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Use separate randomization lists for women with and without a self-reported history of depression. Within each stratum, the central service could assign intervention and control in a $1:1$ ratio using randomly permuted blocks, preferably with concealed and varying block sizes. This is stratified randomization; the internet service can retain allocation concealment because the recruiting staff do not know the next assignment.

History is plausibly prognostic for the outcome. Keeping its distribution similar between arms reduces the risk of a chance imbalance in that important baseline factor and can improve precision. It also allows a comparison within each history stratum. Stratification does not guarantee balance of every other covariate, and staff must not be allowed to choose assignments. The regression model can retain history as a baseline covariate, respecting the design.

Assume that, conditional on the recorded embarrassment category, answering the item is independent of virginity status. Also assume that this category is assessed comparably for both groups and that both response strata have positive observation probabilities. This is covariate-dependent missing completely at random for the item response with embarrassment as the fully observed covariate; it supports MAR standardization over a fully observed covariate.

Use the responder probabilities $0.18$ and $0.08$ within strata, but the stratum sizes in the full group of responders plus item nonresponders: $300$ and $450$. This givesEquivalently, the estimated missing positive counts are $100(0.18)=18$ and $50(0.08)=4$, adding 22 to the 68 observed positives. The marginal estimate changes because the full group contains a larger proportion judged embarrassed. Merely copying the unstratified responder percentage would ignore that difference. The conditional independence assumption cannot be verified using the missing item responses.

Use each matched pair as a separate stratum with its own baseline hazard and fit one common treatment coefficient $\beta$. The Stratified Cox model partial likelihood multiplies the within-pair risk-set contributions, eliminating all pair-specific baselines. Test $H_0:\beta =0$ by the corresponding conditional score, likelihood-ratio, or Wald test.

Within each prespecified stratum, choose a block containing fixed equal counts of the two treatment assignments, then randomly permute their order. Every completed block gives exact treatment balance. Variable block sizes and allocation concealment protect against predicting the next assignment. Incomplete final blocks permit a small unavoidable imbalance; odd stratum sizes cannot have exact equal allocation.

Divide participants into strata defined by prespecified baseline prognostic variables and randomize independently within each stratum. Permuted blocks can keep treatment counts close throughout recruitment. This balances the stratification variable between arms by design, while allocation concealment keeps upcoming assignments hidden. Analyses should account for important design strata where appropriate.