Cost-effectiveness analysis in health care (I)
Yesterday’s SMBC was awesome, and I couldn’t help myself from including it here (click to view full size):
In a way the three words I chose to omit from the post title are rather important in order to know which kind of book this is – the full title of Gray et al.’s work is: Applied Methods of … – but as I won’t be talking much about the ‘applied’ part in my coverage here, focusing instead on broader principles etc. which will be easier for people without a background in economics to follow, I figured I might as well omit those words from the post titles. I should also admit that I personally did not spend much time on the exercises, as this did not seem necessary in view of what I was using the book for. Despite not having spent much time on the exercises myself, I incidentally did reward the authors for including occasionally quite detailed coverage of technical aspects in my rating of the book on goodreads; I feel confident from the coverage that if I need to apply some of the methods they talk about in the book later on, the book will do a good job of helping me get things right. All in all, the book’s coverage made it hard for me not to give it 5 stars – so that was what I did.
I own an actual physical copy of the book, which makes blogging it more difficult than usual; I prefer blogging e-books. The greater amount of work involved in covering physical books is also one reason why I have yet to talk about Eysenck & Keane’s Cognitive Psychology text here on the blog, despite having read more than 500 pages of that book (it’s not that the book is boring). My coverage of the contents of both this book and the Eysenck & Keane book will (assuming I ever get around to blogging the latter, that is) be less detailed than it could have been, but on the other hand it’ll likely be very focused on key points and observations from the coverage.
I have talked about cost-effectiveness before here on the blog, e.g. here, but in my coverage of the book below I have not tried to avoid making points or including observations which I’ve already made elsewhere on the blog; it’s too much work to keep track of such things. With those introductory remarks out of the way, let’s move on to some observations made in the book:
“In cost-effectiveness analysis we first calculate the costs and effects of an intervention and one or more alternatives, then calculate the differences in cost and differences in effect, and finally present these differences in the form of a ratio, i.e. the cost per unit of health outcome effect […]. Because the focus is on differences between two (or more) options or treatments, analysts typically refer to incremental costs, incremental effects, and the incremental cost-effectiveness ratio (ICER). Thus, if we have two options a and b, we calculate their respective costs and effects, then calculate the difference in costs and difference in effects, and then calculate the ICER as the difference in costs divided by the difference in effects […] cost-effectiveness analyses which measure outcomes in terms of QALYs are sometimes referred to as cost-utility studies […] but are sometimes simply considered as a subset of cost-effectiveness analysis.”
“Cost-effectiveness analysis places no monetary value on the health outcomes it is comparing. It does not measure or attempt to measure the underlying worth or value to society of gaining additional QALYs, for example, but simply indicates which options will permit more QALYs to be gained than others with the same resources, assuming that gaining QALYs is agreed to be a reasonable objective for the health care system. Therefore the cost-effectiveness approach will never provide a way of determining how much in total it is worth spending on health care and the pursuit of QALYs rather than on other social objectives such as education, defence, or private consumption. It does not permit us to say whether health care spending is too high or too low, but rather confines itself to the question of how any given level of spending can be arranged to maximize the health outcomes yielded.
In contrast, cost-benefit analysis (CBA) does attempt to place some monetary valuation on health outcomes as well as on health care resources. […] The reasons for the more widespread use of cost-effectiveness analysis compared with cost-benefit analysis in health care are discussed extensively elsewhere, […] but two main issues can be identified. Firstly, significant conceptual or practical problems have been encountered with the two principal methods of obtaining monetary valuations of life or quality of life: the human capital approach […] and the willingness to pay approach […] Second, within the health care sector there remains a widespread and intrinsic aversion to the concept of placing explicit monetary values on health or life. […] The cost-benefit approach should […], in principle, permit broad questions of allocative efficiency to be addressed. […] In contrast, cost-effectiveness analysis can address questions of productive or production efficiency, where a specified good or service is being produced at the lowest possible cost – in this context, health gain using the health care budget.”
“when working in the two-dimensional world of cost-effectiveness analysis, there are two uncertainties that will be encountered. Firstly, there will be uncertainty concerning the location of the intervention on the cost-effectiveness plane: how much more or less effective and how much more or less costly it is than current treatment. Second, there is uncertainty concerning how much the decision-maker is willing to pay for health gain […] these two uncertainties can be presented together in the form of the question ‘What is the probability that this intervention is cost-effective?’, a question which effectively divides our cost-effectiveness plane into just two policy spaces – below the maximum acceptable line, and above it”.
“Conventionally, cost-effectiveness ratios that have been calculated against a baseline or do-nothing option without reference to any alternatives are referred to as average cost-effectiveness ratios, while comparisons with the next best alternative are described as incremental cost-effectiveness ratios […] it is quite misleading to calculate average cost-effectiveness ratios, as they ignore the alternatives available.”
