Multilevel latent class casemix modelling: a novel approach to accommodate patient casemix

Survival from cancer varies according to many factors including place of diagnosis and treatment centre (Trust), [1, 2] stage at diagnosis, [3, 4] and associated risk factors such as age at diagnosis, sex, and socioeconomic background (SEB) [5–9]. Some Trusts perform better or worse than others in terms of average survival rates perhaps due to patient casemix at the time of entry into the healthcare system, though patient outcome differences will reflect underlying differences in the effectiveness of healthcare organisations. Much interest lies in identifying good and poor performing healthcare providers, to identify best practice and advocate changes in under-performing institutions. It is important to account for patient casemix when evaluating institutional performance and there are currently several strategies.

Regression (linear or logistic) is a traditional and well-documented approach, [10] where variables relating to patient characteristics are modelled, effectively to adjust the outcome in relation to the likely influences of these factors. Methods such as matching, stratification, [10] or propensity score analysis, [11, 12] may also be used, though these techniques make potentially untestable assumptions and never account for the impact of unmeasured variables or accommodate Trust-level variation. Although multilevel modelling accounts for patients nested within Trusts, and provides improved estimates compared with logistic regression, [13, 14] parametric assumptions are made that may not be tenable. Other methods, such as boosted decision trees, [15] have occasionally been used, though these can be difficult to interpret.

No casemix-adjustment strategy will eliminate all bias due to unmeasured differences amongst patients; [16] some procedures increase bias [17]. Accommodating patient variation through measured variables only is crude: models ought to reflect the uncertainty associated with patient casemix characteristics. Furthermore, casemix adjustment does not account for differences in patient treatments. Failure to capture variation in patient pathways and their consequences may result in over-simplistic interpretation of healthcare processes and consequent outcomes. Models need to accommodate patient casemix, the patient experience, and uncertainty in both.

Multilevel latent class (MLLC) modelling is proposed to: (i) adjust for patient casemix whilst accommodating uncertainty surrounding unrecorded patient characteristics; (ii) adjust for patient pathways in terms of the delivery of appropriate healthcare (e.g. treatments); and (iii) differentiate patient outcomes in relation to institutional process characteristics (e.g. delays to treatment). To demonstrate and validate all three steps simultaneously is challenging. The first of these is explored here. We contrast the MLLC model ranking of Trust performance with that of ranks derived from calculating Trust standardised mortality ratios (SMRs). To illustrate our methodology, we study routine data on colorectal cancer patients from a large UK health region.

In a standard multilevel setting, where a continuous latent variable is adopted at the Trust level, the implicit assumption is that Trust-level outcomes have an underlying normal distribution (conditional on Trust-level covariates): Trusts are effectively treated as a random sample of a larger (infinite) population of Trusts. Trusts are not, however, randomly placed geographically and nor are patients randomly assigned to Trusts. Parametric assumptions were therefore replaced by other assumptions which are less restrictive by adopting discrete latent variables, although there remains a degree of geographical dependency that is not accounted for. This remains a limitation. The simplest MLLC model adopted was therefore where the continuous latent variable at the upper level is replaced by a categorical latent variable. The model estimates the mean outcome for each Trust class and the size of each Trust class (summation of Trust probabilities for each Trust class) and no assumptions were made regarding the underlying distribution or class sizes. More complex models can extend this approach to accommodate the spatial dependencies, though this will be part of future developments.

An upper-level discrete latent variable allows for individual Trusts to be assigned probabilistically across the discrete latent classes, providing less restricted weighting of Trust relative performance. This may improve the accuracy of the estimated patient outcome differences across Trust classes, which improves the estimated patient casemix adjustment for individual Trusts. The MLLC model is more likely to capture contextual effects due to the inherent data hierarchy than either a standard multilevel approach or by merely estimating Trust ranks according to their SMRs. Continuous and discrete latent variables, if combined, may prove more parsimonious, with variation within each Trust class captured by the continuous latent variable, potentially leading to fewer Trust classes needed to describe overall Trust-level variation. Where determination of Trust ranks is important, the estimation of Trust outcomes is simpler if the categorical latent variable only is adopted at the Trust level, avoiding derivation of the normally distributed effects within each Trust class. Addressing spatial dependencies amongst the Trusts may nevertheless warrant incorporating upper-level effects.

