APOYO AL BENEFICIO

Decision tree is tree-like diagram with branches of decision, uncertain events, consequences, and multiple criteria describing the consequences (Phillips, 2010b). The models are derived from decision theory, and operate by decomposing complex problem into its elements.

Probabilities and utilities about relevant pieces are then assessed and reassembled (Phillips, 2010b). It works on the basis of three theorems that:

11 T-scores can be further defined but it is unclear on how to do so.

Chapter 3 | 97 (1) probabilities exist,

(2) utilities exist, and

(3) options with the highest expected utility should be most preferred

Each option on the decision tree is assessed by multiplying the associated probabilities and utilities along a “consequence” branch to give the expected utility which then gets evaluated.

A simple example of a decision tree is shown in Figure 3.6 for choosing whether to take folic acid supplement during pregnancy (Ashby, 2000; Spiegelhalter, 2004a). Let ( ) be the expected utility for taking decision ( ), be the probability of chance event given

, and be the cost associated with , then,

( ) ( )

and, option is then preferred to option if ( ) ( ). By substituting the expected utilities and rearranging the inequality, the relationship between utilities in the decision tree to NNT when cost was involved can be expressed as (Ashby, 2000):

Figure 3.6 Decision tree of folic acid supplements for pregnant women

(Reconstructed from Spiegelhalter et al. (Spiegelhalter, 2004a) with the square representing a decision, hollow circles representing chance events, and solid circles representing the utilities)

𝜋

Decision Event? Utility of consequences

U1 – c0

U0 – c0

U1 – c1

U0 – c1

Chapter 3 | 98 3.9.9 Multi-Criteria Decision Analysis approach

The idea of multi-criteria decision analysis (MCDA) is so natural and attractive (Figuera, 2005) that many literatures on, and variants of, the approach exist; and that BLRA method (Chuang-Stein, 1994) has been regarded as a reinvention of the MCDA technique (Phillips, 2010b). Belton and Stewart (2002) labels MCDA as an umbrella term to describe a collection of approaches that explicitly take into account multiple criteria in decision making (Belton, 2002; Mussen, 2009). However, in a 2010 risk-benefit technology review, MCDA is specifically referred to the work of Keeney and Raiffa in 1976 based on decision theory (Keeney, 1976; Phillips, 2010b), which is essentially the definition I adopt in this thesis.

MCDA breaks the problem down into smaller manageable pieces through the application of decision trees to accommodate different criteria. This forces the stakeholders to think about the problem or decision to be made in a structured way thus eliminate “gut-feel” decisions on the importance of different criteria (Mussen, 2009). There are three main phases of an MCDA analysis: (1) problem identification and structuring, (2) model building and use, and (3) development of action plan. The detailed stages in building an MCDA model is shown in Figure 3.7.

MCDA is very desirable since it can explicitly account for multiple and conflicting criteria (Belton, 2002), particularly in making decisions on risk and benefit of drugs. MCDA approach can accommodate risks in terms of incidence of adverse events, discontinuation rates due to adverse events, as well as other risk factors (Guo, 2010). It can accommodate benefits of drugs through clinically relevant outcomes obtained from clinical trials, as well as other benefits criteria (Guo, 2010). The readily-available method within MCDA to trade off risks and benefits and integrate them into a single measure is what making it attractive, and it is conceptually simple (Belton, 2002). It is relatively easy to understand and to be used by people who are not familiar with decision analysis techniques (Mussen, 2009). MCDA allows the stakeholders to focus on the best data (evidence) available, the scoring of options, and the weightings of criteria – without the need to concern heavily about the underlying model itself (Mussen, 2009). There are specialised software to facilitate the application of MCDA including the underlying model building such as Hiview 3 from Catalyze Ltd (Winchester, UK) (Catalyze Ltd., 2010a).

Chapter 3 | 99 MCDA produces better considered, justifiable, and explainable decisions together with an audit trail for the decisions, making it transparent (Belton, 2002). However, the internal validity of MCDA critically relies on the evidence from clinical trials (Guo, 2010) and the quality of qualitative value judgements. Its application in post-approval phase of a drug is still limited and threatened by the quality of data available thus remains a challenge (Mussen, 2009).

