Annex 4.1: Basic Relationships

Baseline Risk and Relative Risk (Acute and Chronic)

The “background” level of risk for clinical trials has effects on the clinical effectiveness measurements. As discussed above, treatments with apparently very large benefits (relative risks > 1 in our convention) may have actually have a small clinical therapeutic effect where the population comprising the trial participants has a very low likelihood of having a poor outcome. The effect of changing background levels of risk (measured by the number of events in control arm/number of patients in control arm) is less pronounced for acute (Fig. 4.1A) than for chronic conditions (Fig. 4.1B).


Figure 4.1A

Figure 4.1B

Baseline Risk and NNT (Acute and Chronic)

With an increasing likelihood that people without treatment will get the disease, fewer patients need to be treated to produce a beneficial result. This mean that, for instance, the resulting NNT will be small as the “background” risk increases (See Figures 4.1C and 4.1D).

Figure 4.1C

Figure 4.1D

Effect of Unequal Numbers on NNT

The vast majority of RCTs have approximately equal numbers in each arm. Calculations of NNT using a “pooled” approach, which adds all the data for like arms across trials as we have done, can be influenced by imbalance[i]. The risk of such imbalance having an effect increases with (a) increasing discrepancy in size of treatment groups, (b) increasing variation in control group event rates, (c) increasing heterogeneity in treatment effects between the studies

The average ratio : control group/treatment group for chronic conditions so far analyzed is 0.96 with a median of .98 (see Table ) These descriptive statistics suggest that for our present purposes of providing a framework for public health policy analyses, we can ignore the issue of imbalance and NNT.

Mean
/ 0.964
Standard Error / 0.012
Median / 0.988
Mode / 1
Standard Deviation / 0.259
Sample Variance / 0.067
Range / 2.569
Minimum / 0.243
Maximum / 2.813
Count / 401


Risk Ratios: Relationship between pooled and weighted calculations

We noted above in the Methods Background Document, Figure 4.1, that the pooled relative risk (128/356 divided by 137/344) of 0.902, is NOT 0.85 which is the relative risk based on the weighted the data by the number of participants in the clinical trials. We compared the relative risk ratios as calculated using the unweighted pooled estimates with the relative risk ratios from the weighted random or fixed effects models. For both acute ( Figure 4.1E) and chronic (Figure 4.1F) conditions. the strength of the relationship between these two parameters is NOT statistically significant from a 1:1 relationship as the 95% confidence intervals for the slope include 1.00. This means that the relative risk from pooled raw data is a reasonable approximation of the relative risk from the trial-weighted dataset.

Figure 4.1E Relationship between weighted average Relative Risk (taken directly from already-calculated data in the Cochrane review) and Pooled relative risk (calculated using pooled raw data from same Cochrane review)

Regression Statistics
Multiple R / 0.993
R Square / 0.987
Adjusted R Square / 0.9861
Standard Error / 0.127
Observations / 24
Coefficients / S.E. / t Stat / p / Lower 95% / Upper 95%
Intercept / -0.039 / 0.040 / -0.97 / 0.340 / -0.124 / 0.044
Slope / 1.043 / 0.025 / 41.51 / 2E-22 / 0.991 / 1.095

Figure 4.1F Relationship between weighted average Relative Risk (taken directly from already-calculated data in the Cochrane review) and Pooled relative risk (calculated using pooled raw data from the same Cochrane review)

Regression Statistics
Multiple R / 0.984
R Square / 0.968
Adjusted R Square / 0.968
Standard Error / 0.196
Observations / 77
Coefficients / S.E. / t Stat / p / Lower 95% / Upper 95%
Intercept / 0.0006 / 0.033 / 0.019 / 0.985 / -0.065 / 0.0669
Slope / 0.986 / 0.020 / 48.404 / 3E-58 / 0.946 / 1.02

Risk and Benefit Using NNT and NNH

We provide a schematic diagram below (Fig. 4.1G) , illustrating the matrix that can be generated using the NNT and NNH values that we also have calculated. A LOW NNT denotes a treatment that is effective. A LOW NNH denotes a treatment that carries a high risk. We divide this matrix into 4 quadrats, as noted and interventions can be assigned to one of the quadrats, as determined by their respective NNH and NNT pairs.

We have calculated the NNT for our CDSR dataset in both acute and chronic conditions. We have also calculated the corresponding NNH values for those outcomes that were “adverse events” as registered by the CDSR. Figures 4.1H and 4.1I show the resulting matrices for acute and chronic conditions, respectively. Based on our review of the NNT and NNH values in the literature for various conditions, we have arbitrarily assigned NNT values less than 20 as being “beneficial”, since low NNT numbers represent “good” outcomes. We have arbitrarily assigned NNH numbers less than 20 as representing high risk, since low NNH numbers denote “bad” outcomes. Thus, each quadrat number 3 (benefit, high risk) in the two Figures would include NNT/NNH pairs in which each of the pairs has NNT and NNH values adding up to a maximum of 40 (20 for NNT and 20 for NNH). In Table 4.1(Annex) we list those interventions for Chronic conditions whose NNT+NNH scores are no greater than 40.

A.  Acute Conditions

Figure 4.1H. NNT and NNH Matrix for Acute Conditions

D. Chronic Conditions

Figure 4.1I. NNT and NNT Matrix for Chronic Conditions


Table 4.1Annex

Chronic Interventions in Quadrat 3 (above) as measured by combined NNT+NNH Scores

Quadrat Number 3 (combined score < 40)
Beneficial, potential for increased side effects
Crohns
Either azathioprine or 6- mercaptopurine
COPD
Methylxanthines
Oral corticosteroids
Rheumatoid Arthritis
Sulfasalazine
Leflunomide
Cyclophosphamide
Methotrexate
Celocoxib
Antidepressants
L-tryptophan and 5-HTP
TCA- imipramine
MAOI-phenelzine
SSRI- sertraline
Ritanserin
Amineptine
Schizophrenia
Chlorpromazine
Thioridazine
Haloperidol
Acute Stroke
Calcium antagonists: Flunarizine
Alzheimers (high doses)
Galantamine
Anti dementia medications
Thioridazine

4.1-1

[i] See Altman, Deeks, available from:http://www.biomedcentral.com/1471-2288/2/3