Statistical quality control charts: New tools for studying the body mass index of populations from the young to the elderly

Abstract

Background and aims

Statistical quality control charts (SQCCs) have been widely used in numerous manufacturing processes to keep fluctuations within the acceptable limits but no applications have been applied to weight management studies yet. The aims of the present study were (1) to show that using the mean Body Mass Index (BMI) values as the only indicator to assess the weight status of populations might be misleading in clinical weight management studies; and (2) to introduce a powerful tool, SQCCs, to keep fluctuations in BMIs within acceptable limits in a given population for healthy aging.

Methods

The study design was cross-sectional. The distributions of individual BMIs (n=829) between specified limits (USL=24.9 and LSL=18.5) and the pattern of BMI change by age were studied using X-charts, tolerance charts and a capability analysis.

Results

The mean BMI increased in both genders by age. In some groups, although a significant number of people were outside the normal weight BMI limits the mean BMI values were within the normal limits (18.5<BMI < 24.9). In addition, although the number of overweight individuals was greater in some groups, their mean BMIs were lower compared to the groups with fewer overweight individuals. Capability tests clearly show that each group, even the groups with a mean BMI in the normal weight ranges and also the groups which are referred as being “under control” according to the X-charts, was not in energy balance (Cp<l and Cpk<l).

Conclusion

The results clearly indicate that using the mean BMIs as the only indicator might be misleading in weight management studies. This study introduces SQCCs as a potential tool for clinical nutrition studies to maintain the fluctuations of individual BMIs within acceptable limits for healthy aging populations

Introduction

The proportion of the population over 60 years of age will triple throughout the world in the next half century (1). Some issues, such as health and medical care, care giving, nutrition and diet, are gaining importance because the world population is growing older. Weight management is one of the most important factors in healthy aging because obesity is rapidly becoming one of the major public health problems in many parts of the world (2, 3). A better understanding of the typical weight characteristics of a population at different stages of adulthood may help people age more successfully.

Weight gain or loss is a result of natural biological phenomenon occurring in the body, which can be explained by the energy balance equation:

$$\text{Energy Input}-\text{Energy Consumption}=\text{Energy Accumulation}$$ (1)

Input is the energy consumed in foods; consumption is the use of energy for cellular and physical activities. The balance between energy input and energy consumption determines the energy stored in the body. In cases when energy intake is higher than energy consumption, the excess energy accumulates in the body, usually as fat, causing weight gain. An individual loses body weight when his or her energy consumption is higher than his or her energy input. The BMI (body mass indexes) of a healthy adult will remain within the normal BMI limits without significant fluctuations when a person's energy balance is maintained. The caloric requirements necessary to maintain energy balance, as described by Equation (1), differ by age and gender.

In manufacturing processes, quality is defined as the degree (poor, good, or excellent) to which a set of quality factors fulfills the requirements. Quality control is the use of activities to achieve, sustain, and improve the quality (4). Therefore, in weight management studies, if aging is the process, the BMI values can be considered to be a quality factors, whereas being in the normal weight range is a requirement, and the activities performed to keep Equation (1) under control and achieve the requirements are the quality control. Statistical quality control (SQC) is generally applied to large populations when it is not feasible to measure the quality factor of each item; therefore, the tests are performed on the randomly chosen samples (5).

All processes have variability resulting from either natural causes or unnatural causes. In any process there will be a natural variance about the mean in terms of desired product quality. Physical and personal properties of people, habits, the time the data is collected are examples of common causes of natural variability (6). Unnatural variations, such as machine failure, chronic diseases, change in availability of healthy foods, have a dominant effect on the process stability as compared to the natural variations. Statistically controlled process is completely stable over time and displays a consistent amount of natural variability about a constant process mean. The existence of unnatural variations indicates an out-of control process.

Statistical quality control charts (SQCC) are the one of the most important techniques in understanding of the type of variation exists in the process. The SQCC technique makes it possible to monitor quality of individual products about the mean product quality so that any increase in quality variance about the mean above the natural expected variance can be picked up quickly and the process refined to minimize the increased number of defective or less than optimal products produced.

There are several common types of quality control charts. Choosing the correct control chart for a given process and data is very critical in analysis. In some cases, it may be more feasible to take a single measurement of the quality factor. In such cases, an X chart may be a better choice. An X chart has the advantage of providing a direct comparison of an individual value with specifications.

