cardiorespiratory fitness ( crf ) maintenance is important for functional independence and physical capacity throughout aging [ 1 , 2 ] .
substantial declines in the ability to tolerate physical exertion generally predict mobility problems and cardiovascular morbidity and mortality , particularly in the sedentary elderly [ 3 , 4 ] . despite the importance of crf assessment , very low functional capacity and frailty
may hinder the use of exercise tests in this population [ 5 , 6 ] . in this context ,
nonexercise prediction models become practical alternatives to estimate crf   and may have important applications both in clinical and epidemiological settings .
these models are developed by means of regression - based equations that usually include variables of simple and fast assessment , such as anthropometric measures , demographic characteristics , and daily habits .  
cross - validated an equation developed primarily in middle - aged adults by jurca et al .   and suggested that nonexercise models could be used to estimate the crf of older adults .
however , the prevalence of chronic diseases such as cardiovascular disease and diabetes increases dramatically with age , and is associated to lower physical capacity , inactivity , and limitations in the ability to exercise
. it would be therefore important to take into account that elderly populations are not always healthy and free of cardiovascular and metabolic diseases , which on the contrary , are common in the later life . notwithstanding to date nonexercise models to assess the crf in elderly subjects with chronic diseases
hence the present study aimed to develop a crf nonexercise prediction linear model of cardiorespiratory fitness and test its validity in elderly men presenting chronic cardiovascular and metabolic diseases .
the sample consisted initially of 108 subjects admitted to the elderly care center of the open university of the third age ( unati ) of the rio de janeiro state university ( uerj ) .
these subjects went through clinical exams in order to detail their medical history and completed a brief questionnaire providing demographic information , which was used to determine whether they could perform maximal aerobic exercise testing .  
the inclusion criteria were asymptomatic patients , stable disease , and no abnormalities in rest electrocardiogram for at least six months .
tests interrupted due to clinical reasons were not considered as maximal and therefore have been excluded from the study .
twelve participants did not complete the exercise testing ( five were not allowed by the physicians to perform the test , four asked to stop before achieving maximal effort , and three exhibited high blood pressure ) . from the initial sample ,
a total of 96 subjects remained in the study ( 6091 years ) , being randomly assigned into two groups : validation ( 70% ) and cross - validation ( 30% ) .
the command  sample 70  from stata statistical package version 10.1 ( stata , college station , tx ) was used with this purpose .
the validation group was used to develop the statistical model while the cross - validation group was used to confirm the generalization potential of the obtained model .  
the experimental protocol was approved by institutional ethical committee and participants provided a written informed consent for the use of their data for research prior to the commencement of the study , as stated in the declaration of helsinki .
individual data on anthropometry , self - reported physical fitness , and physiological measurements were assessed .
anthropometric measurements included weight and height   from which the body mass index ( bmi ) was calculated .
the physical activity history was assessed by the self - reported physical activity index ( srpa ) .
the subjects were asked to choose one of five activity categories that best described their usual pattern of daily physical activities .
self - rated fitness was evaluated by means of the rating of perceived capacity scale ( rpc ) , a 1 - 20-scale previously adapted and translated to the brazilian portuguese language , in which the subject chooses the most strenuous activity that can be sustained for at least 30  min . the rpc score is expressed in mets and the listed activities include walking , jogging , running , and cycling at different paces . instead of asking of the physical activity history ,
the blood pressure at rest and during exercise was measured by auscultation with a sphygmomanometer welchalln ( tycos , arden , mn , usa ) .
a 12-lead electrocardiogram was used to assess the resting heart rate ( rhr ) and maximal heart rate ( micromed , brasilia , df , brazil ) .
handgrip strength ( hg ) was measured with subjects keeping their shoulder adducted and neutrally rotated , with the arm fully extended and being encouraged to exert maximal grip force on a lafayette dynamometer 78010 ( lafayette , in , usa ) .
the highest value in kilograms ( kg ) was determined after four trials in the dominant and nondominant hands and the relative handgrip strength ( i.e. , handgrip strength normalized to body weight and represented as the ratio handgrip / weight ) was then used for further analyses .
