The results of our study, all other individual studies and all data combined showed that 6 MWD and peak VO2 were significantly correlated. Although, the site-specific prediction equations, which are presented in Table 1, differed somewhat, they all had large SEE's, particularly as a percent of mean peak VO2. LMM analysis showed that inter-site variability such as disease type and different testing protocols did not substantially increase the SEE. The LMM II error estimates for the fixed (3.82 ml/kg/min) and random models (3.66 ml/kg/min), although statistically significantly different, were almost identical. The fixed effects SEE of 3.82 ml/kg/min is the average error estimate of all sites . The random effects SEE of 3.66 ml/kg/min is the SEE statistically excluding all factors associated with variability among the sites and study groups by utilizing empirical Bayes predictor, or the best linear unbiased predictor , which accounts for the variability among test sites. The degree of error that is due to differences in test site variation was just 0.16 ml/kg/min or 4% of the SEE. The analysis of the residuals in Figure 3 documents this small difference in measurement error. This finding indicates that a generalized equation can be used to estimate peak VO2 from 6 MWD with little loss of accuracy. Generalized across the 11 test sites, the SEE was 3.82 ml/kg/min, which was about 27% of mean peak VO2.
Intuitively, it might be thought that inter-site factors would have a larger effect on the SEE. Most of the authors from the 10 additional studies we evaluated used patients with a uniform disorder and exercised them in a uniform manner in an attempt to minimize any error introduced by these factors. However, our study found that these factors were a minor source of error. We believe this is because the major source of error is the random, inherent, within-subject measurement errors associated with CPET and the 6 MWT. In this regard, although the test-retest reliability for peak VO2 from CPET for normal people has been found to be about 0.96, this represents a standard error of measurement of about 2 ml/kg/min . Similar results have been found for patients. A group of patients with fibrotic interstitial pneumonia had a coefficient-of-variation of 10.5% of peak VO2. This represented approximately 2 to 2.5 ml/kg/min . This value is about 15% of the mean peak VO2 of the pooled patient data we obtained.
The 6 MWT also has significant inherent variability. In one study, the within-subject variability for 6 MWD was 4.2% or about ± 34 m . In another study, after an initial learning period, patients with chronic heart or lung disease had a within-person standard deviation for 6 MWD of about 6%. This represented a 95% likelihood of about ± 40 m . Since the vast majority of the patients evaluated in the studies we reviewed had a 6 MWD between 200 and 600 m, this could lead to as much as 20% variability in 6 MWD. Based on the correlation equation we obtained, this could contribute an additional error in estimating peak VO2 of about +/- 1 ml/kg/min.
Although walking is an aerobic activity and, for people with significant aerobic limitation, may be a maximal exercise activity, there are many reasons why people with a similar peak VO2 might have a different 6 MWD. The 6 MWT is a voluntary effort where the person's walking speed can vary and the person might even stop and rest for a period of time. Two people with the same peak VO2 might choose different walking strategies. One might walk more slowly, the other faster but rest periodically. Patients might chose different average walking speeds based on physiological factors such as work-of-breathing, auto-PEEP , work-of-the-heart or how much carbon dioxide retention the individual can comfortably tolerate. For example, in a group of patients with congestive heart failure, the VO2 measured at the end of the 6 MWT was on average 15% lower than peak VO2. However, it was equal to or higher than measured peak VO2 from CPET in about 25% of the patients . Psychological factors such as anxiety or a patient's unique perception of pain, dyspnea or discomfort due to their abnormal physiology also can affect 6 MWD. In this regard encouragement has been shown to increase 6 MWD in sick patients .
If the test-retest variations are random for both peak VO2 and 6 MWD measurements, as would be expected, it is not surprising that we obtained a SEE of 3.66 ml/kg/min independent of the error introduced by site differences. It is unlikely that utilizing a different walk time would improve predictive accuracy, as the physiological principles are the same. Similar correlations and standard errors have been found utilizing the two and the twelve-minute walk tests [21, 22] as well as for predicting peak VO2 from maximal exercise treadmill time .