“A life table provides a method of summarizing the mortality experience of a group of individuals. […] There are two main types of life table. First, there is a cohort life table, which is constructed based on the mortality experience of a group of individuals […]. While this approach can be used to characterize life expectancies of insects and some animals, human longevity makes this approach difficult to apply as the observation period would have to be sufficiently long to be able to observe the death of all members of the cohort. Instead, current life tables are normally constructed using cross-sectional data of observed mortality rates at different ages at a given point in time […] Life tables can also be classified according to the intervals over which changes in mortality occur. A complete life table displays the various rates for each year of life; while an abridged life table deals with greater periods of time, for example 5 year age intervals […] A life table can be used to generate a survival curve S(x) for the population at any point in time. This represents the probability of surviving beyond a certain age x (i.e. S(x)=Pr[X>x]). […] The chance of a male living to the age of 60 years is high (around 0.9) [in the UK, presumably – US] and so the survival curve is comparatively flat up until this age. The proportion dying each year from the age of 60 years rapidly increases, so the curve has a much steeper downward slope. In the last part of the survival curve there is an inflection, indicating a slowing rate of increase in the proportion dying each year among the very old (over 90 years). […] The hazard rate is the slope of the survival curve at any point, given the instantaneous chance of an individual dying.”
“Life tables are a useful tool for estimating changes in life expectancies from interventions that reduce mortality. […] Multiple-cause life tables are a way of quantifying outcomes when there is more than one mutually exclusive cause of death. These life tables can estimate the potential gains from the elimination of a cause of death and are also useful in calculating the benefits of interventions that reduce the risk of a particular cause of death. […] One issue that arises when death is divided into multiple causes in this type of life table is competing risk. […] competing risk can arise ‘when an individual can experience more than one type of event and the occurrence of one type of event hinders the occurrence of other types of events’. Competing risks affect life tables, as those who die from a specific cause have no chance of dying from other causes during the remainder of the interval […]. In practice this will mean that as soon as one cause is eliminated the probabilities of dying of other causes increase […]. Several methods have been proposed to correct for competing risks when calculating life tables.”
“the use of published life-table methods may have limitations, especially when considering particular populations which may have very different risks from the general population. In these cases, there are a host of techniques referred to as survival analysis which enables risks to be estimated from patient-level data. […] Survival analysis typically involves observing one or more outcomes in a population of interest over a period of time. The outcome, which is often referred to as an event or endpoint could be death, a non-fatal outcome such as a major clinical event (e.g. myocardial infarction), the occurrence of an adverse event, or even the date of first non-compliance with a therapy.”
“A key feature of survival data is censoring, which occurs whenever the event of interest is not observed within the follow-up period. This does not mean that the event will not occur some time in the future, just that it has not occurred while the individual was observed. […] The most common case of censoring is referred to as right censoring. This occurs whenever the observation of interest occurs after the observation period. […] An alternative form of censoring is left censoring, which occurs when there is a period of time when the individuals are at risk prior to the observation period.
A key feature of most survival analysis methods is that they assume that the censoring process is non-informative, meaning that there is no dependence between the time to the event of interest and the process that is causing the censoring. However, if the duration of observation is related to the severity of a patient’s disease, for example if patients with more advanced illness are withdrawn early from the study, the censoring is likely to be informative and other techniques are required”.
“Differences in the composition of the intervention and control groups at the end of follow-up may have important implications for estimating outcomes, especially when we are interested in extrapolation. If we know that the intervention group is older and has a lower proportion of females, we would expect these characteristics to increase the hazard mortality in this group over their remaining lifetimes. However, if the intervention group has experienced a lower number of events, this may significantly reduce the hazard for some individuals. They may also benefit from a past treatment which continues to reduce the hazard of a primary outcome such as death. This effect […] is known as the legacy effect“.
“Changes in life expectancy are a commonly used outcome measure in economic evaluation. […] Table 4.6 shows selected examples of estimates of the gain in life expectancy for various interventions reported by Wright and Weinstein (1998) […] Gains in life expectancy from preventative interventions in populations of average risk generally ranged from a few days to slightly more than a year. […] The gains in life expectancy from preventing or treating disease in persons at elevated risk [this type of prevention is known as ‘secondary-‘ and/or ‘tertiary prevention’ (depending on the circumstances), as opposed to ‘primary prevention’ – the distinction between primary prevention and more targeted approaches is often important in public health contexts, because the level of targeting will often interact with the cost-effectiveness dimension – US] are generally greater […one reason why this does not necessarily mean that targeted approaches are always better is that search costs will often be an increasing function of the level of targeting – US]. Interventions that treat established disease vary, with gains in life-expectancy ranging from a few months […] to as long as nine years […] the point that Wright and Weinstein (1998) were making was not that absolute gains vary, but that a gain in life expectancy of a month from a preventive intervention targeted at population at average risk and a gain of a year from a preventive intervention targeted at populations at elevated risk could both be considered large. It should also be noted that interventions that produce a comparatively small gain in life expectancy when averaged across the population […] may still be very cost-effective.”
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