Three horizontal lines; the centerline (CL), the upper control limit (UCL) and the lower control limit (LCL); are calculated and plotted on the SQCC. These lines are established to assure a tolerance band for natural variability.

The lines are calculated as (4, 5):

(2)

(3)

(4)

where; &xmacr; is the average of the measurements, s (standard deviation) is a measure of the spread of a set of data from its mean and n is the number of measurements.

Along with these lines, the sample values are also graphed on the chart. Each point on the chart represents a single observation. The process is referred to as “in the state of control” if all of the plotted values remain within the control limits (4, 5, 6).

The statistically controlled process is not necessarily capable of producing products meeting requirements. Specification limits are the tolerances set by the manufacturers or consumers, based on the product requirements. The process consistently meets the requirements when it is statistically under control and capable to produce products between the specification limits. Capability indices are calculated to compare the observed data to a set of specification limits, the USL (upper specification limit) and the LSL (the lower specification limit) (4, 5):

(5)

(6)

(7)

In both cases, the index must be greater than 1.0 if the process is capable of maintaining almost the entire product within the specifications. In practice, most studies prefer the values of Cp and Cpk to be greater than 1.33 (4).

Although statistical quality control methods have been widely used in different research areas, there are no scientific publications about the statistical quality control chart applications in weight management and BMI studies (7, 8, 9, 10). The use of SQCC to monitor the distribution of individual BMI value about the mean BMI could help health professionals to pick-up quickly any increase in BMI variance about the mean above the natural expected variance and could enable earlier precautions to minimize the increased number of underweight, overweight, and obese people in the population. This article applies the statistical quality control charts to explain the pattern of change in BMI values of Turkish people by age and gender over the adult lifetime. This study is unique in this area.

Participants and Methods

Samples

Analogy between manufacturing and aging processes is proposed in the present study. In manufacturing processes measurements of the quality factors are done with samples, which are “representative” of the population undergoing the process at time t. The samples are required to convey suitable information of the quality indicator and be unbiased. These can only be achieved by random sampling from the populaion (11). In the present study the individuals correspond to the randomly chosen objects of the manufacturing process. Figure1 describes the aging process analyzed in this paper. It is analogous to the similar figures employed in the manufacturing processes.

Figure 1.

Aging - Manufacturing process analogy. BMI is chosen as one of the properties of the process, which may be controlled to maintain the desired quality in the aging process. Stage 1: age 18-29; Stage 2: age 30-49; Stage 3: age 50-69; Stage 4: age 70+

The design of the study was cross-sectional. A total of 829 randomly chosen individuals (418 females and 411 males) participated in this study. The participants were Turkish people in the age range of 18 to 70+ years. The subjects were classified according to age and gender to obtain homogeneous groups with similar physiological properties. The participants aged 18 to 29 were classified as young, 30 to 49 were classified as middle-aged, 50 to 69 were classified as old, and 70 and older were classified as the elderly. Among all participants, 170 females were in the young range, 162 were in the middle-aged range, 32 were in the old range, and 54 were in the elderly range. Among the males, 137 were in the young age group, 169 were in the middle-aged range, 66 were in the old range, and 39 were in the elderly range. The age cut-off points used in this study for age grouping were similar to those of the (USDA), United States Department of Agriculture, which were used to construct MyPyramid (12).

The participants were informed about the purpose of the study, and their consent was required prior to commencement of the study. The data for those who were pregnant or had known diseases were excluded.

BMI calculation

Self-reported weight and height values were used to calculate the BMI of the groups, excluding the eldest subjects. For the elderly group, measurements were taken to calculate the BMI since the sensitivity of self-reported values decreases by the ages 60 years (13).

The data collection was performed over the same period for all groups. The BMI was calculated as the weight in kilograms divided by the square of the height in meters (BMI=kg/m²). Subjects with a BMI of 18.5 to 24.9 were classified as normal weight, 25 to 29.9 were classified as overweight, and 30 or greater were classified as obese (3, 14, 15). BMI values were used to construct the percentile graphs.

Percentile BMI graphs

Individual's percentile rank indicates how his or her BMI value compares to the given population. In this study percentile values were obtained from the MedCalc statistical software, (Version 11.1.1, Belgium).

