The National Institute for Health and Care Excellence (NICE) is responsible for assessing new medicines, medical technologies and diagnostics to identify the most clinically- and cost-effective treatments available. This helps to ensure that those products which offer the best value for patients are adopted for use by the NHS and in public health programmes implemented by local government. NICE therefore needs to evaluate the trade-off between how well a new treatment works and how much it will cost.
One method of working out how effective a treatment is, is to look at the average change in life expectancy for the person to whom it was given. However, this does not give the full picture; the quality of life of the patient should also to be taken into account, i.e. factoring-in their ability to carry out daily activities, freedom from pain and mental anguish. All of this information can be combined into one metric, frequently used in health economics, called a quality-adjusted life year (QALY). This is a measure of the life expectancy of a patient, weighted by a quality of life score (on a scale from 0 to 1) over each year. For example, one QALY could represent either 12 months at ‘perfect health’ (a quality of life score of 1), or 24 months at ‘50% health’ (a quality of life score of 0.5). These scores are routinely calculated from questionnaire responses where patients are asked to rate aspects of their quality of life including mobility, ability to self-care and anxiety/depression.
Generally, QALYs are calculated using a naive method. This involves plotting quality of life scores over time and measuring the area under the curve (AUC) individually for each subject included in the study. This fragmented approach does not apply statistical modelling to bring the data together and make inferences across the whole dataset. This leads to limitations in two main areas:
- Bias being introduced where there are missing data for a patient, as there is no natural means of accounting for missing values with this naive approach. This can give rise to inaccurate AUC estimates.
- Inefficient use of the available data. For each patient in a QALY study, we have information about their expected survival and what their quality of life is like. Using the simplistic AUC calculations does not allow us to take account the association between these outcomes; intuitively we expect the quality of someone’s life to be linked with their life expectancy.
These limitations associated with the standard approach to calculating QALYs motivate the use of a more rigorous statistical approach which will enable us to calculate more accurate estimates, more efficiently.
Joint longitudinal-survival modelling can be applied to data including life expectancy and quality of life information to help obtain improved QALY estimates. Joint modelling is a new statistical approach that has recently been developed. It essentially combines two established types of model: mixed effects models and survival models. Mixed effects models are appropriate for analysing longitudinal data, accounting for repeated observations collected for the same subject over time. Survival models are designed to analyse time-to-event data, such as survival times. They account for censoring where, for example, we may only know that the time to the event is greater than the current number of days of follow-up. A joint longitudinal-survival model is designed to analyse datasets that include both of these types of data, allowing inferences to be made about the survival and the quality of life over time trends from a single model.
Data collected to calculate QALYs fit this scenario. For each patient, we have survival times with censoring information, and repeated measurements over time recording the quality of life scores the patients gave. We can combine both types of data into one joint model which can examine the association between patients’ survival and how good their quality of life is, as well as looking at overall trends in survival and quality of life and factors that can affect these two things separately. The joint model also reduces bias due to missing data, by sharing information across all of the subjects included in the study, rather than considering each patient individually (as with the AUC method).
The final fitted model can then be used to estimate QALYs under different scenarios through simulation and taking expectations. For example, they might be used to compare the average QALY for a patient who was taking a new, experimental treatment, with someone taking the standard, currently available treatment. Combining this information with estimates of the costs of each treatment, these results can then be used to assess their cost effectiveness and decide whether it is worth investing in a new treatment.
By applying a more rigorous statistical analysis, joint models can increase both the accuracy and the efficiency of calculating QALY estimates. This in turn can help to improve the service provided to the public by NICE and the NHS in two major ways.
Firstly, by accounting for the correlation between quality of life and life expectancy, joint modelling allows more efficient use of the available data to be made. This may help to reduce the sample sizes required in studies contributing to life expectancy and quality of life estimates, thereby reducing costs and potentially shortening timelines. This will allow decisions to be made more quickly and cost-effectively.
Secondly, by reducing biases and therefore obtaining more accurate QALY estimates, NICE and the NHS can make better informed choices as to which treatments and technologies it would be most cost-effective to spend taxpayers’ money on. This in turn will help improve overall resource management, maximising the health benefits provided for a given cost and leading to an improved service for the public.