Accessible Unlicensed Requires Authentication Published by De Gruyter October 11, 2021

Evaluating the power of the causal impact method in observational studies of HCV treatment as prevention

Pantelis Samartsidis, Natasha N. Martin, Victor De Gruttola, Frank De Vocht, Sharon Hutchinson, Judith J. Lok, Amy Puenpatom, Rui Wang, Matthew Hickman and Daniela De Angelis

Abstract

Objectives

The causal impact method (CIM) was recently introduced for evaluation of binary interventions using observational time-series data. The CIM is appealing for practical use as it can adjust for temporal trends and account for the potential of unobserved confounding. However, the method was initially developed for applications involving large datasets and hence its potential in small epidemiological studies is still unclear. Further, the effects that measurement error can have on the performance of the CIM have not been studied yet. The objective of this work is to investigate both of these open problems.

Methods

Motivated by an existing dataset of HCV surveillance in the UK, we perform simulation experiments to investigate the effect of several characteristics of the data on the performance of the CIM. Further, we quantify the effects of measurement error on the performance of the CIM and extend the method to deal with this problem.

Results

We identify multiple characteristics of the data that affect the ability of the CIM to detect an intervention effect including the length of time-series, the variability of the outcome and the degree of correlation between the outcome of the treated unit and the outcomes of controls. We show that measurement error can introduce biases in the estimated intervention effects and heavily reduce the power of the CIM. Using an extended CIM, some of these adverse effects can be mitigated.

Conclusions

The CIM can provide satisfactory power in public health interventions. The method may provide misleading results in the presence of measurement error.


Corresponding author: Pantelis Samartsidis, MRC Biostatistics Unit, University of Cambridge, Cambridge, UK, E-mail:

  1. Research funding: This study was funded by Merck Sharp & Dohme Corp., a subsidiary of Merck & Co., Inc., Kenilworth, NJ, USA, and the National Institute for Health Research (NIHR) Programme Grants for Applied Research programme (Grant Reference Number RP-PG-0616-20008). The study was further supported by the National Institute for Health Research Health Protection Unit on Evaluation of Interventions. NNM and VDG were partially supported from the San Diego Center for AIDS Research (SD CFAR), an NIH-funded program (P30 AI036214). JJL acknowledges NIH funding from NIH/NIAID R01 AI10072 and NSF funding from NSF DMS 1854934. RW acknowledges support R01 AI136947 from the National Institute of Allergy and Infectious Disease (NIAID). DDA was funded by the UK Medical Research Council grant MC_UU_00002/11. The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care.

Appendix A: Supplementary simulation results

In this section we provide further results for the simulation study of Section 3. Table 4 presents mean prediction error (MPE) of the causal estimates, standard error of the PE (sd-PE), mean credible interval width (CIW) and false discovery rate (FDR) in all baseline settings and sensitivity analyses. Figure 4 shows simulated p 0 t ( 0 ) against estimates θ ̂ t obtained in baseline simulations, for all three post-intervention times. Figures 5 and 6 show the power achieved by the CIM in all baseline settings and sensitivity analyses, at t 1 + 2 and t 1 + 3, respectively.

Table 4:

Simulation results for Section 3.

t 1 MPE sd-PE CIW FDR
t 1=6* −0.35 0.70 0.37 11.36 11.30 11.33 0.211 0.226 0.239 0.100 0.086 0.071
t 1=9 −0.31 0.61 0.40 11.61 11.52 11.59 0.196 0.213 0.226 0.064 0.052 0.038
t 1=12* 0.04 0.44 0.50 11.73 11.69 11.76 0.185 0.202 0.217 0.050 0.038 0.027
t 1=24 −0.26 0.12 0.32 11.96 11.93 11.97 0.167 0.184 0.199 0.034 0.023 0.013
σ y 2 MPE sd-PE CIW FDR
0.005 (t 1=6) −0.06 0.23 0.17 10.88 10.86 10.87 0.056 0.060 0.063 0.103 0.088 0.073
0.005 (t 1=12) 0.04 0.17 0.19 10.90 10.89 10.91 0.049 0.054 0.057 0.052 0.039 0.028
0.04 (t 1=6) −0.24 0.55 0.32 11.13 11.08 11.11 0.156 0.167 0.177 0.101 0.086 0.071
0.04 (t 1=12) 0.08 0.37 0.44 11.33 11.30 11.36 0.137 0.150 0.160 0.050 0.038 0.027
0.075 (t 1=6)* −0.35 0.70 0.37 11.36 11.30 11.33 0.211 0.226 0.239 0.100 0.086 0.071
0.075 (t 1=12)* 0.04 0.44 0.50 11.73 11.69 11.76 0.185 0.202 0.217 0.050 0.038 0.027
k 1 MPE sd-PE CIW FDR
6 (t 1=6)* −0.35 0.70 0.37 11.36 11.30 11.33 0.211 0.226 0.239 0.100 0.086 0.071
6 (t 1=12)* 0.04 0.44 0.50 11.73 11.69 11.76 0.185 0.202 0.217 0.050 0.038 0.027
12 (t 1=6) −0.28 0.63 0.20 11.28 11.23 11.26 0.217 0.232 0.245 0.108 0.094 0.077
12 (t 1=12) 0.02 0.57 0.39 11.68 11.64 11.69 0.190 0.206 0.220 0.055 0.040 0.030
24 (t 1=6) −0.19 0.72 0.13 11.22 11.17 11.19 0.223 0.237 0.250 0.116 0.103 0.085
24 (t 1=12) 0.05 0.65 0.40 11.60 11.56 11.61 0.195 0.212 0.225 0.058 0.044 0.034
k 2 MPE sd-PE CIW FDR
2 (t 1=6)* −0.35 0.70 0.37 11.36 11.30 11.33 0.211 0.226 0.239 0.100 0.086 0.071
2 (t 1=12)* 0.04 0.44 0.50 11.73 11.69 11.76 0.185 0.202 0.217 0.050 0.038 0.027
4 (t 1=6) −0.21 0.42 0.35 11.35 11.28 11.31 0.213 0.228 0.240 0.065 0.059 0.047
4 (t 1=12) 0.50 0.28 0.20 11.71 11.65 11.72 0.188 0.204 0.217 0.026 0.019 0.013
6 (t 1=6) −0.18 0.38 0.34 11.35 11.27 11.31 0.214 0.229 0.241 0.049 0.043 0.035
6 (t 1=12) 0.02 0.20 −0.12 11.70 11.61 11.71 0.190 0.206 0.219 0.014 0.012 0.007
ρ MPE sd-PE CIW FDR
0.6 (t 1=6) −0.16 0.68 0.37 11.34 11.31 11.28 0.211 0.227 0.240 0.159 0.137 0.113
0.6 (t 1=12) 0.31 0.57 0.31 11.47 11.46 11.46 0.203 0.220 0.233 0.122 0.103 0.075
0.7 (t 1=6) −0.23 0.70 0.39 11.35 11.30 11.29 0.211 0.227 0.240 0.134 0.115 0.098
0.7 (t 1=12) 0.16 0.53 0.45 11.60 11.57 11.59 0.196 0.213 0.227 0.094 0.074 0.055
0.8 (t 1=6)* −0.35 0.70 0.37 11.36 11.30 11.33 0.211 0.226 0.239 0.100 0.086 0.071
0.8 (t 1=12)* 0.04 0.44 0.50 11.73 11.69 11.76 0.185 0.202 0.217 0.050 0.038 0.027
Table 4:

