BY-COVID - WP5 - Baseline Use Case: COVID-19 vaccine effectiveness assessment

Survival analysis

Survival plot

We estimate the survival function using the Kaplan-Meier estimator and represent this function visually using a Kaplan-Meier curve, showing the probability of not getting infected by SARS-CoV-2 at a certain time after onset of follow-up. The survival function is estimated for the control and intervention group.

The cumulative incidence of the event (SARS-CoV-2 infection) was additionally plotted.

Survival (time-to-event)

The probability of not getting infected by SARS-CoV-2 beyond a certain time after onset of follow-up (survival function, estimated using the Kaplan-Meier estimator) is reported for different periods.

Strata Time Number at risk Cumulative sum of number of events Cumulative sum of number censored Survival Std. error Cumulative hazard Std. error cumulative hazard
Not fully vaccinated 0 8126 0 0 1.0000000 0.0000000000 0.0000000000 0.0000000000
Not fully vaccinated 100 2763 66 5318 0.9847823 0.0019551902 0.0153314345 0.0019849453
Not fully vaccinated 200 847 263 7036 0.8726674 0.0080760848 0.1360739611 0.0092447105
Not fully vaccinated 300 560 376 7191 0.7281129 0.0141570284 0.3168612254 0.0194130720
Not fully vaccinated 400 438 397 7296 0.7002962 0.0148648089 0.3557712590 0.0211948820
Not fully vaccinated 500 94 397 7642 0.7002962 0.0148648089 0.3557712590 0.0211948820
Fully vaccinated 0 8126 1 0 0.9998769 0.0001230542 0.0001230618 0.0001230618
Fully vaccinated 100 2766 56 5323 0.9875784 0.0017356656 0.0124969379 0.0017571346
Fully vaccinated 200 865 218 7065 0.8959358 0.0073702553 0.1098006111 0.0082190834
Fully vaccinated 300 580 324 7223 0.7587970 0.0137746103 0.2756498893 0.0181253151
Fully vaccinated 400 467 333 7332 0.7469473 0.0141146006 0.2913728635 0.0188680215
Fully vaccinated 500 98 333 7707 0.7469473 0.0141146006 0.2913728635 0.0188680215

Median survival time

The median survival time is the time corresponding to a probability of not obtaining a SARS-CoV-2 infection probability of 0.5. (if NA, the probability of not obtaining a SARS-CoV-2 infection did not drop below 50%)

Characteristic Median survival (95% CI)
fully_vaccinated_bl
    FALSE — (—, —)
    TRUE — (—, —)

Cox regression and estimation of the average treatment effect

A Cox regression model was built to examine the relationship between the distribution of the probability of not obtaining a SARS-CoV-2 infection (survival distribution) and completing a primary vaccination schedule (covariate). The Cox proportional hazards regression model was fitted with ‘fully_vaccinated_bl’ as a covariate and accounts for clustering within individuals (as one individual can be re-sampled as control).

A hazard ratio (HR) is computed for the covariate ‘fully_vaccinated_bl’. A hazard can be interpreted as the instantaneous rate of SARS-CoV-2 infections in individuals that are at risk for obtaining an infection (Cox proportional hazards regression assumes stable proportional hazards over time). A HR < 1 indicates reduced hazard of SARS-CoV-2 infection when having completed a primary vaccination schedule whereas a HR > 1 indicates an increased hazard of SARS-CoV-2 infection.

Parameter estimate SE coefficient Robust SE P-value Hazard Ratio (HR) (95% CI for HR)
fully_vaccinated_blTRUE -0.196 0.074 0.095 0.039 0.822 (0.636, 1.008)

The overall significance of the model is tested.

Test statistic Df P-value
Likelihood ratio test 6.976777 1 0.008257419
Wald test 4.270000 1 0.038863280
Score (logrank) test 6.970222 1 0.008287722
Robust score test 3.980840 1 0.046020612

Proportional hazards during the study period might be unlikely. As such, the RMST and RMTL ratios are additionally calculated, providing an alternative estimate for the the Average Treatment Effect (ATE), without requiring the proportional hazards assumption to be met.

Arm Measure Estimate SE CI.lower CI.upper
fully_vaccinated_bl==FALSE RMST 319.029 2.153 314.809 323.250
fully_vaccinated_bl==TRUE RMST 326.172 2.014 322.224 330.119
fully_vaccinated_bl==FALSE RMTL 45.971 2.153 41.750 50.191
fully_vaccinated_bl==TRUE RMTL 38.828 2.014 34.881 42.776
Measure Estimate CI.lower CI.upper p_value
RMST (fully_vaccinated_bl==TRUE)-(fully_vaccinated_bl==FALSE) 7.142 1.363 12.921 0.015
RMST (fully_vaccinated_bl==TRUE)/(fully_vaccinated_bl==FALSE) 1.022 1.004 1.041 0.016
RMTL (fully_vaccinated_bl==TRUE)/(fully_vaccinated_bl==FALSE) 0.845 0.737 0.969 0.016