of age and AHI values. Lastly, the study is a retrospective analysis; a randomized study would reduce additional biases in this study. Further study is warranted to investigate the correlation between age and AHI.