all subjects performed a clinically supervised maximal exercise test in an electromagnetically braked cycloergometer ( cateye ec-1600 , osaka , japan ) using an individualized ramp protocol .
subjects were submitted to a familiarization trial to get used to the cycloergometer and mouthpiece on the day prior to the exercise test .
prediction equation was used to estimate the test incremental workload in watts in order to achieve maximal exertion in approximately 10 minutes .
paul , mn , usa ) was used for gas exchange measures , using a medium flow pneumotachometer ( 10120  lmin ) .  
peak oxygen uptake ( vo2  peak ) was determined as the maximal oxygen uptake at the point of test termination due to volitional exhaustion .
the borg cr-10 perceived exertion scale was used to estimate the degree of exertion   and standard clinical criteria for terminating exercise testing have been applied . before each test
, the equipment was calibrated as recommended by the manufacturer , using standard reference gases .
the test was considered maximal when at least two of the following criteria were observed : ( a ) respiratory exchange ratio ( rer ) > 1.1 , ( b ) vo2 plateau despite an increase in workload ( increase < 2.0  mlkgmin between the last two loads ) , and ( c ) maximum volitional exhaustion .
differences between the validation and cross - validation groups were analyzed by t - test student 's and chi - square tests .
age , relative strength index ( handgrip strength / body weight ) , an anthropometric measure ( bmi ) , self - related fitness ( rpc scale ) , self - related physical activity ( srpa index ) , and resting heart rate ( rhr ) were entered , respectively , into the first , second , third , fourth , fifth , and sixth blocks of the hierarchical linear regression procedure to develop a model to predict metpeak ( i.e. , the number of mets achieved at vo2  peak ) .   the coefficient of determination ( r ) and the standard error of estimate ( see ) were calculated and the prediction equation generated
was then cross - validated using the press method ( predicted residual sum of squares ) , a statistical jack - knife procedure that consists of refitting the proposed model many times , leaving each observation out of the model fit in turn , so as to predict and then calculate the residual for that observation .
the second series of cross - validation analyses based on the independent sample was performed using the pearson correlation between the metpeak predicted by the model and the metpeak measured , as well as the difference between the crf estimated by the prediction model and measured crf ( defined in the maximal exercise testing ) was analyzed by the t - test .
a bland - altman analysis of measurement differences plotted versus mean values was used to assess the degree of agreement .   in order to evaluate the accuracy of the model in screening individuals that present very low cardiorespiratory fitness , and
therefore are at higher risk for mortality and morbidity , a disability index was used to dichotomize crf .
basically , the crf level below which successful independent living is significantly compromised ( i.e. , 5 mets ) , was used as a cutoff to calculate the model sensitivity , specificity , and the area under the receiver operation curve ( auc ) . a 95% confidence interval ( 95% )
the auc is a measure of diagnostic power of the model and describes the probability that the model will correctly identify subjects with low crf .
the predicted and measured crf categories from the validation and cross - validation groups were cross - tabulated to detect classification accuracy .

 table 1 presents the descriptive statistics , as well as values for cardiorespiratory variables at rest and in response to maximal exercise for subjects in both validation and cross - validation groups .
these groups did not significantly differ in any of the variables studied ( p > 0.05 ) .
all subjects attended at least two of the criteria adopted to consider the cardiopulmonary exercise testing as maximal : respiratory exchange ratio ( rer ) > 1.1 ( 87% of the sample ) , vo2 plateau despite an increase in workload ( 75% ) , and ( c ) maximum volitional exhaustion ( 100% ) .  
three levels of physical activity were detected by the srpa index : inactivity or little activity other than usual daily activities ( 58% of the whole sample ) , participation in physical activities requiring low levels of exertion that result in slight increases in breathing and heart rate for at least 10 minutes at a time ( 38% ) , and participation in aerobic exercises such as brisk walking , jogging or running , cycling , swimming , or vigorous sports at a comfortable pace or other activities requiring similar levels of exertion for 20 to 60 minutes per week ( 4% ) .
