We thank Dr Oyama for his comments and questions, which have prompted us to examine the changes in VHS more closely than was possible in the paper,[1] which was strictly an evaluation of heart size and its rate of increase as diagnostic tests using the recommended monitoring intervals of dogs with mitral valve regurgitation.[2] Concerning measurement variability, although the VHS velocity (∆VHS/month) around the cutoff value of 0.08 is much lower than the 95% limits of agreement[3] for intra-observer variability in Table 3 of the paper,[1] the actual ∆VHS values measured at Interval 1 (interval ending at CHF) (1.33; SD, 0.60), were above the range of intra-observer 95% limits of agreement (Fig 1) and at Interval 2, about the same (0.55; SD, 0.41). Only 9/93 ∆VHS values at CHF were lower than the 95% limits of agreement (Fig 1). The values of ∆VHS/month are much lower because ∆VHS is divided by the number of months in the interval. For measurements of intervals before interval 1, the ∆VHS values were small (mean 0.55) and the denominator large, about 12 (months), decreasing further the values and variability of ∆VHS/month. The measurement variability did not prevent the likelihood ratios for VHS velocity from having a large effect on pretest probability, because the overlap between CHF and not CHF was very small (Fig 1B of the paper).[1]

Although ∆VHS had a slight tendency to increase as the interval ending with CHF (interval 1) increased (y = 0.91 + 0.06 x, R^{2} = 0.13, *P *< .001), ∆VHS/month decreased logarithmically as the interval increased (Fig 2). This decreasing measured ∆VHS/month could not be dependent on ∆VHS but on the duration of the interval. The longer the interval, the greater the true or instantaneous velocity at CHF is underestimated, because ∆VHS is then averaged over more months. The true velocity can only be measured with a relatively short time interval. The shorter the interval, the higher the measured ∆VHS/month (Fig 2), and the closer it is to the true velocity. This explanation assumes that the heart size does not accelerate and then plateau for a while before CHF, an unlikely scenario.[4] True velocities within a few months of CHF are probably close to, or even greater than, the higher values in Figure 2, but it would require frequent (monthly?) monitoring to measure them.

To determine if absolute VHS at time 1 could “alert a clinician to recheck heart size more frequently in the subsequent months,” we looked at the relationships among ∆VHS during interval 1, VHS at the observation before CHF (time 1), and interval 1. Shorter intervals (R^{2} = 0.13, *P *< .001) and higher VHS at time 1 (Fig 1) were associated with less increase in heart size (lower ∆VHS) during interval 1, just before CHF, and the relationship between VHS at time 1 and ∆VHS/month at CHF was not significant (*P *= .55, R^{2} = 0.04). Perhaps heart enlargement after time 1 is limited by interdependence with the lungs or pericardium restricting further dilation and the dog with a high VHS at time 1 may have progressed to a stage where little further change is required to cause the dog to develop signs of pulmonary congestion and edema.

We then did a multivariate regression analysis with months to CHF as the dependent (outcome) variable and VHS at the last measurement and ∆VHS/month at CHF (interval 1) as the independent variables. As the data for ∆VHS/month were not linearly distributed (Fig 2) the values were converted to log_{10}. R^{2} was considerably higher for ∆VHS/month (R^{2} = 0.51) than for VHS (R^{2} = 0.21) (both *P *< .001). Combining the two variables in the same model increased the R^{2} from 0.51 to 0.61 and both variables were still significantly associated with time to CHF. Finally, adding the interaction factor of VHS x ∆VHS/month only marginally increased the model R^{2} to 0.62 (ie, interaction factor was nonsignificant). These results imply that both VHS at the observation before CHF (time 1) and ∆VHS/month are independently predictive of time to CHF, and that ∆VHS/month is a more powerful predictor than VHS at time 1. A regression plot of months to CHF against VHS at all times gave a 95% confidence interval of 5–40 months to CHF for 11.6 VHS units, the cutoff point for dichotomized data at time 1, a range too great to be useful. The overlap between VHS at time 1 and at CHF (Fig 1A of the paper)[1] was too much for VHS at time 1 to reliably detect dogs at risk of impending CHF as was also shown by the wide confidence intervals of the likelihood ratios of test 3 (Table 2 of the paper).[1]

Although absolute VHS is limited in its value to detect when “to initiate more frequent radiographic vigilance”, an *increase* in VHS may be useful. Summary statistics for ∆VHS/month at the interval preceding CHF (interval 2) (Fig 2) were mean and median, both 0.03 ∆VHS units/month; 75^{th} percentile, 0.04 (95% CI, 0.03–0.05); 90^{th} percentile 0.06 (95% CI, 0.05–0.07), and 95^{th} percentile 0.07 (95% CI, 0.06–0.13). At the annual measurement, those dogs which do not develop CHF before the rise is detected at the yearly examination and whose values exceed a selected percentile could be deemed to have entered the risk zone for impending CHF, and could be monitored more frequently, and a risk/benefit analysis done to determine if the veterinarian should “intervene and potentially change the outcome.” We can only guess the most efficient interval (longest interval that gives the desired prediction) that gives the result of detecting impending CHF, as no prospective study has been done.

Concerning “combining absolute VHS *and* rate of change of VHS” at suspected onset of CHF: when their dependence was taken into account,[5] the interval likelihood ratios for both tests (Table 3 of the paper)[1] being positive increased from 13 and 15 respectively to 130 (95% CI, 911-18), and for both tests being negative decreased from 0.04 and 0.05 to 0.01 (95% CI, 0.09-0.002). Simply multiplying them as if they were independent[5] gave likelihood ratios of 195 and 0.002, the difference being due to the dependence between them. When the positive and negative interval likelihood ratios of the combined tests VHS and ∆VHS/month are applied to intermediate < 90 > 10%) pretest probabilities using the nomogram (Fig 3 of the paper),[1] they practically rule in or out the diagnosis of CHF in Cavalier King Charles Spaniels. The limitations of VHS discussed in the paper[1] also apply to the combined test results. In a previous study, 2D echocardiographic dimensions did not seem to have less interdog variability than VHS.[4] Perhaps 3D echocardiographic measurements of chamber volumes and left ventricular eccentricity,[6] independent of dog and breed variations and body size would have the desired accuracy to predict time to CHF, as they are calculated from a detailed reconstruction of the endocardial surface.

To summarize: measurement variation had little effect on the accuracy of ∆VHS/month to diagnose onset of CHF; true ∆VHS/month was underestimated by averaging the change in VHS during the interval before CHF and the true velocity is likely to be much higher than the cutoff value (0.08 VHS units/month) used to derive the likelihood ratio to diagnose CHF; measured rate of change was affected by the time interval; VHS was of little use to predict time to onset of CHF; a rise of ∆VHS/month above a selected percentile of the values at the interval preceding the last one might be a useful sign of impending CHF; combining interval likelihood ratios for VHS and ∆VHS/month greatly improved the accuracy of diagnosis of CHF. The study shows the value of incorporating the element of time dependency from serial measurements as rate of change, a summary of the response over time of each subject.[7]