Risk ratio calculation

Usually, the main purpose of meta-analysis is quantitative. The goal is to develop better overall estimates of the degree of benefit achieved by specific exposure and dosing techniques, based on the combining (pooling) of estimates found in the existing studies of the interventions. This type of meta-analysis is sometimes called a pooled analysis (Gerbarg and Horwitz, 1988) because the analysts pool the observations of many studies and then calculate parameters such as risk ratios or odds ratios from the pooled data. 

The environmental risk assessment approach most commonly adopted consists of estimation of the risk quotient (RQ) (as suggested by Hernando et al. [103]), which is defined as the ratio between the environmental concentration (measured or predicted, respectively MEC and PEC) and the predicted no-effect concentration (PNEC), and can be used to collocate compounds in one of three risk bands RQ < 0.1, minimal risk to aquatic organisms 0.1 < RQ < 1, median risk and RQ > 1, high risk [103—105]. In their risk assessment calculations, [106], further to [107], estimated PNEC values at 1,000 times lower than the most sensitive species assayed, so as to take into account the effect on other, potentially more sensitive, aquatic species to those used in toxicity studies. 

The Swedish Classification Scheme initiated in 2005 by the Swedish Association of Pharmacy Industries (LIF), the Swedish Medical Products Agency, Apoteket (National Corporation of Swedish Pharmacies), the Swedish Association of Local Authorities and Regions and the Stockholm County Council, take in account Persistence, Bioaccumulation and Toxicity (PBT) characteristics of pharmaceutical products. This voluntary scheme looks at the environmental hazard and the associated risk of pharmaceutical products. The environmental risk is calculated based on the ratio PEC/PNEC according to the EMEA guideline [17,124, 127]. The obtained information is only available on the website www.fss.se, since due to European restrictions it is not possible to include warning labels on the packaging of medications [17]. 

The relative risk is defined again as a ratio, this time in relation to the risks calculated for the two treatments. For the trastuzumab group the risk is the proportion of patients suffering SAEs which takes the value 117/1677 = 0.070 while for the observation only group this is 81/1710 = 0.047. The relative risk (RR) (sometimes called the risk ratio) is then the ratio of these risks ... 

The results were striking. When all the pediatric trials were pooled, the rate of definite or possible suicidality among children assigned to receive antidepressants was twice that in the placebo group. (The summary risk ratio was 2.19 95 percent confidence interval.) Although the FDA staff did not provide this information to the committee, according to my own calculations, such a dramatic result could be expected... 

To compare the risk of cancer in smokers to the risk in nonsmokers, one can calculate the risk ratio- The risk ratio, from the above study, is 0.3/0,1 - 3,0. The risk ratio is a number that contains two different rates of risk. Risk ratio is also called relative risk-... 

Stepping back to view the big pictun , one can see that the values for the risk ratio (3,0) and edds ratio (3.86), as calculated above, are not exactly the same. For both risk ratio and odds ratio, a value of 1.0 corresponds to a situation where no association exists betwHCcn the risk factor and the outcome. Fhe use of the risk ratio or odds ratio for expressing epidemiological data can be a matter of personal taste and custom. However, it should be noted that odds ratio has a valuable property not shared by risk ratio, as illustrated with imaginary data involving cholesterol and diabetes (Feinstein, 1985). 

This concerns whether one should use risk ratio or odds ratio for expressing results when evaluating a retrospective or prospective study. It is possible to calculate risk and risk ratio using data from a case-control study, and to acquire mathematical results, but it is not correct to do so. This is because the denominator (the number in the denominator) in the risk formula does not represent a broad random sampling of the population. The number in the denominator represents two groups of subjects who were screened and recruited into the study, Ksk and risk ratio are used for prospective studies. Odds ratio can be accurately used for both retrospective and prospective studies but is customarily only used for retrospective studies. 

ALGEBRA USED FOR CALCULATING RISK RATIO AND ODDS RATIO... 

Some diseases are so rare that the prospects of conducting a clinical trial are remote. It is unlikely that enough patients could ever be collected at any reasonably small number of study sites for any useful randomization. These diseases may be found in the literature as case reports. In these cases, probably the best that can be accomplished is to collect and retrospectively analyze as many such cases as possible. If the drug of interest has been used in a sufficient number of patients, then retrospective risk ratios for benefit and harm can be calculated. This may be the strongest evidence that can ever be collected about a particular drug under these rare conditions, albeit never as strong as a controlled clinical trial. One example is the effectiveness of dantrolene in malignant hyperthermia (Strazis and Fox, 1993). 

Noncancer effects are not expressed in terms of a probabilistic approach. Instead, the potential for noncarcinogenic effects is evaluated by comparing an exposure level over a specified period (typically, a lifetime) with a reference dose (RfD) derived for a similar exposure period (9). Reference doses may also be found in toxicological databases, such as IRIS. Noncancer risk is presented as a ratio of exposure to toxicity and is called a hazard quotient (HQ) (9). Using these assumptions, noncarcinogenic risk is calculated by the following equation (9) ... 

The three most commonly used measures to compare two treatment groups are risk difference, risk ratio, and odds ratio. The estimate 0, and the Mantel-Haenszel estimate of Wj can be calculated for each measure as follows (Cochran, 1954 Mantel and Haenszel, 1959 Nurminen, 1981 Tanone, 1981) ... 

To obtain an estimate of the risk ratio for major malformations and spontaneous abortion in exposed versus imexposed infants, an overall summary odds ratio (ORs) was calculated according to the protocol established by Einarson et al. Additionally, homogeneity of the included studies, power analysis and the extent of publication bias were also examined as described by Einarson et al. ... 

Polymorphisms in the CYP2C9 and CYP2C19 genes have been studied in 292 Tamils who were taking phenytoin, 58 of whom had phenytoin toxicity [244. Risk ratios were calculated for each mutant CYP2C9 genotype separately, and the adjusted odds ratio for CYP2C9 l/ 3 allele was 15 (95% Cl = 5.8, 40) for intoxicated patients compared with the others. 

Subsequently, a great number of safety measures were studied, their risk reduction calculated, and their cost estimated. Figure 12.14 shows the principal measures represented in a risk/cost diagram. The most interesting measures are those with the best risk/cost ratio. It is readily apparent that the underpass is ill advised due to the high cost and the limited risk-reduction effect. 

Paediatric pulmonary disease In a nationwide retrospective cohort study using a pharmacy prescription database, the use of drugs for paediatric pulmonary diseases in children with a history of in utero exposure to antidepressants (TCAs, SSRIs) was compared with those without such exposure. A total of 35,546 children from 23,576 women were identified. For each woman, exposure was calculated for each of the three trimesters of pregnancy [22 ]. A small but significant increase in the incidence risk ratio (IRR) for the use of drugs for pulmonary disease was foxmd following any in utero exposure to SSRIs (1.17). Similarly, an increased risk was noted when exposure occurred in at least in the first trimester (IRR 1.18). 

Table 12-3. The relative risk of culpability in a crash with different drugs, based on culpability ratios calculated from Australian fatal crash data (from Drummer et al, 2004, with permission...

Using the information and result of Problem 4, Calculate the Bimbaum, Inspection, Fussell-Vescly, Risk Reduction Worth Ratio, Risk Reduction Worth Increment, Risk Achievement Worth Ratio, and Risk Achievement Worth Increment for each of the components A through G. Do your results agree with the equivalences in Table 2.8-1 ... 

Importance - calculates and displays three importance measures, Fussell-Ve.scly, Risk Reduction Ratio, Risk Increase Ratio, for each event in the system, sequence, or end state. 

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