Transcript Handout/Slides

Biostatistics Case Studies 2005
Session 6:
“Number Needed to Treat” to Prevent One Case
Peter D. Christenson
Biostatistician
http://gcrc.humc.edu/Biostat
Case Study
Results
Main Figures for Results
Studies in Ocular Hypertensive Subjects:
Studies in Glaucoma Subjects:
Goals of this Session
1. Define “Number Needed to Treat” (NNT).
2. Show how to calculate NNT for published studies
analyzed with methods for equal follow up for all
subjects.
3. Show how to calculate NNT for published studies
analyzed with survival (time-to-event) methods.
4. Reproduce NNT values for the case study.
5. Disadvantages of NNT.
NNT: Subjects Followed Equally
NNT = the number of subjects who need to be
treated in order to expect to prevent one case,
relative to subjects not treated.
•
•
•
•
Let pt = proportion of treated subjects who have
the event in the fixed time period, and pc the
proportion of control subjects with the event.
The absolute risk reduction, ARR, is pc-pt.
Since ARR is the proportion of treated subjects in
whom events were prevented, NNT=1/ARR.
95% CI for NNT is 1/AU to 1/AL, where (AL,AU) is
the 95% CI for ARR.
Examples: Subjects Followed Equally
N
Pc
Pt
Sc
St
ARR NNT
AL
AU
NNT 95%CI
100
0.2 0.1 0.8
0.9
0.10
10
0.002
0.198
5.1 to 500
100
0.4 0.2 0.6
0.8
0.20
5
0.076
0.323
3.1 to 13.2
100
0.8 0.4 0.2
0.6
0.40
2.5
0.276
0.523
1.9 to 3.6
1000 0.2 0.1 0.8
0.9
0.10
10
0.069
0.130
7.6 to 14.5
1000 0.4 0.2 0.6
0.8
0.20
5
0.160
0.239
4.2 to 6.2
1000 0.8 0.4 0.2
0.6
0.40
2.5
0.360
0.439
2.3 to 2.8
St = treated proportion surviving, i.e., w/o event = 1-Pt.
AL = ARR – 1.96*Standard Error (ARR)
= ARR – 1.96*square root [Pc*Sc/N + Pt*St/N].
Comments: Subjects Followed Equally
1. NNT (and ARR) refer only to the fixed follow up
time for all subjects.
2. NNT is based on risk difference, not risk ratio (RR).
Note that RR = 2.0 for all of the previous
examples.
3. CIs can be obtained from reported Ps (or Ss) and
Ns using formula on previous slide.
4. Cannot obtain NNT (or ARR) from RR only. Need
risk or survival (one of Pc, Pt, Sc, or St). Usually
underlying risk Pc for target population is used.
Generalization to Unequal Subject Follow Up
1. NNT is still specific to a particular specified time of follow up.
2. NNT is still 1/ARR = 1/(St-Sc), but St and Sc are found from
survival methods: either Kaplan-Meier or Cox regression.
3. To find NNT from a published paper, we need either:
•
St and Sc, and for a CI on NNT, either their standard
errors (which could be found from their CIs) or the
numbers of subjects at risk at the F/U time (which are
often in graphs).
•
The hazard ratio (HR) and Sc (or St), and for a CI on
NNT, the standard error of HR (which could be found from
its CI) . This is the typical way that results are reported.
NNT Results for the Case Study
Reproduce NNT for the Case Study
Studies in Ocular Hypertensive Subjects:
• Hazard Ratio HR = 0.56 (95% CI: 0.39 to 0.81).
• Sc is assumed to be 0.80.
• The key to obtaining ARR, and thus NNT, is that the Cox
regression model assumes that St = [Sc]HR.
• Here, St = [0.80]0.56 = 0.8825.
• Thus, ARR = 0.8825-0.80 = 0.0825.
• NNT = 1/ARR = 1/0.0825 = 12.12, reported as 12.
• AU = [0.80]0.39 – 0.80 = 0.9167-0.80 = 0.1167.
• AL = [0.80]0.81 – 0.80 = 0.8346-0.80 = 0.0346.
• 95% CI for NNT is 1/AU to 1/AL = 1/0.1167 to 1/0.0346 = 8.6 to
28.9, reported as 9 to 29.
Reproduce NNT for the Case Study
Studies in Glaucoma Subjects:
• Hazard Ratio HR = 0.65 (95% CI: 0.49 to 0.87).
• Sc is assumed to be 0.40.
• The key to obtaining ARR, and thus NNT, is that the Cox
regression model assumes that St = [Sc]HR.
• Here, St = [0.40]0.65 = 0.5512.
• Thus, ARR = 0.5512-0.40 = 0.1512.
• NNT = 1/ARR = 1/0.1512 = 6.61, reported as 7.
• AU = [0.40]0.49 – 0.40 = 0.6383-0.40 = 0.2383.
• AL = [0.40]0.87 – 0.40 = 0.4506-0.40 = 0.0506.
• 95% CI for NNT is 1/AU to 1/AL = 1/0.2383 to 1/0.0506 = 4.2 to
19.8, reported as 4 to 20.
Disadvantages of NNT: Heterogeneity
• Scaling: NNT differs for subpopulations with
different underlying risk, but equal RR.
• Questionable use for meta analysis summary
overall measure since underlying risk may differ
among studies. Could find NNT for studies
separately and give range of NNTs.
• In a single study, subgroups may also have
differing underlying risk, so again separate NNTs
may be more useful.
Disadvantages of NNT: Non-Significant
Treatment Effect
• If p<0.05 for treatment effect, then the 95% CI for
NNT contains negative numbers; e.g., need to treat
between -18 and 8 subjects from the Kamal study!
• Negative values refer to NNT for harm. Positive
values refer to NNT for benefit.
• Some have suggested an interpretation using
the fact that treatment effect zero corresponds to
∞ subjects. In my opinion, NNT should not be
used here: if the CI is narrow and contains 0, we
are sure there is no effect, so NNT is irrelevant,
and if the CI is wide, NNT is not useful anyway.
Other References
• Original NNT suggestion:
Cook et al. BMJ 1995; 310: 452-454.
• More detail on NNT in survival analyses:
Altman et al. BMJ 1999; 319: 1492-1495.
• Negative NNT confidence interval issues:
Altman et al. BMJ 1998; 317: 1309-1312.
Personal Conclusions
• NNT can be useful way to express the effort
needed (many treated subjects) for treatments with
moderate relative risks and small underlying risk.
• Limit NNT to groups that are homogeneous for
underlying risk, and to treatments that show
significant effects.