only three of four variables were significantly associated ( p < 0.01 ) with crf after the linear regression procedure ( table 2 ) .
age , relative handgrip strength , and rpc explained 44% , 22% , and 13% of crf variance , respectively .
the bmi ( r = 0.003 , p = 0.44 ) , srpa index ( r = 0.003 , p = 0.37 ) , and rhr ( r = 0.001 , p = 0.53 ) were not significant predictors .
based on the r value , the obtained model explained 79% of the variability in vo2  peak .
the low shrinkage of adjusted r and the r - press conferred a good generalization to the model .
the following prediction equation was generated from the coefficients presented in table 2 : metpeak = 6.095  0.096
( age ) + 8.84 ( handgrip strength / weight ) + 0.67 ( rpc ) .
once the statistical model was established it was then further tested in an independent sample for cross - validation .
there were no significant differences between predicted crf mean and actual crf mean in both validation and cross - validation groups ( figure 1 ) .
the pearson correlation coefficient between predicted and actual crf in the cross - validation group was 0.85 ( p < 0.01 ) , ratifying that the model was appropriate to estimate crf in elderly subjects with cardiovascular and metabolic diseases .
the bland altman analysis ( figure 2 ) showed that few values fell outside the ranges established by the 2 sds , which suggests a good agreement between the values estimated by the statistical model and the actual met values .  

table 3 exhibits the model accuracy from the validation and cross - validation groups after diagnostic tests .
the model was almost equally efficient in identifying subjects with crf  5 mets and with crf > 5 mets .
the auc further confirmed the high accuracy of the model in screening subjects presenting crf either below or above 5 mets .
  the negative effect of aging on crf as well as the use of self - reported fitness are both well documented in the literature and are frequently included in prediction models [ 8 , 20 ] . although not previously used in other models , the relative handgrip strength was a very significant predictor of crf in the present study .
one could argue that the inclusion of handgrip strength may limit the widespread applicability of this equation , given that it requires equipment that may not be routinely used in epidemiological studies .
in fact , the handgrip dynamometry has been a very important tool to assess the functional status of elderly samples , and the inclusion of this measurement in epidemiological settings should be reconsidered .
the handgrip strength test is very simple and inexpensive , and has been previously related to mortality , mobility , functional capacity , and correlated with walking speed and overall strength , which are variables strongly related to the functional independence and health in older persons [ 1 , 21 , 22 ] .   despite of the fact that 79% ( r ) of variance in the prediction of crf was explained by the obtained statistical model , the see ( table 2 )
suggests that more precise methods as maximal tests are recommended if the exactly crf value is needed .
on the other hand , the auc values ( table 3 ) suggested that the model has good accuracy to stratify elderly men with very low ( i.e. , crf  5 mets ) and higher cardiorespiratory capacity ( i.e. , crf > 5 mets ) .
in other words , the model was capable to identify elder subjects whose functional and exercise capacity are compromised .
based on this finding , the proposed model can be useful for population - based investigations or epidemiological studies , especially those searching for associations between crf and other physical and mental health outcomes , such as cognitive function and wellbeing . in clinical studies our model
mailey et al .   tested the validity of the nonexercise model proposed by jurca et al .  
in old adults , and reported a multiple r of 0.72 ( p < 0.001 ) for the regression in a sample composed mainly of old women , which were somewhat more physically active than our subjects .
our model was developed in a sample of elderly men with cardiovascular and metabolic diseases and produced a multiple r of 0.89 ( p < 0.001 ) .
it is also worthy to note that metabolic and cardiovascular diseases in the elderly are highly prevalent , reinforcing the relevance of the present model for this population .  
although comparisons between the two models are difficult because they were developed in different populations , we have included variables from mailey 's model in our regression model , and they were not significant .
we have also compared the crf estimation accuracy of the models , and the results were favorable to the present equation ( mailey 's model in the validation group : r = 0.47 ; epe = 1.7 mets , and in the cross - validation group : r = 0.33 ; epe = 1.6 mets ) .   the adoption of a cycloergometer maximal exercise testing protocol to assess the metpeak must be justified .
