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A guided tour of research study design and statistics II Mustafa Soomro Consultant psychiatrist St James Hospital, Portsmouth 1 Plan • • • • Systematic Review and Meta-analysis Economic evaluation Survival analysis Factor analysis 2 Systematic Review and Meta-Analysis 3 Systematic Review and Meta-Analysis • Definitions – SR: Objective review of all available relevant studies using standard methods of SR • • • • • Formulating focussed question Comprehensive searching Using objective study selection criteria Quality assessment of studies Qualitative or quantitative synthesis of data from included studies – MA: Quantitative synthesis of data from included studies 4 Meta-analysis • Quantitative synthesis or pooling of results from several similar studies • Steps involved in meta-analysis – Data extraction from individual studies – Analysing heterogeneity – Pooling of results using appropriate statistical methods (fixed vs. random effects [the DerSimonian-Laird] model) 5 Data needed for meta-analysis • For continuous outcome you need: – Mean change and SD of the mean change within treatment and within control groups – Number of individuals in treatment and control group 6 Data needed for meta-analysis • For dichotomous outcome you need: – Events in treatment group and events in control group – Number of individuals in treatment group and in control group 7 Publication bias and funnel plot test 8 Publication bias and funnel plot test 9 Graphical exploration of statistical heterogeneity L’ Abbe Plot Y axis= the event rate in the experimental (intervention) group and X axis= the event rate in the control group 10 Graphical exploration of statistical heterogeneity – Forest plot • Forest plot (visual test) 11 Assessing statistical heterogeneity • Cochran’s Q test (chi square test): • Q has low power when the number of studies is small; Q has too much power as if the number of studies is large (Higgins et al. 2003); • Gives you chi square statistic and p value; with small number of trials p should be fixed at 0.1 • Q forms part of the DerSimonian-Laird random effects pooling method (DerSimonian and Laird 1985). 12 Assessing statistical heterogeneity • I² statistic: – the percentage of variation across studies that is due to heterogeneity rather than chance (Higgins and Thompson, 2002; Higgins et al., 2003). – I² = 100% x (Q-df)/Q. – Unlike Q it does not inherently depend upon the number of studies considered. • A confidence interval for I² is constructed using either i) the iterative non-central chisquared distribution method of Hedges and Piggott (2001); or ii) the test-based method of Higgins and Thompson (2002). 13 Assessing statistical heterogeneity • I² statistic: interpretation of – 0% to 40%: might not be important; – 30% to 60%: may represent moderate heterogeneity*; – 50% to 90%: may represent substantial heterogeneity*; – 75% to 100%: considerable heterogeneity*. • *The importance of the observed value of ‘I square’ depends on (i) magnitude and direction of effects and (ii) strength of evidence for heterogeneity (e.g. P value from the chi-squared test, or a confidence interval for ‘I square’). 14 Forest plot for dichotomous data 15 Forest plot for continuous data 16 When heterogeneity is present • To pool or not pool that is the question. – To pool using random effects model – Not to pool – And investigate heterogeneity 17 Investigating heterogeneity • Meta-regression • Subgroup analysis 18 Economic analysis / evaluation 19 Methods of economic evaluation • Cost Minimisation – Intervention with less cost (£s) [input] is selected (used when outcome [output] of two interventions are considered as broadly similar) • Cost effectiveness – Cost (£s) [input] for each intervention for the same magnitude of improvement on a particular outcome scale [output]. Less costly option would be more cost effective • Cost Utility – Cost (£s) [input] for each intervention in terms of life utility units (QUALYS or QOL or DALYS) • Cost benefit – Cost (£s) [input] for each intervention as input; and different types of outputs are translated into monetary terms (£s). • Cost consequences: 20 – Cost (£s) [input] input; and output are natural units like days Economic evaluation - CEAC • Cost effectiveness acceptability curve: – Y = probability that an intervention is cost-effective compared with the alternative – X = for a range of λ (Willingness to Pay) values. 21 Survival time / event history / time to vent analysis 22 Survival time analysis Type of data: Any outcome that is dichotomous occurs once during follow up 23 Survival time analysis • Survival rate does not provide time to event information (it only gives rate towards the end of a period e.g. 5 year survival rate) • Time to event data provide more detailed information of probability of survival at any given point. • However time to event data are often censored – therefore require special consideration in terms of analysis • Censored data refer to incomplete data. – Examples of incomplete data are: • individuals still alive (no event) at end of study • individual lost to follow up or left study before the end • event not recorded properly – Data in above examples are right censored 24 Censored data • Censored data – Suppose a set of components are being monitored to see how long they last. If the monitoring stops before all the components have broken, then the information concerning the lifetimes of the unbroken components 25 has been censored Survival time analysis • Life tables and survival curve analysis (KM survival curve) – Calculates probabilities of survival at any point during follow up period – Censored data are removed before probabilities are calculated – Probability of survival at particular point is conditional probability at that point (Kirkwood 1988, p118; Altman 1991, p368) • Log rank test (compares two curves) • Cox regression analysis (estimates of hazard ratio controlling for confounders) – Hazard ratio (HR) is the ratio of hazard rates for group1 to group2 over the same time period • Hazard rate is the ratio of number of events within the group to total number within the group, over a given time period 26 Survival time analysis – life table 27 Survival time analysis – KM curves 28 Survival time analysis – KM curve details 29 Exploratory factor analysis 30 Exploratory factor analysis Principal (common) factor analysis and principal component analysis • Basic idea: – Multiple variable correlation is used to extract underlying dimensions (i.e. groups of variables which correlate highly with one another). 31 Exploratory factor analysis Principal (common) factor analysis and principal component analysis • Principal (common) factor analysis: uses common variance (correlationfocussed method) only to find out underlying dimensions composed of common variances only (this approach is used in SEM). This accounts for only common variance between variables. 32 Exploratory factor analysis • Principal component analysis: uses both common and unique variances between variables (variance-focussed method) to find out underlying dimensions; used for data reduction. This accounts for all variance between variables. 33 Exploratory factor analysis • Factor loading: correlation coefficient between a variable and a factor (this is also interpreted as regression coefficient predicting variable from factor). • Communality: communality measures the proportion of variance of a given variable explained by all the factors jointly. • Eigenvalue: The eigenvalue for a given factor measures the amount of variance in all the variables, which is accounted for by that factor. 34 Exploratory factor analysis • How many factors to extract: all factors with eigenvalue greater than 1 – Or using scree plot [factors x axis and eigenvalues y axis], thus all factors before the point of inflexion would be selected • Factor rotation is carried out to maximise factor loadings (to help in interpretation of factors). Varimax (orthogonal) rotation is most common method; other is oblique rotation 35