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
Effect of "Baseline Risk" on Relative Risk: Acute Conditions
10
9
8
Relative Risk
7
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Number of Events in Control Arm/Number of Patients in Control Arm
4.1-1
0.9
1
Annex 4.1: Basic Relationships
Figure 4.1B
Effect of "Baseline" Risk on Relative Risk: Chronic Conditions
18
16
14
Relative Risk
12
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
Number of Events in Control Arm/Number Patients in Control Arm
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
Effect of"Baseline Risk" on NNT: Acute Conditions
600.0
Number Needed to Treat
500.0
400.0
300.0
200.0
100.0
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Number of Events in Control Arm/Number of Patients in Control Arm
4.1-2
0.9
1
Annex 4.1: Basic Relationships
Figure 4.1D
Effect of "Baseline Risk" on NNT: Chronic Conditions
Number Needed to Treat
1000.0
500.0
0.0
0
0.2
0.4
0.6
0.8
1
1.2
Number of Events in Control Arm/Number of Patients in Control Arm
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 imbalancei. 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.
0.964
0.012
0.988
1
0.259
0.067
2.569
0.243
2.813
401
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Range
Minimum
Maximum
Count
4.1-3
Annex 4.1: Basic Relationships
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)
Risk Estimates (Acute Conditions)
6
Relative Risk (raw data pooled)
5
4
3
2
1
0
0
1
2
3
4
5
6
Relative Risk (Weighted averages )
Regression Statistics
Multiple R
0.993
0.987
0.9861
0.127
24
R Square
Adjusted R Square
Standard Error
Observations
Intercept
Slope
Coefficients
S.E.
t Stat
p
-0.039
1.043
0.040
0.025
-0.97
41.51
0.340
2E-22
Lower 95%
-0.124
0.991
Upper
95%
0.044
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)
4.1-4
Annex 4.1: Basic Relationships
Risk Estimates (Chronic Conditions)
7
Relative Risk (Raw Data Pooled)
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
Relative Risk (Weighted averages)
Regression Statistics
0.984
0.968
0.968
0.196
77
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Intercept
Slope
Coefficients
S.E.
t Stat
p
Lower 95%
Upper
95%
0.0006
0.986
0.033
0.020
0.019
48.404
0.985
3E-58
-0.065
0.946
0.0669
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.
4.1-5
Annex 4.1: Basic Relationships
RISK BENEFIT MATRIX (NNT and NNH)
50
40
3
NNH
30
1 No benefit, benign risk
2 No benefit, non benign risk
3 Benefit, benign risk
4 Benefit, non benign risk
1
20
10
2
4
0
200.0
100.0
NNT
0.0
Increasing Benefit
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.
4.1-6
Annex 4.1: Basic Relationships
A. Acute Conditions
Figure 4.1H. NNT and NNH Matrix for Acute Conditions
RISK BENEFIT MATRIX (NNT and NNH)
50
1 No benefit, benign risk
2 No benefit, non benign risk
3 Benefit, non benign risk
4 Benefit, benign risk
4
40
1
NNH
30
20
2
10
3
0
200.0
100.0
NNT
0.0
Increasing Benefit
D. Chronic Conditions
Figure 4.1I. NNT and NNT Matrix for Chronic Conditions
200.0
LEGEND: Benefit: Risk
180.0
1- Lack of benefit
2- Lack of benefit
3- Benefit
4 - Benefit
Benign
Risk
Risk
Benign
160.0
140.0
120.0
100.0
80.0
60.0
4
1
40.0
20.0
3
2
100.0
50.0
4.1-7
Number Needed to Treat
0.0
0.0
Annex 4.1: Basic Relationships
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
i
See Altman, Deeks, available from:http://www.biomedcentral.com/1471-2288/2/3
4.1-8