Figure 3.7 Detailed stages in MCDA

Extracted and modified from the MCDA manual (Dodgson, 2009) 1. Establish the decision context

a. to establish the purpose of the analysis, and identify the main stakeholders involved b. to design the socio-technical system for conducting the MCDA

c. to consider the context of MCDA 2. Identify the options to be appraised

a. to explicitly list the different options available 3. Identify objectives and criteria

a. to identify criteria of each option

b. to organise the criteria by objectives in a hierarchical fashion 4. ‘Scoring’

a. to describe the consequences of the options

b. to score each option for each criteria usually on a 0-100 scale

c. to check the consistency of the scores given relative to each other across different criteria 5. ‘Weighting’

a. to assign weights to the criteria reflecting the relative importance in the decision 6. Combine the weights and scores for each option to derive an overall value

a. to calculate overall weighted scores at each level in the hierarchy b. to calculate overall weighted scores

7. Examine the results 8. Sensitivity analysis

a. to evaluate how other preference weights affect the ordering of options and the decision b. to evaluate and compare the advantages and disadvantages of the options

c. to determine whether new options are possible and probably better than those considered originally

d. to elicit the best model to be used for making decision

Chapter 3 | 100 3.10 Bayesian statistics

Main analyses in this thesis use classical regression techniques especially for evidence data mining exercise. But some Bayesian analyses are carried out when Bayesian would offer clear greater advantage to classical analysis e.g. in mixed treatment comparison described in Section 3.4. Some applications of what I call a “hybrid Bayesian”-classical approach are explained in Chapter 9.

This section does not intend to give a thorough documentation on Bayesian school of thoughts but only a general overview of the concept as applied to case study. Thorough discussions on Bayesian statistics can be found in good statistical textbooks (Berger, 1985;

Bernardo, 1994; Parmigiani, 2002a; Spiegelhalter, 2004b). The use of Bayesian in medical decision making has also been discussed elsewhere (Ashby, 2000; Parmigiani, 2002a;

Spiegelhalter, 2004b).

The history of Bayesian statistics originating from Reverend Thomas Bayes in 1763 has been discussed in a recent review on the use of Bayesian statistics in medicine (Ashby, 2006).

Bayesian statistics has become popular in recent years mainly due to computational advances that facilitates its application (Ashby, 2006). This is in some way attributed to the development of WinBUGS (Bayesian inference Using Gibbs Sampling for Windows) software (Lunn, 2000) which is currently considered as the main tool for performing Bayesian analysis. It is being succeeded by OpenBUGS (Lunn, 2009).

For a hypothesis and data , the simplest form of Bayes theorem is (Bernardo, 1994), where ( ) denotes the probability:

( | ) ( | ) ( ) ( )

( ) is the subjective probability of the hypothesis independent of the data known as the priors, and ( | ) is the posterior probability of the hypothesis having observed the data.

This simple principle forms the basis of Bayesian statistics we are now familiar with.

The most problematic issue in Bayesian statistics is the elicitation of priors. Weak priors or sometimes known as uninformative or uniform priors are usually used when there is no prior knowledge. In this circumstance, the posterior probability of the hypothesis is driven by the

Chapter 3 | 101 data. When informative priors are used in the model, the priors would influence the posterior depending on how strong or certain the priors are. This often gets Bayesian analysts in trouble when too strong priors are chosen, i.e. being too confident in the judgement of the evidence, then the priors would overpower evidence from data. In Bayesian analysis, the inferences are made from the examination of posterior distribution.

WinBUGS and OpenBUGS are dedicated to performing Bayesian analysis using Gibbs sampler to implement Markov Chain Monte Carlo (MCMC) method. In an application of iterative methods such as Gibbs sampling, it is usual that consecutive observations of the posterior distributions being sampled are correlated – referred to as autocorrelation in WinBUGS/OpenBUGS. The autocorrelation for each stochastic node or parameter is inspected using the built-in software diagnostic function to ensure convergence and mixing of the MCMC chains. Other diagnostic tools available are the trace plots and the Gelman-Rubin plot.

WinBUGS and OpenBUGS also save the (explicitly monitored) estimates at each MCMC iteration as Convergence Diagnostic and Output Analysis (CODA) files from each chain (Best, 1995). CODA outputs are commonly used for convergence and diagnostic tests when the analyses are carried out outside WinBUGS/OpenBUGS software. CODA outputs are used in this thesis (Section 9.4) to perform sensitivity analysis of the Bayesian models in Stata 10 (StataCorp, 2007) to gain computing speed.

“Confidence intervals” (CI) for a parameter from a Bayesian analysis is known as the credible intervals (CrI). CrI is the highest posterior density that covers the ( ) significance level (in classical sense – see Section 3.11).

Chapter 3 | 102 3.11 Power and sample size determination

Power and sample size are the two fundamental requirements when designing clinical trials.

They ensure that the clinical trial to be conducted is large enough to make inference on the hypothesis and not too large to be resource inefficient.

Typically a clinical trial requires power at 80% or 90% level. Power indicates how reliably a trial could detect the hypothesised difference, and often labelled as ( ). Another parameter required is the significance level which typically is chosen to be 5%. Greater power and smaller lead to larger sample size provided other parameters are constant – hypothesised difference and variance.

All illustrative sample size calculations in Chapter 10 are done in classical way in Stata 10 (StataCorp, 2007).

Application to case study | 103

Part II

Application to case