Statistical Quality Control Charts

Descriptive statistics are presented as mean values and standard deviations. All data was checked for normality, using a Kolmogorov-Smirnov test. Normal distribution was assumed if P is higher than 0.05 (MedCalc, Version 11.1.1). The X charts and tolerance charts were constructed, which show the data with 3-sigma limits and specified limits respectively. The CL, UCL, and LCL were calculated from the data by using (2), (3), (4). The normal weight BMI cut-off points (18.5 and 24.9) were set as the upper and lower specified limits (USL and LSL, respectively). The process capability analysis was carried out for all groups. STATGRAPHICS Centurion statistical software (StatPoint Technologies, Inc) was used for construction and analyses of all SQQC.

Results and Discussion

Statistical quality control charts (SQCCs) have been widely used to understand the nature of fluctuations in many manufacturing processes, but no applications have been applied to weight management studies yet. The percentile BMI graphs is used extensively in weight management studies since they make it possible to follow up the changes in BMI in relation to age from the young to the elderly. Generally, the weight of the population is considered under control if the mean BMI is between the normal BMI ranges. The aims of this study were (1) to show that using the mean BMI values as the only indicator to assess the weight characteristics and nutritional status of populations might be misleading in clinical weight management studies; and (2) to introduce a powerful tool, SQCCs, to study the BMI status of populations.

The percentile BMIs of the adult males and females are given in Figure 2 for the various age groups. Although the pattern of change was different, each percentile line had a curved shape for both genders, indicating a weight gain up to certain ages during adulthood even for thinner individuals. Supporting our findings Rurik et al. (2009), reported a weight gain among the Hungarian people after the age of 20. According to our results, males had higher BMIs than females until the end of the middle-aged years (30-49), which is most likely because males tend to have more muscle, whereas females tend to have more fat, and muscle weighs more than fat (16). However, after the age of 50, females had higher BMI values compared to males (figures 2A and 2B; tables 1 and 2). The mean BMIs indicated that males tend to gain weight by the end of the middle-age years, and a gradual decline in weight occurs until the 50 to 69 age range because males lose muscle mass after age 50 (17) (figure 2A). The mean BMI of the males stayed almost constant after the age of 70. Females gained weight until the end of the old-age years (fig. 2B and table 2). After this age, the BMI stayed almost constant for the whole female population. During the middle-age or late middle-age years, major changes in body composition occur. Lean body mass, collagen synthesis and bone mineral decrease, while abdominal fats and waist to hip ratio increase (18, 19). One of the longitudinal studies has shown the importance of nutrition on the body composition change and organ function in relation to the aging process and health status of elderly (20). There is disagreement about the reasons for weight gain among females in the middle-aged or late middle-aged years. In one of the studies, psychological factors were concluded to be the most critical factor in weight gain among middle-aged females, and menopause was not associated with weight gain (21). On the other hand, according to another study, menopause and changes in hormone levels, a decline in the energy expenditure during rest and physical activity, and an increase in the loss of fat-free mass and abdominal fat accumulation were associated with weight gain (22). Even though the reasons for the middle-aged related weight gain in females remain undetermined, similar results as those of our study were also reported in studies done with British, German, French, and Italian females (18). Percentile graphs help to indicate how individual data compares to the given population and also help to follow-up variations in process parameters depending on where they fall on the graph in relation to the rest of the population mean. Corresponding mean BMI values are calculated to construct each percentage curve. Common and uncommon variations are included in the mean values and it is not possible to visualize and distinguish the nature of variations with percentile graphs.

Figure 2.

BMI percentiles of (A) males and (B) females by age

Table 1.

Distribution of individual BMI values between the specification limits and the patterns of BMI change in the male populations by age

	Young Males (N=137)	Mid-aged Males (N=169)	Old Males (N=66)	Eldest Males (N=39)
Body Mass
Index (Mean ±SD)	24.46 ± 3.47	26.78 ± 3.77	25.87 ± 5.01	24.69 ± 4.21
Total out of limits (%)	37.96	69.23	54.55	56.41
Over upper specific control limits (%)	35.7	68.64	50.00	53.85
Below lower specific control limits (%)	2.19	0.59	4.55	2.56
Cpk	0.05	-0.16	-0.06	0.02
Cp	0.37	0.28	0.21	0.23

Table 2.

