Correlation coefficients between longitudinally measured markers in pediatric liver transplant candidates with biliary atresia

Biliary atresia (BA) is the most common pediatric liver disease leading to liver transplantation during childhood, with very poor prognosis if untreated. In this study, we aimed to apply a linear mixed effect (LME) model to estimate the correlation coefficients among longitudinally measured total serum bilirubin, international normalized ratio (INR) for prothrombin time, and serum albumin, the three important prognosis predictors of pretransplant mortality. The dataset was obtained from the Standard Transplant Analysis and Research (STAR) of the United Network of Organ Sharing (UNOS). The primary analysis cohort consists of 1,700 pediatric liver transplant candidates who started their liver transplant waiting list between February 27, 2002 and June 24, 2010 with at least one follow-up measurement and had primary diagnosis of biliary atresia at the time of listing. In applying the LME model, we estimated the longitudinally measured markers via two different correlation structures: autoregressive of order one (AR1) and compound symmetry (CS) in rearranged data by a 7-day equally spaced repeated measures interval. Under the AR(1) structure, the estimated total correlation coefficients between total bilirubin and INR, total bilirubin and albumin, and INR and albumin were 0.4151, -0.2404, and -0.206, respectively, whereas the partial correlation coefficients (within-subject correlation) were 0.0656, 0.0916, and -0.0451, respectively. Under the CS structure, the estimated total correlation coefficients were 0.4307, -0.2432, and -0.1912, respectively and the partial correlation coefficients were 0.1742, -0.0678, and -0.0509, respectively for the above analysis. AR(1) structure had a better fit based on the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Several sensitivity analyses were conducted to understand the stability of the estimated overall correlation. The magnitudes of the estimates obtained from different sensitivity methods do not differ substantially. Public health significance: For two repeatedly measured markers, the total correlation, the between-subject correlation with time-averaged values, and partial correlation for within-subject measurements will provide a more complete picture of the correlations for these markers. Correlation by stacking all measurements of a subject together or between-subject correlation with time-averaged values is a measurement ignoring time effects and could either over or under estimate the total correlation coefficients. The estimated correlations between any two markers measured repeatedly for patients awaiting liver transplantation will give physicians a tool to analyze the relationship between two markers for patients during the waitlist period and may further help physicians understand disease progression and refine treatment strategy for candidates prior to receiving a transplant

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The pairwise correlations among features.

<p>The pairwise correlations among features.</p

The pairwise correlation between the corresponding event time and feature.

<p>The pairwise correlation between the corresponding event time and feature.</p

The minimum, quartile, and maximum error values for predictions of the three events.

<p>The minimum, quartile, and maximum error values for predictions of the three events.</p

The Pearson correlation coefficients among the key event times.

<p>The Pearson correlation coefficients among the key event times.</p

The significance test of comparing our solution with the solution using the SpikeM model.

<p>The significance test of comparing our solution with the solution using the SpikeM model.</p

The significance test of comparing our solution with the solution using all features.

<p>The significance test of comparing our solution with the solution using all features.</p

The significance test of comparing our solution with the solution using the BLR model.

<p>The significance test of comparing our solution with the solution using the BLR model.</p