(continued)

Prior MPE sd-PE CIW FDR
Default (t 1=6) 0.06 0.80 0.43 11.06 11.03 11.02 0.239 0.251 0.262 0.116 0.104 0.088
Default (t 1=12) 0.06 0.68 0.28 11.41 11.39 11.41 0.211 0.227 0.241 0.063 0.048 0.034
Calibrated (t 1=6)* −0.35 0.70 0.37 11.36 11.30 11.33 0.211 0.226 0.239 0.100 0.086 0.071
Calibrated (t 1=12)* 0.04 0.44 0.50 11.73 11.69 11.76 0.185 0.202 0.217 0.050 0.038 0.027

  1. The table presents the mean prediction error (MPE) of the point estimates, the standard error of the MPE (sd-PE), the mean credible interval width (CIW) and the false discovery rate (FDR), in all baseline settings and sensitivity analyses. Baseline settings are indicated by a (*) symbol. For each performance measure, the three columns correspond to the three post-intervention time points. The values of the MPE and sd=MPE are multiplied by 103 and 102, respectively. Results are based on 10,000 simulated datasets.

Figure 4: 
Baseline simulation results. The figure shows the simulated values of the prevalence 




p


0
t



(

0

)





${p}_{0t}^{\left(0\right)}$



 in the post-intervention period against the estimates 






θ

̂



t




${\hat{\theta }}_{t}$



 provided by the CIM. The top and bottom rows correspond to t
1=6 and 12, respectively. The left, middle and right columns correspond to the first, second and third post-intervention time point respectively. Each plot contains 10,000 points, one for each simulated dataset.

Figure 4:

Baseline simulation results. The figure shows the simulated values of the prevalence p 0 t ( 0 ) in the post-intervention period against the estimates θ ̂ t provided by the CIM. The top and bottom rows correspond to t 1=6 and 12, respectively. The left, middle and right columns correspond to the first, second and third post-intervention time point respectively. Each plot contains 10,000 points, one for each simulated dataset.

Figure 5: 
Results of the simulation study for the second post-intervention time point t=t
1 + 2. The figure presents the power for detecting an intervention effect achieved by the CIM as a function of the intervention effect magnitude, in all baseline settings and sensitivity analyses. All results are based on 10,000 simulated datasets.

Figure 5:

Results of the simulation study for the second post-intervention time point t=t 1 + 2. The figure presents the power for detecting an intervention effect achieved by the CIM as a function of the intervention effect magnitude, in all baseline settings and sensitivity analyses. All results are based on 10,000 simulated datasets.

Figure 6: 
Results of the simulation study for the second post-intervention time point t=t
1 + 3. The figure presents the power for detecting an intervention effect achieved by the CIM as a function of the intervention effect magnitude, in all baseline settings and sensitivity analyses. All results are based on 10,000 simulated datasets.

Figure 6:

Results of the simulation study for the second post-intervention time point t=t 1 + 3. The figure presents the power for detecting an intervention effect achieved by the CIM as a function of the intervention effect magnitude, in all baseline settings and sensitivity analyses. All results are based on 10,000 simulated datasets.

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Received: 2020-06-08
Revised: 2021-01-31
Accepted: 2021-02-15
Published Online: 2021-10-11

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