Distribution of individual BMi values between the specification limits and the patterns of BMi change in the female populations by age

	Young Females (N=170)	Mid-aged Females (N=162)	Old Females (N=32)	Eldest Females (N=54)
Body Mass index
(Mean±SD)	20.27 ± 2.29	24.30 ± 4.44	27.10 ± 4.26	27.07 ± 4.38
Total out of limits (%)	25.29	41.36	68.75	62.96
Over upper specific control limits (%)	4.11	37.65	68.75	62.96
Below lower specific control limits (%)	21.18	3.71	0	0
Cpk	0.50	0.05	-0.19	-0.17
Cp	0.90	0.26	0.28	0.24

SQQCs visualize the distribution of individual BMIs values around the mean BMI and limits and visualize the possible inconsistencies between these distributions and the mean BMI of the given population. The distributions of individual BMI data around the mean and between the control limits and normal weight BMI limits were plotted using X-charts and tolerance charts for a better understanding of the BMI fluctuations by age and gender (figures 3 and 4). The normality of the distribution of data was tested before constructing SQCCs. Results from the tests clearly indicate that each data was distributed normally (figures 3 and 4). The distributions of individual male BMI values around the specified limits (USL and LSL) for different age groups are given in Figure 3 in conjunction with table 1. Statistical quality control charts clearly visualize some inconsistencies between the distribution of the individual BMis around the specified limits and the mean BMI of the male populations. Among the young males, although a significant number of people were outside the normal weight BMi ranges with the majority being over the USL, the mean BMI was between the specified limits (figures 3C and 3D and table 1). The results from SQCCs for the young male population prove that a population might have a mean BMI between normal weight limits while a significant number of people that are outside the specified limits. The proportion of people who were out of the normal weight BMI limits increased in the middle-aged group, and almost all of these individuals were over the USL (figure 3H and table 1). Even though the proportion of people over the USL was almost doubled in the middle-aged groups compared to the young males, the increase in the mean BMI was not that dramatic (figures 3D and 3H; table 1). In the older and elderly groups, the percentages of people outside the specified limits were smaller compared to the middle-age group, and the mean BMIs were lower. The proportion of people over the USL was higher in the elderly group, while the mean BMI was lower compared to those of the old-male group, which had fewer people above the USL (figures 3L and 3P; table 1).

Figure 3.

Plots for the results of normality and capability tests and distribution of individual BMIs between the limits at different stages of the aging process. (A) Capability histogram (n=137, mean=24.38) for young males; (B) Probability plot (normal distribution, p=0.058) for young males; (C) x -control chart using specification limits (35.77% beyond USL, 2.19% beyond LSL) for young males; (D) Tolerance chart (Cp=0.37, Cpk=0.05) for young males; (E) Capability histogram (n=169, mean=26.78) for mid-aged males; (F) Probability plot (normal distribution, p=0.275) for mid-aged males; (G) x-control chart using specification limits (68.64% beyond USL, 0.59% beyond LSL) for mid-aged males; (H) Tolerance chart (Cp=0.28, Cpk=-0.16) for mid-aged males; (I) Capability histogram (n=66, mean=25.87) for old males; (J) Probability plot (normal distribution, p=0.399) for old males; (K) x -control chart using specification limits (50% beyond USL, 4.55% beyond LSL) for old males; (L) Tolerance chart (Cp=0.21, Cpk=-0.06) for old males; (M) Capability histogram (n=39, mean=24.69) for eldest males; (N) Probability plot (normal distribution, p=0.733) for eldest males; (O) x -control chart using specification limits (53.85% beyond USL, 2.56% beyond LSL) for eldest males; (P) Tolerance chart (Cp=0.21, Cpk=0.01) for eldest males

Figure 4.

Plots for the results of normality and capability tests and distribution of individual BMIs between the limits at different stages of the aging process. (A) Capability histogram (n=170, mean=20.27) for young females; (B) Probability plot (normal distribution, p=0.140) for young females; (C) x -control chart using specification limits (4.11% beyond USL, 21.18% beyond LSL) for young females; (D) Tolerance chart (Cp=0.90, Cpk=0.50) for young females; (E) Capability histogram (n=162, mean=24.30) for mid-aged females; (F) Probability plot (normal distribution, p=0.18) for mid-aged females; (G) x -control chart using specification limits (37.65% beyond USL, 3.70% beyond LSL) for mid-aged females; (H) Tolerance chart (Cp=0.26, Cpk=0.05) for mid-aged females;(I) Capability histogram (n=32, mean=27.10) for old females; (J) Probability plot (normal distribution, p=0.89) for old females; (K) x -control chart using specification limits (68.75% beyond USL, 0% beyond LSL) for old females; (L) Tolerance chart (Cp=0.28, Cpk=-0.19) for old females; (M) Capability histogram (n=54, mean=27.07) for eldest females; (N) Probability plot (normal distribution, p=0.794) for eldest females; (O) x -control chart using specification limits (62.96% beyond USL, 0% beyond LSL) for eldest females; (P) Tolerance chart (Cp=0.24, Cpk=-0.17) for eldest females