It is possible that part of the large SEE may not have come from the intrinsic variability of the testing techniques but from improper patient selection. The physiologic basis behind utilizing the 6 MWT to estimate peak VO2 is that maximal exercise tests correlate quite well with peak VO2 . However, the 6 MWT is a submaximal exercise test for most people with normal or mild-to-moderately reduced aerobic capacity. Submaximal exercise tests require some estimate of internal effort, such as exercise heart rate so that maximal exercise capacity can be predicted, before they can be used to adequately estimate peak VO2. That is, if the 6 MWT is a submaximal effort, there is no physiologic basis for a close correlation between maximal walking speed and peak VO2. Therefore, it is possible that including people whose 6 MWD was not limited by aerobic factors might have affected the size of the SEE we found. In normal people, the distance walked in 6 minutes of voluntary non-markedly-encouraged walking does not vary due to peak VO2 but to other factors such as gait limitation . Normative values for the 6 MWT have been published . For a 60 year old man, the lower limit of normal would be about 450 m. To exclude the effect that people with a potentially normal aerobic capacity might have on the SEE, we analyzed the combined data using only subjects who walked <450 m. There were 742 patients in this group. The mean peak VO2 was 12.9 ml/kg/min and the SEE for this group was +/- 3.44 ml/kg/min or 26.7% of the mean. Thus, even when patients with potentially normal functional capacity are excluded, the accuracy for estimating an individual's peak VO2 is poor. This indicates that the large SEE that we observed was not due to improper patient selection.
Although the SEE is 3.82 ml/kg/min when predicting an individual's peak VO2, it is only 1.1 ml/kg/min when predicting the mean peak VO2 of a study group (Table 4). This much smaller SEE also indicates that inter-site factors are not as important as the intrinsic variability of the test results. Further, this finding suggests the variability is random because with larger numbers, random effects would tend to cancel out and the SEE would be smaller. This is what we found.
A meta analysis is used to combine data from several studies to expand generalizability. The common method is to use the means of published results weighted by sample size. This is the first instance, to our knowledge, to reproduce data at the individual level from scanned scattergrams. Our comparative analyses of the scanned and published data documented that the errors were small and likely random. The major advantage of this approach is that we cannot only examine mean differences, but more importantly, estimate individual variation. This is shown by comparing the results provided in Figures 2 and 3 and the data in Table 4. The error analysis in Figure 3 showed that 33% of individual differences between measured and peak VO2 estimated with the fixed effect equation (LMM II) were greater than ± 3.5 ml/kg/min and nearly 20% were greater than ± 5 ml/kg/min. In contrast, the data in Table 4 shows that when the level of analysis was the average value, the prediction error was quite small, varying from -2.1 to 1.8 ml/kg/min. The correlation between peak VO2 and 6 MWD for all 1,083 individual patient data was 0.59. The correlation between peak VO2 and 6 MWD for the means of the 11 data sets was 0.82.
Our findings suggest that 6 MWD has too large of a SEE to be clinically useful for estimating peak VO2 for an individual. However, we were able to obtain only 6 MWD and peak VO2 for each data point. It is possible that with more information, and utilizing multiple linear regression analysis, a more accurate equation could have been derived. Several studies have utilized multiple linear regression analysis for patients with uniform diseases exercised with uniform protocols and still had relatively large standard errors [2, 3, 27]. Therefore, we doubt that this would dramatically improve accuracy.
Although the 6 MWT does not accurately predict an individual's peak VO2, many investigators have found it useful for therapeutic decision-making in moderate-to-severely ill patients . 6 MWD has also been found to correlate reasonably well with the New York Heart Association (NYHA) lower functional classes . The 6 MWT may act as a somewhat more objective, expanded NYHA scale  which could potentially allow researchers to monitor more subtle changes in exercise capacity in an individual or in a group. In this regard, serial exercise testing over about one year revealed that changes in peak VO2 were directly proportional to changes in 6 MWD .
Presently, no equation has been published that allows estimation of mean peak VO2 from mean 6 MWD across a large spectrum of patient groups with different diseases and exercise protocols. Our study provides this equation. Its accuracy is similar to population specific equations. However, when using this equation researchers should be cautious to exclude individuals whose 6 MWD is not limited by aerobic factors as this could lead to large errors. Maximum walking speed is generally less than 4-4.5 mph or about 700 m. in six minutes. Only 5 people in the studies we reviewed had a 6 MWD > 700 m. Based on the equation we derived, a 6 MWD of 700 m would predict a peak VO2 of about 21 ml/kg/min. In one of the studies we reviewed, the peak VO2 and 6 MWD of 10 normal subjects were reported . Peak VO2 ranged from 26 to 35 ml/kg/min. The corresponding 6 MWD for these two subjects, at the extremes, were 666 m and 700 m, respectively. Our predictive equation would estimate a peak VO2 of 21.3 and 22.2 ml/kg/min. That is, utilizing the equation we derived, 6 MWD poorly predicts, and substantially underestimates, peak VO2 in people with a relatively normal aerobic capacity. Thus, people with a peak VO2 above about 20 ml/kg/min should be excluded from the group, when utilizing the equation we derived, to estimate mean peak VO2. If an individual's peak VO2 is not known, we recommend utilizing the equation only for people with moderate-to-severe heart or lung disease, excluding people whose 6 MWD is above 600 meters, as few of the patients we evaluated walked further than this and this value would estimate a peak VO2 of about 20 ml/kg/min.