Community Medicine

Wednesday, January 2, 2019

Discounting (Economic evaluation)

•Health benefits and costs related to an intervention occur at different points in time

•Society has a preference for interventions where benefits occur sooner

•Adjusts future health benefits and costs to present value

•What is the present value of ₹ 5,000 received 10 years from now?

Ans. 3,720.47

Standard Discount Rates

•US Panel on Cost Effectiveness in Medicine

•3% costs and benefits

•5% and 0% in sensitivity analyses

•United Kingdom

•NICE (National Institute of Health and Care Excellence) guidance: 3.5% for cost and benefits

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Cost Effectiveness Acceptability Curves (CEAC)

•Represents the uncertainty concerning the cost-effectiveness of a health-care intervention in the context of decisions involving two interventions

•It acts as an alternative to confidence intervals around ICERs

•CEACs have been interpreted as representing the ‘probability that the intervention is cost-effective’ given the data

Cost Analysis

Conditional logistic regression

Logistic regression analysis studies the association between a binary dependent variable and a set of independent (explanatory) variables using a logit model.

Conditional logistic regression (CLR) is a specialized type of logistic regression usually employed when case subjects with a particular condition or attribute are each matched with n control subjects without the condition. In general, there may be 1 to m cases matched with 1 to n controls. However, the most common design is 1:1 matching, followed by 1:n matching in which nvaries from 1 to 5

Ref. https://ncss-wpengine.netdna-ssl.com/wp content/themes/ncss/pdf/Procedures/NCSS/Conditional_Logistic_Regression.pdf

In CLR we must remember that observations are not independent, and participants in different treatment groups have been matched for at least 1 characteristic, and this must be taken into account in the analysis.

The philosophy is the same with logistic regression with the exception that the estimates from conditional logistic regression are conditional on the matched treatment groups or on the cases being linked to the controls in a matched case-control study. This type of analysis is required in individually matched studies.

However, it is different when studies use frequency matching, which deals with selecting individuals for different groups to have the same overall distribution on a matching variable. In this case, it is acceptable to use unconditional (ordinary) logistic regression and include the matching factor in the model.

In conditional logistic regression model, likelihood is formulated in a way that subjects from different treatment groups (or case controls) are only compared within the same matched set; this is called conditional likelihood. The general form of a conditional logistic regression model with a single binary exposure is:

Log odds = a + set + beta1 exposure

- Where (a + set) represents constant term in each set of matched individuals, and beta1 exposure represents estimate of effect
of exposure of interest.
- Constant in each set is eliminated from the model using conditional likelihood, and only the effect of the exposure and other potential predictors are retained. This means that there is no constant term as in the usual logistic regression in the output from a con- ditional logistic regression.

- When modeling our data with conditional logistic regression, we can additionally include other potential

predictor variables or confounders and test for interac- tions in the same way that this is done using ordinary lo- gistic regression

Ref http://dx.doi.org/10.1016/j.ajodo.2017.04.009

Odds ratio, Relative risk, Attributable risk, Population attributable risk

Odds ratio (OR) is a measure of association between an exposure and an outcome. OR represents odds that an outcome will occur given a particular exposure, compared to the odds of outcome occurring in absence of that exposure. Odds ratios are most commonly used in case-control studies, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions).

Odds ratios are used to compare relative odds of the occurrence of the outcome of interest (e.g. disease or disorder), given exposure to the variable of interest (e.g. health characteristic, aspect of medical history). The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome, and to compare the magnitude of various risk factors for that outcome.

1. OR=1 Exposure does not affect odds of outcome

2. OR>1 Exposure associated with higher odds of outcome

3. OR<1 Exposure associated with lower odds of outcome

Relative risk (RR): A synonym for risk ratio. However, the term is also commonly

used to refer to the rate ratio and even to the odds ratio (OR). To minimize confusion,

it may be better to avoid this term in favor of more specific terms.

Rate ratio The ratio of two rates; e.g., the rate in an exposed population divided by the rate

in an unexposed population.

Relative Risk (RR) = (incidence in exposed)/(incidence in non-exposed)

Attributable risk (AR) = (incidence in exposed - incidence in non-exposed)/(incidence in exposed)

Risk difference (RD) = (incidence in exposed - incidence in non-exposed)

Population attributable risk (PAR) = (incidence total- incidence in non-exposed)/(incidence total)

or PAR = P_e (RR_e-1) / [1 + P_e (RR_e-1)]

where, Pe is prevalence of exposure

RRe is relative risk of that exposure

Ie - incidence in exposed

Iu - incidence in unexposed (non-exposed)

Ip - incidence total (exposed + nonexposed)

Asymmetry test of EGGER

•Linear regression approach to measure funnel plot asymmetry on the natural logarithm scale of the odds ratio

•The standard normal deviate (SND), defined as the odds ratio divided by its standard error, is regressed against the estimate's precision, the latter being defined as the inverse of the standard error

•(regression equation: SND= a+ bxprecision)

•As precision depends largely on sample size, small trials will be close to zero on the × axis

•Null hypothesis –symmetry exists in the funnel plot

Freeman-Tukey transform

•Freeman-Tukey transform

seek to adjust data to make the distribution more similar to a Normal distribution

•Was specifically designed for Poisson-like data, especially with a mean value >1.

•The FT angular or arcsine transform was developed for Binomial-like data, in particular, data representing proportions or percentages.

Duval and Tweedie’s Trim and Fill method

•Uses an iterative procedure to remove most extreme small studies from positive side of funnel plot, re-computing effect size at each iteration until funnel plot is symmetric about new effect size

•Yield an unbiased estimate of effect size

•Trimming also reduces variance of effects, yielding a too narrow C.I.

•Therefore algorithm then adds original studies back into analysis, and imputes a mirror image for each.

•This fill has no impact on point estimate but serves to correct the variance

the black dots are studies added after the method...

Publication Bias

Publication Bias:

•The publication or non-publication of research findings, depending on the nature and direction of the results (ref. Cochrane Handbook)

•Publication bias exists when the studies included in the analysis differ systematically from all the studies that should have been included.

•Typically, studies with larger than average effects are more likely to be published and this can lead to upward bias in the summary effect

•Publication bias is when studies with positive findings are more likely to be published

•This means that any meta analysis or literature reviews based only on published data will be biased, so researchers should make sure to include unpublished reports in their data as well

Funnel Plot:

•Plots of “trials’ effect estimates”against“sample size”

•Funnel plot is based on the fact that precision in estimating underlying treatment effect will increase as sample size of component studies increases

•Results from small studies will scatter widely at bottomofgraph, with spreadnarrowing among larger studies

•In absence of biasplot will resemble a symmetrical inverted funnel

•Conversely, if there is bias, funnel plots will often be skewed and asymmetrical

•Symmetry (or asymmetry) - visual examination(so it is subjective)

How to calculate relative risk from odds ratio ?

Q. How to calculate relative risk from odds ratio ?