sim_markov("actt2") generates synthetic daily health states from a
first-order Markov proportional-odds model based on data from the
Adaptive COVID-19 Treatment Trial 2 (ACTT-2),
which compared Baricitinib plus Remdesivir with placebo plus Remdesivir in
adults hospitalized with COVID-19 (Kalil et al., 2021). States follow the
trial's
NIAID eight-point ordinal scale:
outside hospital, with usual activities unrestricted
outside hospital, with restricted activities, oxygen at home, or both
in hospital, without oxygen and no further medical care needed
in hospital, without oxygen but still needing medical care
in hospital, needing supplemental oxygen
in hospital, needing high-flow oxygen or noninvasive ventilation
in hospital, needing invasive ventilation or extracorporeal membrane oxygenation (ECMO)
dead
The output has 28 rows per patient by default, and dead patients stay in state 8.
Details
Patients. Each patient's state on the day before follow-up (yprev) is
drawn from states 4 to 7 with probabilities 0.1374637, 0.5459826,
0.2090997, and 0.1074540. Treatment is assigned independently with
probability treatment_prob: tx = 1 stands for Baricitinib plus
Remdesivir and tx = 0 for placebo plus Remdesivir.
Transition model. Write \(Y_t\) for the state on day \(t\) and
\(j\) for the state on the previous day. The log odds of being in state
\(k\) or worse on day \(t\) is
$$\mathrm{logit}\,\Pr(Y_t \ge k \mid Y_{t-1} = j) = \alpha_k +
\gamma_j + f(t) + \beta(t)\,\mathrm{tx}$$
for the cutoffs \(k = 2, \ldots, 8\). Here \(\beta(t)\) is the
treatment effect on day \(t\) described under treatment_effect_decay in
sim_markov(). Every term shifts all cutoffs equally, which makes this a
proportional-odds model. The thresholds are
| Cutoff \(k\) | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| \(\alpha_k\) | -0.6465 | -4.9314 | -5.2230 | -7.4169 | -11.5321 | -15.2262 | -22.0693 |
and the previous-state effects are
| Previous state \(j\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| \(\gamma_j\) | 0 | 0 | 6.2218 | 7.1412 | 9.9809 | 14.1645 | 19.3517 |
The large previous-state effects mean that patients usually stay in, or
move close to, their previous state. The day enters through a restricted
cubic spline, \(f(t) = -0.3084\,t + 2.5186\,t' - 5.0276\,t'' +
3.1714\,t''' - 1.0672\,t''''\), where \(t'\) to \(t''''\) are the
nonlinear basis columns that rms::rcs() creates with knots at days 2, 6,
11, 16, 21, and 27. Days beyond 28, for example with
follow_up_time = 60, extrapolate this spline.
In ACTT-2, state 2 was mostly recorded only at the day 14, 21, and 28 visits, so the transition model was fitted with states 1 and 2 merged. The added lowest threshold, \(\alpha_2\), splits them again, placing the observed 9.3% of the control arm in state 2 on day 14. Both states share the same coefficients, so the split does not change the occupancy of states 3 to 8.
Treatment effect. The default treatment_effect of -0.0730 is the
coefficient fitted to the ACTT-2 data.
Changing the model. sim_markov() expects the thresholds from the
worst state down, so intercepts = rev(alpha) with alpha the
\(\alpha_k\) above in the order of the table reproduces the preset. Change
an element of alpha before reversing it to move one threshold.
References
Kalil AC, Patterson TF, Mehta AK, et al. (2021). "Baricitinib plus Remdesivir for Hospitalized Adults with Covid-19." New England Journal of Medicine, 384(9), 795-807. doi:10.1056/NEJMoa2031994
See also
sim_markov() to simulate, and actt1_preset for the same model
in a sicker population.
Examples
actt2 <- sim_markov("actt2", n_patients = 20, seed = 123)
head(actt2)
#> id time y yprev tx
#> 1 1 1 5 5 1
#> 2 1 2 5 5 1
#> 3 1 3 5 5 1
#> 4 1 4 5 5 1
#> 5 1 5 5 5 1
#> 6 1 6 4 5 1
# The same model with a higher threshold for death
alpha <- c(-0.6465, -4.9314, -5.2230, -7.4169, -11.5321, -15.2262, -21.5)
sicker <- sim_markov(
"actt2",
n_patients = 20,
intercepts = rev(alpha),
seed = 123
)