## 1 Introduction  
Metabolic syndrome (MetS) is a risk factor for cardiovascular disease morbidity and type 2 diabetes mellitus, which can lead to serious disabilities and mortality [1]. Therefore, MetS has become one of the major public health problems worldwide. MetS, also termed insulin resistance syndrome, the deadly quartet, and syndrome X syndrome, is defined as having three or more of five cardiovascular risk factors, including central obesity, hyperglycemia, decreased high density lipoprotein (HDL), elevated triglyceride (TG), and elevated blood pressure [2]. The criteria for MetS usually utilize the three popular definitions provided by the World Health Organization (WHO), the National Cholesterol Education Program (NCEP) Adult Treatment Panel III, and the International Diabetes Federation [3]. MetS is rapidly increasing in Korean society (from 24.9% in 1998 to 29.2% in 2009, and 31.3% in 2007), especially in those in their 50s and older, with a high prevalence rate of more than 40% [4].  
Muscle mass and strength generally increase in adolescents and young people and decrease naturally throughout middle and old age [5]. Handgrip strength (HGS) is a very useful tool because it is an easy and comfortable method for measuring muscle strength [6]. Although muscle mass and muscle strength are highly correlated, muscle strength decreases faster than muscle mass with age [7]. HGS may be a critical important disease predictor because HGS is associated with health outcomes, including type 2 diabetes mellitus (T2 DM) [8], hypertension (HTN) [9], mortality [10], and cognitive impairment [11].  
The use of a relative method for muscle strength is recommended when investigating the association between disease states, because body composition and body size are highly correlated with muscle strength [12; 13]. Relative muscle strength is defined by four popular measuring methods, including body mass index (BMI), body weight, waist circumference (WC), and the waist-hip ratio (WHR) [14; 15].  
Until recently, most studies of HGS, relative HGS, and MetS have reported cross-sectional findings [4; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25], with one follow-up investigation reported [26]. Moreover, adolescent studies have shown that weight relative HGS is associated with MetS [22]. In the median 4-year follow-up survey, weight relative HGS showed significant risk rates in the first and second quartiles for incident MetS (iMetS) in comparison with the high quartile group (1.76 times and 1.67 times for men and 1.28 times and 1.3 times for women, respectively) [26]. In addition, the results of various muscle strength measurements, such as upper body strength/weight and skeleton mass index (SMI), showed significant association with iMetS [27; 28]. Cardiorespiratory fitness is inversely associated with iMetS [29]. To sum up these results, although direct comparison is difficult, the above findings confirm that muscle mass and MetS are related regardless of the muscle mass measurement method or area. Nevertheless, there is no comparison of the effects of HGS, body mass index (BMI), body weight, and WC relative to HGS on metabolic syndrome. Additionally, there were no reported effects of iMetS due to muscle mass changes during the follow-up period.  
Back muscle strength (BMS) decreases with age, similar to HSG, and influences quality of life in older adults [30]. Moreover, the correlation coefficient of HGS and BMS is higher in men (0.67) than in women (0.55) [31]. However, there have been no reports of a relationship between back muscle strength and incident metabolic syndrome. Therefore, this study aimed to assess the relationship between HGS, BMS, BMI-, weight-, WC-relative HGS and BMS, HGS delta change, and iMetS in a 16-year, longitudinal large cohort.