Modelling the effect of a dedicated hip fracture unit on patient outcomes using segmented robust linear regression techniques.

INTRODUCTION: Typically, a healthcare intervention is evaluated by comparing data before and after its implementation using statistical tests. Comparing group means can miss underlying trends and lead to erroneous conclusions. Segmented linear regression can be used to reveal secular trends but is susceptible to outliers. We described a novel method using segmented robust regression techniques to evaluate the effect of introducing a dedicated hip fracture unit (HFU). METHODS: We retrospectively analysed patient outcomes from a total of 2777 patients sustaining proximal femoral fragility fractures over a 6-year period at a Level 1 Major Trauma Centre. We compared time to surgical intervention and length of hospital stay before and after the implementation of the HFU using group comparison tests, segmented ordinary regression and robust regression techniques to evaluate the effect of the intervention. RESULTS: Group comparison tests did not identify a significant difference in time to surgery pre and post- HFU. Segmented regression revealed that there was a significant reduction in time to surgery but that this predated the introduction of the HFU. Group comparison tests did not identify a significant difference in length of stay pre and post-HFU. Ordinary segmented regression demonstrated that there was a constant reduction in length of stay, which accelerated after the introduction of the HFU. Robust regression identified that this change occurred prior to the HFU. DISCUSSION: There was a significant decrease in time to surgical intervention during the study period that occurred long before the introduction of the HFU, and that cannot be attributed to the HFU itself. Length of stay started dropping early in the study period and was unrelated to the HFU. However, with robust regression we concluded that the HFU was effective in reducing relatively long hospital stays (outliers). Several explanatory factors that may have affected the observed trends in time to surgery and length of stay were identified. CONCLUSION: Robust regression is a useful adjunct to ordinary segmented linear regression techniques in modelling retrospective time-series and dealing with outliers. The changes observed in hip fracture patient outcomes over a 6-year period was likely multifactorial.

Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare.

INTRODUCTION: In healthcare, change is usually detected by statistical techniques comparing outcomes before and after an intervention. A common problem faced by researchers is distinguishing change due to secular trends from change due to an intervention. Interrupted time-series analysis has been shown to be effective in describing trends in retrospective time-series and in detecting change, but methods are often biased towards the point of the intervention. Binary outcomes are typically modelled by logistic regression where the log-odds of the binary event is expressed as a function of covariates such as time, making model parameters difficult to interpret. The aim of this study was to present a technique that directly models the probability of binary events to describe change patterns using linear sections. METHODS: We describe a modelling method that fits progressively more complex linear sections to the time-series of binary variables. Model fitting uses maximum likelihood optimisation and models are compared for goodness of fit using Akaike's Information Criterion. The best model describes the most likely change scenario. We applied this modelling technique to evaluate hip fracture patient mortality rate for a total of 2777 patients over a 6-year period, before and after the introduction of a dedicated hip fracture unit (HFU) at a Level 1, Major Trauma Centre. RESULTS: The proposed modelling technique revealed time-dependent trends that explained how the implementation of the HFU influenced mortality rate in patients sustaining proximal femoral fragility fractures. The technique allowed modelling of the entire time-series without bias to the point of intervention. Modelling the binary variable of interest directly, as opposed to a transformed variable, improved the interpretability of the results. CONCLUSION: The proposed segmented linear regression modelling technique using maximum likelihood estimation can be employed to effectively detect trends in time-series of binary variables in retrospective studies.

Segmented Linear Regression Models for Assessing Change in Retrospective Studies in Healthcare.

INTRODUCTION: In retrospective studies, the effect of a given intervention is usually evaluated by using statistical tests to compare data from before and after the intervention. A problem with this approach is that the presence of underlying trends can lead to incorrect conclusions. This study aimed to develop a rigorous mathematical method to analyse temporal variation and overcome these limitations. METHODS: We evaluated hip fracture outcomes (time to surgery, length of stay, and mortality) from a total of 2777 patients between April 2011 and September 2016, before and after the introduction of a dedicated hip fracture unit (HFU). We developed a novel modelling method that fits progressively more complex linear sections to the time series using least squares regression. The method was used to model the periods before implementation, after implementation, and of the whole study period, comparing goodness of fit using F-tests. RESULTS: The proposed method offered reliable descriptions of the temporal evolution of the time series and augmented conclusions that were reached by mere group comparisons. Reductions in time to surgery, length of stay, and mortality rates that group comparisons would have credited to the hip fracture unit appeared to be due to unrelated underlying trends. CONCLUSION: Temporal analysis using segmented linear regression models can reveal secular trends and is a valuable tool to evaluate interventions in retrospective studies.

Modeling Learning in Surgical Practice.

OBJECTIVE: Methods that model surgical learning curves are frequently descriptive and lack the mathematical rigor required to extract robust, meaningful, and quantitative information. We aimed to formulate a method to model learning that is tailored to dealing with the high variability seen in surgical data and can readily extract important quantitative information such as learning rate, length of learning, and learnt level of performance. METHODS: We developed a method where progressively more complex models are fitted to learning data. These include novel models that split the learning data into 2 linear phases and fit adjoining lines using least squares regression. The models were compared and the least complex model was selected unless a more complex one was significantly better. Significance was tested by Fischer tests. We applied this method to total hip and knee replacements using imageless navigation, analyzing the operative time for a surgeon's first 50 and 60 operations, respectively. This method was then tested against 4 sets of simulated learning data. RESULTS: The proposed method of progressive model complexity successfully modeled the learning curve among real operative data. It was also effective in deducing the underlying trends in simulated scenarios, created to represent typical situations that can practically arise in any learning process. CONCLUSIONS: The novel modeling method can be used to extract meaningful and quantitative information from learning data displaying high variability seen in surgical practice. By using simple and intuitive models, the method is accessible to researchers and educators without the need for specialist statistical knowledge.