Jack Wilkinson

Transcript

1. Analysis of complex longitudinal data arising from multistage interventions Jack Wilkinson Supervised by Stephen Roberts and Andy Vail Centre for Biostatistics
2. In Vitro Fertilization (IVF) • Around 1 in 7 straight couples in the UK fail to conceive after one year of trying. • Treatment recommended by NICE is in vitro fertilization (IVF). • IVF is a multistage treatment…
3. Stimulation of ovaries Fertilisation/ culture Embryo selection Embryo transfer Embryo transfer Egg retrieval Pregnancy
4. Egg retrieval Stimulation of ovaries Fertilisation/ culture Embryo selection Embryo transfer Embryo transfer Pregnancy Risk of over- stimulation
5. Stimulation of ovaries Fertilisation/ culture Embryo selection Embryo transfer Embryo transfer Egg retrieval Pregnancy Risk of over- stimulation No eggs
6. Stimulation of ovaries Fertilisation/ culture Embryo selection Embryo transfer Embryo transfer Egg retrieval Pregnancy Risk of over- stimulation No eggs Miscarriage
7. Embryo selection Stimulation of ovaries Fertilisation/ culture Embryo transfer Embryo transfer Egg retrieval Pregnancy Embryo selection Dose of drug? Cancellations? How many eggs? Successful? How many embryos? Good quality embryos? Positive test? Ongoing pregnancy? How many transferred? Do they implant?
10. Treatment Stage 1.Ovarian stimulation 2.Fertilisation of eggs 3.Culture of embryos 4. Embryo transfer 5. Clinical outcome
11. Treatment Stage Response Variable (s) 1.Ovarian stimulation Number of eggs 2.Fertilisation of eggs Fertilisation rate 3.Culture of embryos Quality x 2: Evenness and Fragmentation 4. Embryo transfer One or two embryos transferred 5. Clinical outcome Live birth
12. Treatment Stage Response Variable (s) Response Type (Level) 1.Ovarian stimulation Number of eggs Count (Patient) 2.Fertilisation of eggs Fertilisation rate Count (Patient) 3.Culture of embryos Quality x 2: Evenness and Fragmentation Ordinal 1 to 4 (Embryo) 4. Embryo transfer One or two embryos transferred Binary (Patient) 5. Clinical outcome Live birth Binary (Patient)
13. Treatment Stage Response Variable (s) Response Type (Level) Submodel 1.Ovarian stimulation Number of eggs Count (Patient) Poisson 2.Fertilisation of eggs Fertilisation rate Count (Patient) Poisson 3.Culture of embryos Quality x 2: Evenness and Fragmentation Ordinal 1 to 4 (Embryo) Cumulative logit (multilevel) 4. Embryo transfer One or two embryos transferred Binary (Patient) Probit 5. Clinical outcome Live birth Binary (Patient) Probit
14. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + % & logit 01% 2 = 02 − 1% ) 02 − % 2 % 5 = % 5) 5 + % 5 logit 01% 7 = 07 − 1% ) 07 − % 7, k=1,2,3 log % 8 = log % & + % 8) 8 + % 8 % : = % :) : + % : Specify standard regression models for each response (latent variable representations)
15. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + logit 01% 2 = 02 − 1% 2> 02 − = % 5) 5 + % 5 logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 log % 8 = log % & + % 8) 8 + = % :) : + % : Specify standard regression models for each response (latent variable representations) …all for embryo i in cycle j
16. ~ , & K M & 8 K & 2 N & 7 O & P & . 8 R 8 2 S 8 7 T 8 U 8 . . 2 MV 2 7 MM 2 MK 2 . . . 7 MN 7 MO 7 . . . . 1 MP P & … . . . . . . . . . 1 Accommodate dependency between responses through multivariate Normal latent variable structure. Estimate the parameters together with the rest of the model. Assume that, conditional on the latent variables, the responses are independent.
17. Number of eggs Fertilisation Rate Evenness Frag Degree Live Birth Event Double Embryo Transfer & 8 2 7 5 : & 8 2 7 5 Cycle j Embryo i
18. Number of eggs Fertilisation Rate Evenness Frag Degree Live Birth Event Double Embryo Transfer & 8 2 7 5 : & 8 2 7 5 Cycle j Embryo i How can we interpret these latent correlations?
19. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 Specify standard regression models for each response (latent variable representations) = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j Add each response variable as a covariate in submodels for downstream responses
20. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 Specify standard regression models for each response (latent variable representations) = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j Add each response variable as a covariate in submodels for downstream responses
21. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 Specify standard regression models for each response (latent variable representations) = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j Add each response variable as a covariate in submodels for downstream responses
22. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 Specify standard regression models for each response (latent variable representations) = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j Add each response variable as a covariate in submodels for downstream responses
23. Response Variable (s) Submodel Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 Specify standard regression models for each response (latent variable representations) = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j Add each response variable as a covariate in submodels for downstream responses
24. Number of eggs Fertilisation Rate Evenness Frag Degree Live Birth Event Double Embryo Transfer & 8 2 7 5 : & 8 2 7 5 Cycle j Embryo i
25. Number of eggs Fertilisation Rate Evenness Frag Degree Live Birth Event Double Embryo Transfer & 8 2 7 5 : & 8 2 7 5 Cycle j Embryo i
26. Why tie? Suppose we’re interested in effect of transferring two rather than one embryos on birth. = :V + % :M + % : So in our live birth submodel: Double transfer indicator But double transfer and live birth will have common causes, not included in model. This makes double transfer correlated with the error term (endogeneity). = % 5) 5 + % 5 Double transfer submodel:
27. Why tie? Suppose we’re interested in effect of transferring two rather than one embryos on birth. = :V + % :M + % : So in our live birth submodel: Double transfer indicator But double transfer and live birth will have common causes, not included in model. This makes double transfer correlated with the error term (endogeneity). = % 5) 5 + % 5 Double transfer submodel: ~ MVN (, Σ) Σ = 1 1
28. Why tie? Suppose we’re interested in effect of transferring two rather than one embryos on birth. = :V + % :M + % : So in our live birth submodel: Double transfer indicator But double transfer and live birth will have common causes, not included in model. This makes double transfer correlated with the error term (endogeneity). = % 5) 5 + % 5 Double transfer submodel: ~ MVN (, Σ) Σ = 1 1
29. Example: Does ovarian stimulation affect uterine environment? Does stimulating the ovaries to get eggs (using drugs) negatively affect the patient’s uterus -> less hospitable to embryos? Important, because if so, might be better to freeze embryos and wait until normal. Can we see how dose directly affects the responses at different stages, given the causal ordering of the variables? Routine clinical database: 2962 treatments, 12911 embryos.
30. Response Variable (s) Submodel Log(Dose) Normal Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 log % _ = % _) _ + = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j
31. Response Variable (s) Submodel Log(Dose) Normal Number of eggs Poisson Fertilisation rate Poisson Quality x 2: Evenness and Fragmentation Cumulative logit (multilevel) One or two embryos transferred Probit Live birth Probit log % & = % &) + + log % 8 = log % & + % 8) 8 + logit 01% 2 = 02 − 1% 2> 02 − logit 01% 7 = 07 − 1% 7> 07 − , k=1,2,3 log % _ = % _) _ + = % 5) 5 + % 5 = % :) : + % : …all for embryo i in cycle j
32. • Fit in Bayesian software (Stan) • Identification – include instrumental variables in submodels • Fix parameters (intercepts in probit submodels)-implications? • Patience! Two days+ to fit.
33. Instrumental variables in IVF: Example Method of fertilisation Fertilisation rate Embryo Evenness Embryo Fragmentation Double Transfer Live Birth Event Inject sperm into egg or mix together in a dish?
34. Instrumental variables in IVF: Example Method of fertilisation Fertilisation rate Embryo Evenness Embryo Fragmentation Double Transfer Live Birth Event Inject sperm into egg or mix together in a dish?
35. Number of eggs Fertilisation Rate Evenness Fragmentation Live Birth Event Median and 50% pointwise posterior intervals
36. Closing thoughts/ worries • Should we take additional measures to deal with drop out? • Multivariate/sequential model checking? • Prediction eg: probability a patient will have a safe response to stimulation and go on to have a baby. • Extension to frozen transfers? • Other multistage treatments?