although treadmill tests are known to engage larger muscle mass and therefore may elicit higher peak vo2 [ 16 , 23 ] , some authors have proposed that cycloergometer tests would be more appropriate to assess the cardiorespiratory fitness in older subjects , mainly for safety reasons .
for instance , it has been suggested that high - intensity treadmill exercise should be avoided in older subjects with balance restrictions or joint problems . moreover , the poor mechanical efficiency while running seems to reduce the performance of older compared to younger subjects during treadmill exercise , which would very likely limit the peak vo2 in maximal cardiopulmonary tests .
such limitation has been considered by previous research that adopted cycloergometer protocols to assess the cardiorespiratory fitness in older populations [ 4 , 26 ] .
the main finding of this study was that crf of elderly men with cardiovascular and metabolic diseases and low physical capacity can be classified without aerobic tests using a combination of information on the subject 's daily activity levels , relative handgrip strength , and a self - report of physical fitness level .
maximal aerobic tests have a higher cost , demand familiarization with ergometers , and are frequently difficult to perform in old adults due to poor balance and coordination , gait problems , and fear of exercising .
it is also worthy to mention that the accuracy of some submaximal exercise testing models to estimate crf [ 28 , 29 ] could be comparable to the accuracy of the present prediction model .
it also represents an alternative to some walking tests because it does not require encouragement , which can be a source of disparity across trials , and does not require fatigue and dyspnea measurements .  
this study has some limitations , namely , the relatively small sample size , the prediction model restricted to unhealthy men .
it is worthy to mention that since running tests may potentially produce higher metpeak values , the reproducibility of our findings in treadmill exercise testing should also be addressed , despite the fact that cycloergometer tests are frequently indicated due to safety and mechanical efficiency reasons .
probably , changes in age , handgrip strength , and self - related fitness would influence the functional capacity and the mets levels , but only longitudinal studies could confirm this possibility .
additionally , the main objective of the present study was similar to other studies that developed nonexercise models , which were not conceived to detect slight longitudinal variations . in brief , the model aims to classify and compare individuals within a given population , and does not intend to replace cardiopulmonary exercise testing to precisely assess the crf .
therefore , it is possible that small changes in crf due to training can not be detected by our equation .
however , the crf assessment is usually limited due the mobility issues and the risk of cardiovascular events especially in older people with chronic conditions .
the present study presented an accurate fitness prediction model for elderly men with cardiovascular and metabolic diseases .
the model provides a very fast and safe assessment of fitness , without any chance for cardiovascular events during assessment , which could be very feasible in many healthcare settings to estimate crf and stratify elderly subjects accordingly , and very attractive for epidemiological studies .
 low cardiorespiratory 
  ( crf ) is associated with health problems in elderly people , especially cardiovascular and metabolic disease . 
 however , physical limitations in this population frequently preclude the application of aerobic tests . 
 we developed a model to estimate crf without aerobic testing in older men with chronic cardiovascular and metabolic diseases . 
 subjects aged from 60 to 91 years were randomly assigned into validation ( n = 67 ) and cross - validation ( n = 29 ) groups . 
 a hierarchical linear regression model included age , self - reported fitness , and handgrip strength normalized to body weight ( r2 = 0.79 ; see  =  1.1 mets ) . 
 the press ( predicted residual sum of squares ) statistics revealed minimal shrinkage in relation to the original model and that predicted by the model and actual crf correlated well in the cross - validation group ( r = 0.85 ) . 
 the area under curve ( auc ) values suggested a good accuracy of the model to detect disability in the validation ( 0.876 , 95% ci : 0.7930.959 ) and cross - validation groups ( 0.826 , 95% ci : 0.6770.975 ) . 
 our findings suggest that crf can be reliably estimated without exercise test in unhealthy elderly men . 
1. Introduction
2. Materials and Methods
3. Results
4. Discussion
5. Conclusion