Answer Key: Structuring the Markov Model Group Exercise

Answer: Natural History

m_R0 =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	-(r_AP/10+r_Db)	r_AP/10	0 \(\quad \quad \quad\)	r_Db
Progressive Disease	0 \(\quad \quad \quad\)	-(HR_PDd * r_Db + r_Db)	HR_PDd * r_Db	r_Db
Disease Mortality	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)	0 \(\quad \quad \quad\)
Background Mortality	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells

Answer: Natural History

m_P0 = exp(m_R0) =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	1-p_AP-p_ADb	p_AP \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)	p_ADb \(\quad \quad \quad\)
Progressive Disease	0 \(\quad \quad \quad \quad \quad\)	1-p_PDd-p_PDb	p_PDd\(\quad \quad \quad \quad \quad\)	p_PDb\(\quad \quad \quad \quad \quad\)
Disease Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)	0 \(\quad \quad \quad \quad \quad\)
Background Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells

Answer: Strategy A

Basis is m_P0

m_P_A =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	1-RR_AP * p_AP-p_ADb	RR_AP p_AP \(\quad\)	0 \(\quad \quad \quad \quad\)	p_ADb \(\quad \quad \quad\)
Progressive Disease	0 \(\quad \quad \quad \quad \quad\)	1-p_PDd-p_PDb	p_PDd\(\quad \quad \quad \quad \quad\)	p_PDb\(\quad \quad \quad \quad \quad\)
Disease Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)	0 \(\quad \quad \quad \quad \quad\)
Background Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells

Answer: Strategy B

Basis is m_P0

m_P_B =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	1-p_AP-p_ADb	p_AP \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)	p_ADb \(\quad \quad \quad\)
Progressive Disease	0 \(\quad \quad \quad \quad \quad\)	1-((OR_PDd / (1 - p0_OR_PDd + (p0_OR_PDd * OR_PDd ))) * p_PDd)-p_PDb	(OR_PDd / (1 - p0_OR_PDd + (p0_OR_PDd * OR_PDd ))) * p_PDd	p_PDb\(\quad \quad \quad \quad \quad\)
Disease Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)	0 \(\quad \quad \quad \quad \quad\)
Background Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells

Answer: Strategy B

Note that because p0_OR_PDd is fairly low (i.e., 0.03), you could just use the odds ratio as a relative risk.

Basis is m_P0

m_P_B =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	1-p_AP-p_ADb	p_AP \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)	p_ADb \(\quad \quad \quad\)
Progressive Disease	0 \(\quad \quad \quad \quad \quad\)	1- OR_PDd * p_PDd)-p_PDb	OR_PDd * p_PDd	p_PDb\(\quad \quad \quad \quad \quad\)
Disease Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)	0 \(\quad \quad \quad \quad \quad\)
Background Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells

Answer: Strategy C

Basis is m_R0

m_R_C =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	-(r_AP/10+r_Db)	r_AP/10	0 \(\quad \quad \quad\)	r_Db
Progressive Disease	r_PA_trtC/10	-(r_PA_trtC/10 + HR_PDd * r_Db + r_Db)	HR_PDd * r_Db	r_Db
Disease Mortality	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)	0 \(\quad \quad \quad\)
Background Mortality	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells

Answer: Strategy C

m_P_C = exp(m_R_C) =

	Asymptomatic	Progressive Disease	Disease Mortality	Background Mortality
Asymptomatic	1-p_AP-p_ADb	p_AP \(\quad \quad \quad\)	0 \(\quad \quad \quad \quad\)	p_ADb \(\quad \quad \quad\)
Progressive Disease	p_PA \(\quad \quad \quad \quad\)	1-p_PDd-p_PDb	p_PDd\(\quad \quad \quad \quad \quad\)	p_PDb\(\quad \quad \quad \quad \quad\)
Disease Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)	0 \(\quad \quad \quad \quad \quad\)
Background Mortality	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	0\(\quad \quad \quad \quad \quad\)	1.0\(\quad \quad \quad \quad \quad\)

Rate adjusted for timestep

Hazard Ratio

Probability

Relative Risk

Odds Ratio

Constructed from other cells