Similar inconsistencies between the mean BMI and the number of people outside the specification limits in each group were also observed for some female groups, as observed in the male groups. Although a significant number of people were below the LSL, the mean BMI was between the normal weight BMI limits in the young age group (fig. 4C and 4D; table 2). Despite the fact that the proportion of people over the USL was higher in the oldest group compared to those in the elderly-female group, the mean BMIs of both groups were almost equal (fig 4K, 4L, 4O and 4P; table 2).

In fact, these contradictions may be the result of the BMI distribution around the mean and between the specified limits. The distance of individual BMIs from the centerline (mean BMI) and the specified limits should be taken into consideration, as well as the proportion of people outside the specified limits, to decide whether the weight change process is under control in a given population. The number of points falling close to one of the limits affects the mean average of the populations. In some cases, one group might have a lower mean BMI value compared to a group with more people under the LSL; if the individual BMIs are mainly distributed closer to the lower specification limit, the opposite might also be true.

The X-chart results might also be helpful to detect the unnatural variations in the populations, which are referred to as “out of control”, since they exhibit BMI values outside the control limits (UCL and LCL). It may be concluded from the X-charts that some groups were in the state of control and variations around the mean come from the natural sources since there were no BMI values outside the upper and lower control limits (figures 3G, 3K, 3O, 4K and 4O). Further studies should be designed to identify and remove the common causes of the variations in order to achieve a consistent and in-control energy balance in a given group.

A process consistently meets the requirements when it is statistically under control and capable to produce products between specification limits. Capability indices were computed to summarize the comparison of the distribution to the specifications for each group. The Cpk values were less than 1.0 for all groups, even for the groups with a mean BMI in the normal weight ranges and also for the groups which are referred as being “under control” according to the X-charts. Overall, it may be concluded from the capability test results that each age group for both genders were not in energy balance, and a large proportion of the populations had BMIs well above or below the specified (normal) BMI limits.

The results from this article reveal some very important points. Firstly, the mean BMI alone is not an accurate indicator; distribution of individual BMIs around the mean and the limits should also be considered for the assessment of weight characteristics, nutritional status and related health risks of the population. The SQCC could be a helpful tool to tease apart the natural variation (such as dietary habits, gender, food choice, physical activity level) about the mean observed in a population from unnatural variation about the mean that may be due to uncommon causes (such as a change in the availability of soft drinks, fast foods, or healthy foods, moving, chronic diseases). The use of SQCC could help health professionals to monitor the BMI value of each subject in the population against a set of specifications, quickly pick-up any increase in BMI variance about the mean above the natural expected variance and could enable earlier precautions to minimize the increased number of underweight, overweight, and obese people in the population. In the present study upper and lower control limits were based on the WHO suggestions. These limits do not consider age and gender and race differences. There is an ongoing discussion about whether there is a need for modification of these limits to consider these differences (23, 24, 25). As seen in figures 3 and 4, the control limits shifted by age for both genders. This is the clear indication of BMI fluctuation by age. Shifting control limits also means shifting the boundaries for the uncommon variability. This might be the result of natural changes (processes) occurring in the body by age. There might be more common (natural) causes for BMI fluctuations or the effect of the same causes might be different in the body as people get older. This result may point the need for questioning the validity of applying the same BMI cut-off points to all age groups and genders in health and weight management studies.

Conclusion

Statistical Quality Control Charts (SQCCs) have not been previously used in weight management and nutrition studies. This study has successfully demonstrated their application in the characterization of the BMIs of a population based on age and gender. The use of SQCCs provides the researchers with visual monitoring of the individual BMIs in a specified group. This study successfully proved that using the mean BMI, as the only parameter to evaluate the weight status of populations might be misleading. The SQCCs give clearer and more explanative results in weight management studies. The SQCCs could be useful to the nutrition community in terms of monitoring the success of interventions designed to improve BMI or weight in study populations.