The use of multi-level modelling to investigate the hydrodynamic function of polyurethane prosthetic heart valves (2001)

This thesis applies multi-level statistical modelling methods, which have been developed and mainly used for analysis of educational and sociological data, to a new type of data analysis problem. There are many engineering problems that have a multi-level structure, which cannot be easily analysed by conventional methods. The particular problem investigated here is the statistical comparison of prosthetic valve hydrodynamic function data. Such data has, until now, been presented in a subjective way, with selection of valves for demonstration of the desired behaviour. Few attempts have been made at objective analysis of such data. The data presented here derive from experimental polyurethane valve designs. Of these, two design configurations have the same leaflet polyurethane material and different physical valve designs. The other design configurations use one of the physical engineering valve designs, but fabricate the leaflets out of one of four different polyurethane materials. Data were collected for seven different measures of hydrodynamic function, over a series of five different applied flow rates. The first section of the thesis examines random regression analysis of the data using summary measures to compare two designs. Data were transformed as required to approximate assumptions of normality and equal variance using a natural logarithmic transformation. It was possible to discriminate the two designs on the basis of several hydrodynamic function measures. However, the data were pooled from iterative testing into individual valve regressions (n = 6 for each design), so information about the test reproducibility was lost. The data from each individual valve regression parameter estimate was pooled to provide a mean value to represent each design. Thus information about valve-to-valve reproducibility was lost. Correlation of residuals from the same test run means that the assumption of independence that underlies ordinary regression analysis is not likely to be valid in this case. The first two designs had common regression slopes, but this is unlikely to be the case for all design configurations and would create problems with the random regression method. The data structure, therefore, has a hierarchical nature with test iterations nested within individual valves, and individual valves being members of specific design configuration groups. This data structure suggests that a multi-level modelling approach might provide useful insights, by permitting the simultaneous comparison of the regression lines, accounting for both "different intercepts" and "different slopes", as well as the data hierarchy. The ability of the multi-level modelling approach to use all the information available for a valve should give more power to detect differences between valve types. The multi-level approach is described with reference to various applications of the methodology. The method is then applied first to a single valve design, followed by comparison of the two designs used for the random regression approach initially investigated. The multi-level approach increased the power of discrimination compared with the random regression approach, so that more hydrodynamic function measures demonstrated significant differences between designs. The precision of estimation of the variances was improved in the two-design model compared with the single design model, probably as a result of the greater numbers of valves available for analysis. The analysis was then extended to include five different design configurations. The analysis was also modelled to include different slope parameters as well as different intercept parameters, with design included as a fixed parameter in the model. The outcome of the multi-level modelling is described for each hydrodynamic function measure investigated. The most important measures of valve performance (mean pressure gradient across the open valve, energy losses during forward flow and maximum effective valve orifice area) were capable of successful discrimination among all the valve designs. Variance estimates were also obtained that would enable an estimate of the acceptable degree of variation allowed for any valve within a design or for the repeatability associated with the hydrodynamic function testing itself.