In fixing patient-level latent class composition and accommodating patient casemix differences, the residual Trust-class differences in outcome reflect variations in Trust performance that depend upon Trust characteristics (differences in the treatments given and healthcare delivery processes). Model improvement might be feasible with more patient-level variables, but this would incorporate incomplete data, which can cause bias. Within a latent class framework the uncertainty surrounding unrecorded or unused patient characteristics is modelled explicitly: 'fuzzy' matching. Trust-level covariates might explain some of the Trust-class outcome differences if included. The optimum number and composition of Trust (and possibly patient) classes may change with the inclusion/exclusion of different covariates.

The probabilities of Trust class membership in Table 3 were marked, with most Trusts belonging entirely or predominantly to one Trust class. This is unsurprising, as there is only a modest difference between the two classes in median survival, and probabilistic assignment differentiates between the two, providing a class weighted combined survival rate. It is not feasible, however, for a Trust to be assigned a class weighted survival rate below that of the poorer survival class, or above that of the better survival class. This is an implicit constraint on the estimated weighted survival for Trusts allocated entirely to one of the two classes (e.g. Trust 1). To alleviate this, more Trust-level classes could be sought, increasing the number until no Trust had a probabilistic assignment of exactly one for classes at the extremities of the range of Trust outcome means. More research is needed, but as applied here, the estimated ranks are robust.

Although the analyses undertaken were primarily for illustration of the proposed methodology, the results are to be taken seriously. Bias may have occurred, however, due to patients with more than one Trust visit having been assigned the most recent Trust visited as the treatment centre. If diagnosis was made at a separate Trust to that which subsequently provided treatment, it would be the latter that was important when modelling healthcare delivery and process variables. In our dataset, 75% of patients visited only one Trust. Nevertheless, some inaccuracies may remain, which could be addressed by screening each patient journey to determine where the majority of interventions take place, or by using multilevel multiple membership models for multiple treatment centres. Furthermore, technically, we have cross-classified data, with patients nested in both area of residence (which yields the patient SEB) and diagnostic centre (Trust); the area level is thus crossed with the Trust level. The number of patients in each area, however, is small and for simplicity of illustration we discarded this level in our model. The methodological principles of MLLC modelling extend theoretically to a cross-classified context, but software does not yet facilitate this.

We have satisfactorily demonstrated the principles of step (i) outlined previously, but there is more research to be undertaken to determine the processes for steps (ii) and (iii), which embark upon modelling patient pathways and the evaluation of process differences that vary across healthcare provider institutions. Distinction could then be made between the delivery of care (e.g. treatments) and health service process characteristics (e.g. delays to treatment) that make up the total patient experience. The proposed methodology paves the way for a more advanced modelling approach to the analysis of treatment centre characteristics (in addition to patient casemix characteristics), where differences in the patient pathway of care are modelled to evaluate organisational features in relation to patient outcomes. Such strategies permit hypothesis generation around which healthcare delivery and organisational features warrant intervention, informing prospective cluster-randomised trials targeted at improving service organisation and delivery. This feeds into existing approaches for quality improvement research, consistent with the principles of the MRC framework for the development and evaluation of complex interventions [28].

The main advantages of the MLLC approach are that it provides accurately derived estimates of the outcome differences across Trust classes, hence improved 'casemix adjustment' for individual Trusts. Trust level covariates may be included, capturing additional casemix complexity. Although deliberately simplified, our illustration demonstrates a principle that could readily extend to a number of more sophisticated scenarios (e.g. time-to-event analysis, multiple treatment centres, cross-classified structures). The MLLC model paves the way to adjust for variations in the patient pathway (especially delivery of appropriate healthcare), permitting the evaluation of institutional processes, which should provide a more robust approach to evaluating institutional performance than is current practice.

The multilevel latent class model used in this study takes the form:

where y _ij is the outcome (death = 1, alive = 0) for patient i within Trust j; is the vector of patient-level covariates; t are the Trust classes (1...T); and c are the patient classes (1...C); p(c|t) is the probability of being in patient class c conditional on being in Trust class t, and in this study C is taken as the same for each Trust. The patient class model, P ^{( c )}, expands to:

where β ₀ ^{( c )} to β ₅ ^{( c )} are the patient-class specific coefficients for the patient-level covariates.